{"count":871,"magmas":[{"canonical_hash":"48f0b800a5867312ab9f9a5a63b98abf45e0196fa8db3fa6670aba7307a8a973","size":1,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":null,"comment":"Trivial.","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/1/48f0b800a5867312ab9f9a5a63b98abf45e0196fa8db3fa6670aba7307a8a973.txt"},{"canonical_hash":"e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5","size":5,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,3,2,4","comment":"Linear magma over Z/5Z (the prime field F_5): x ◇ y = 2x + 4y (mod 5).","submitted_at":"2026-04-23 20:53:46","submitted_by":"claude-smoke-test","url":"https://eq677-magmas.icarm.cloud/magmas/5/e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5.txt"},{"canonical_hash":"baf8b55c9a489d3c0ce2405b9167b3a08aada73c1917019843910c3cbab0f48d","size":7,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"6,0,3,4,1,5,2","comment":"Linear magma over Z/7Z (the prime field F_7): x ◇ y = 4x + 3y (mod 7).","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/7/baf8b55c9a489d3c0ce2405b9167b3a08aada73c1917019843910c3cbab0f48d.txt"},{"canonical_hash":"7981e2df4cc5c795ad295ab69f55b88db1cecb20c1d1ac4df4d7aa42b92757f1","size":7,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"6,0,2,1,4,5,3","comment":"Linear magma over Z/7Z (the prime field F_7): x ◇ y = 4x + y (mod 7).","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/7/7981e2df4cc5c795ad295ab69f55b88db1cecb20c1d1ac4df4d7aa42b92757f1.txt"},{"canonical_hash":"2925dc18176c3a094e546f32ddfbde1b795255106b00f6076737cdc6da05a538","size":9,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,0,3,4,1,7,2,6,5","comment":"Linear magma over the extension field F_9 = F_3[α]/⟨α² + 1⟩.\n\nOperation: x ◇ y = a·x + b·y in F_9 with (a, b) = (1, 2 + α). Note 2 + α is a root of Φ_10(x) = x⁴ - x³ + x² - x + 1 (cyclotomic polynomial for primitive 10th roots of unity) in F_9, and the corresponding α_coef = 1 satisfies α_coef = -β³ - β - 1 - this is Pace Nielsen's \"Type 2\" linear 677 magma family. F_9 is the proper degree-2 extension of F_3; do NOT confuse with the ring Z/9Z = Z/9 (which has zero divisors and is NOT a field).\n\nSize 9, not fully idempotent (only 1 element is idempotent), right-cancellative.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/9/2925dc18176c3a094e546f32ddfbde1b795255106b00f6076737cdc6da05a538.txt"},{"canonical_hash":"9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc","size":11,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,8,3,4,6,10,7,5,2,9","comment":"Linear magma over Z/11Z (the prime field F_11): x ◇ y = 6x + 6y (mod 11).","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/11/9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc.txt"},{"canonical_hash":"abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc","size":11,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,3,5,4,10,7,2,6,8,9","comment":"Linear magma over Z/11Z (the prime field F_11): x ◇ y = 5x + 7y (mod 11).","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/11/abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc.txt"},{"canonical_hash":"15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39","size":11,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,10,6,5,8,4,2,7,9,3","comment":"Linear magma over Z/11Z (the prime field F_11): x ◇ y = 10x + 2y (mod 11).","submitted_at":"2026-04-23 20:56:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/11/15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39.txt"},{"canonical_hash":"ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3","size":11,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,9,3,10,5,2,7,8,6,4","comment":"Linear magma over Z/11Z (the prime field F_11): x ◇ y = 4x + 8y (mod 11).","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/11/ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3.txt"},{"canonical_hash":"babb8d44f43fe9d9743df8ed3cc3b4097f4b750584784526ddba6eb0b769c884","size":13,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"12,0,4,2,7,11,1,9,10,3,6,8,5","comment":"Linear magma over Z/13Z (the prime field F_13): x ◇ y = 9x + 11y (mod 13).","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/13/babb8d44f43fe9d9743df8ed3cc3b4097f4b750584784526ddba6eb0b769c884.txt"},{"canonical_hash":"6fa95655e2bb5ca888155b7b0fa10812ad37b0071f56dd2c82d383c6104fd039","size":16,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,6,14,3,5,13,9,15,12,8,11,4,10,7,2","comment":"Linear magma over the extension field F_16 = F_2[α]/⟨α⁴ + α + 1⟩.\n\nOperation: x ◇ y = a·x + b·y in F_16 with (a, b) = (1 + α³, α³). Since α + β = (1 + α³) + α³ = 1 in F_16 (char 2), this is the \"Type 1\" translation-invariant fully-idempotent linear 677 magma, equivalent to x ◇ y = x + β·(y - x) with β = α³. Note β = α³ is a primitive 5th root of unity in F_16* (which has order 15 = 3·5). In characteristic 2 the primitive 10th-root condition collapses to primitive 5th-root since Φ_10(x) = Φ_5(x) mod 2.\n\nF_16 is the proper degree-4 extension of F_2; do NOT confuse with the ring Z/16Z (which has zero divisors and is NOT a field).\n\nSize 16, fully idempotent, right-cancellative.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/16/6fa95655e2bb5ca888155b7b0fa10812ad37b0071f56dd2c82d383c6104fd039.txt"},{"canonical_hash":"5a03816aba174256cfa17a8e22b2fe728a2ae4efc211c02f8ea790dd7a1bc8f1","size":16,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"15,0,13,8,9,7,12,1,4,5,11,3,14,10,2,6","comment":"Linear magma over the extension field F_16 = F_2[α]/⟨α⁴ + α + 1⟩.\n\nOperation: x ◇ y = a·x + b·y in F_16 with (a, b) = (1 + α + α², 1 + α³). Here β = 1 + α³ satisfies the \"Type 2\" cyclotomic condition β⁴ + β³ + 1 = 0 in characteristic 2 (= β⁴ + β³ + 2β² + 2β + 1 with 2 = 0), and α_coef = -β³ - β - 1 = 1 + α + α². This is Pace Nielsen's Type-2 non-fully-idempotent linear 677 magma family.\n\nF_16 is the proper degree-4 extension of F_2; do NOT confuse with the ring Z/16Z (which has zero divisors and is NOT a field).\n\nSize 16, not fully idempotent, right-cancellative. Compare with magma#6fa95655, the F_16 Type-1 (fully idempotent) variant.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/16/5a03816aba174256cfa17a8e22b2fe728a2ae4efc211c02f8ea790dd7a1bc8f1.txt"},{"canonical_hash":"799616376b98a8ce82c52d37e971b69434275f88d91a868b580ace46337b4f55","size":19,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"18,0,12,9,2,7,6,4,13,5,11,17,10,14,15,8,3,1,16","comment":"Linear magma over Z/19Z (the prime field F_19): x ◇ y = 7x + 4y (mod 19).","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/19/799616376b98a8ce82c52d37e971b69434275f88d91a868b580ace46337b4f55.txt"},{"canonical_hash":"6202539f907cc122b689a42a816b68ea54efdabc37708112e242fad3e40cfb2c","size":19,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"18,0,11,8,13,14,2,12,6,16,7,15,3,10,5,4,1,17,9","comment":"Linear magma over Z/19Z (the prime field F_19): x ◇ y = 7x + 3y (mod 19).","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/19/6202539f907cc122b689a42a816b68ea54efdabc37708112e242fad3e40cfb2c.txt"},{"canonical_hash":"b1cfacfaad3e7ef7df360be50209e98e5da4988905a176ee062ce1dca6b7194c","size":21,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,3,7,6,10,14,2,9,20,12,4,17,18,11,13,8,15,16,1,19,5","comment":"Size-21 = 3·7 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. **The carrier is the cyclic group Z_21 (= Z_3 × Z_7 by CRT)**, and the magma is fully Z_21-translation-invariant — verified by exhibiting an order-21 fix-free magma automorphism. |Aut(M)| = 21, acting REGULARLY on the 21 elements (single orbit; trivial stabilizer at every point).\n\nStructure: x ◇ y = x + f(y − x) in Z_21, where f: Z_21 → Z_21 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 10 transpositions on Z_21 \\ {0}). L_0 has cycle structure (1, 2¹⁰); R_0 has cycle structure (1, 4⁵).\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5 (magma#e549b5f8). The C(21, 2)/C(5, 2) = 210/10 = 21 such sub-magmas form a **Steiner system S(2, 5, 21)**. Since the unique S(2, 5, 21) is the projective plane PG(2, 4), the 21 lines of this magma are exactly the lines of PG(2, 4). Each element lies on (21 − 1)/(5 − 1) = 5 lines.\n\nThis is the **smallest member of the 'Z_n cyclic + involution + Steiner S(2, 5, n)' family** of Eq 677 magmas (admissible whenever n ≡ 1 or 5 mod 20; here 21 ≡ 1 ✓). Other DB sizes with the same template:\n  • Size 21 (this magma, 4 entries total) — Steiner S(2, 5, 21) = PG(2, 4)\n  • Size 25 (29 entries, AG(2, 5) line magmas) — Steiner S(2, 5, 25) = AG(2, 5)\n  • Size 41 (8 entries), 61 (32 entries), 65 (9 entries), 81 (16 entries), 85 (7 entries), 125 (1 entry)\n\nAt sizes 21, 65, 85, etc. (where n ≡ 5 mod 20), the design is structured around the cyclic Z_n group; at sizes 25, 81, 125 (n = p² for various p), the design uses elementary-abelian (Z/p)^k carriers via AG(2, 5) line structures or fiber bundles.\n\nDisplay reorder presents elements as 0, τ(0), τ²(0), …, τ²⁰(0) along the orbit of an order-21 fix-free magma automorphism τ (the additive translation by 1 in Z_21). Under this reorder the Cayley table is fully Z_21-translation-invariant; the rendered image shows clean diagonal banding from the cyclic translation symmetry.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/21/b1cfacfaad3e7ef7df360be50209e98e5da4988905a176ee062ce1dca6b7194c.txt"},{"canonical_hash":"2eea123aebfb6ba7183389b489a8f91e4c155a9f70bba89b817cd29a021a28e3","size":21,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,3,20,2,4,13,17,8,5,18,14,9,6,15,19,10,7,12,16,11","comment":"Size-21 = 3·7 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. **Pencil-through-pivot construction**: 21 = 1 + 5·4 — one pivot element + 5 lines through the pivot, each line of size 5 (1 pivot + 4 non-pivot points).\n\nDistinguishing structure:\n  • There are exactly 5 size-5 sub-magmas in this magma (not 21 like in the PG(2, 4) line magmas), all passing through a unique pivot element (canonical label 0). The pivot lies in all 5 lines; every other element lies in exactly 1 line.\n  • Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5).\n  • Every cross-petal pair (= pair of non-pivot elements in different lines) generates the FULL 21-element magma (no cross-petal size-5 'transversals' exist here — unlike the size-76 pencil magma#875876e7 which has a TD(5, 15) of cross-petal transversals).\n  • L_0 has cycle structure (1, 2¹⁰) — fixed-point-free involution (apart from the pivot fixed point). R_0 has cycle structure (1, 4⁵) — order 4 with the pivot fixed.\n  • |Aut(M)| = 20, acting on 21 elements with orbits {pivot} and {20-element non-pivot orbit}. Aut acts regularly on the non-pivot orbit.\n\nThis is the **smallest pencil magma in the DB**, structurally analogous to magma#875876e7 at size 76 (1 + 5·15) which has petals of size 16, but here with much smaller size-5 petals (each = the F_5 affine magma) and no cross-petal transversal sub-magmas.\n\nOther size-21 magmas (4 of them — magma#b1cfacfa, magma#4bd29022, magma#50e6ad54, magma#b904cba0) are in the DIFFERENT 'Steiner-S(2, 5, 21) = PG(2, 4) line magma' family, with 21 size-5 sub-magmas (one per line of PG(2, 4)) and every pair on a unique line — NOT just 5 sub-magmas through a single pivot.\n\nDisplay reorder: pivot at position 0, then 5 consecutive 4-blocks (positions 1-4, 5-8, …, 17-20) for the 5 lines through the pivot. Within each line block, elements are F_5-affine-ordered using the line's own R_0 operation (0_F → pivot, 1_F → smallest non-pivot, then 2_F = T[1, pivot], 3_F = T[2, pivot], 4_F = T[3, pivot]). The rendered Cayley table shows a clean 5×5 grid of 4×4 blocks plus a pivot row/column.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/21/2eea123aebfb6ba7183389b489a8f91e4c155a9f70bba89b817cd29a021a28e3.txt"},{"canonical_hash":"9bef57c1d44e80971322503e60da3200c76bd26a40439449d3af7ebc5f65e420","size":21,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,3,20,2,4,13,17,8,5,18,14,9,6,10,19,15,7,12,16,11","comment":"Size-21 = 3·7 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. **Pencil-through-pivot construction**: 21 = 1 + 5·4 — one pivot element + 5 lines through the pivot, each line of size 5 (1 pivot + 4 non-pivot points).\n\nDistinguishing structure:\n  • There are exactly 5 size-5 sub-magmas in this magma (not 21 like in the PG(2, 4) line magmas), all passing through a unique pivot element (canonical label 0). The pivot lies in all 5 lines; every other element lies in exactly 1 line.\n  • Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5).\n  • Every cross-petal pair (= pair of non-pivot elements in different lines) generates the FULL 21-element magma (no cross-petal size-5 'transversals' exist here — unlike the size-76 pencil magma#875876e7 which has a TD(5, 15) of cross-petal transversals).\n  • L_0 has cycle structure (1, 2¹⁰) — fixed-point-free involution (apart from the pivot fixed point). R_0 has cycle structure (1, 4⁵) — order 4 with the pivot fixed.\n  • |Aut(M)| = 20, acting on 21 elements with orbits {pivot} and {20-element non-pivot orbit}. Aut acts regularly on the non-pivot orbit.\n\nThis is the **smallest pencil magma in the DB**, structurally analogous to magma#875876e7 at size 76 (1 + 5·15) which has petals of size 16, but here with much smaller size-5 petals (each = the F_5 affine magma) and no cross-petal transversal sub-magmas.\n\nOther size-21 magmas (4 of them — magma#b1cfacfa, magma#4bd29022, magma#50e6ad54, magma#b904cba0) are in the DIFFERENT 'Steiner-S(2, 5, 21) = PG(2, 4) line magma' family, with 21 size-5 sub-magmas (one per line of PG(2, 4)) and every pair on a unique line — NOT just 5 sub-magmas through a single pivot.\n\nDisplay reorder: pivot at position 0, then 5 consecutive 4-blocks (positions 1-4, 5-8, …, 17-20) for the 5 lines through the pivot. Within each line block, elements are F_5-affine-ordered using the line's own R_0 operation (0_F → pivot, 1_F → smallest non-pivot, then 2_F = T[1, pivot], 3_F = T[2, pivot], 4_F = T[3, pivot]). The rendered Cayley table shows a clean 5×5 grid of 4×4 blocks plus a pivot row/column.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/21/9bef57c1d44e80971322503e60da3200c76bd26a40439449d3af7ebc5f65e420.txt"},{"canonical_hash":"4bd29022e5d9f444261306dd6af4078d3173b9f3915cf80ccf08aa4ae0f2ce98","size":21,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,4,12,18,3,8,2,13,17,5,10,6,7,9,11,14,19,15,20,16","comment":"Size-21 = 3·7 idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the Steiner-S(2, 5, 21) = PG(2, 4) family. Every pair of distinct elements generates a 5-element sub-magma (≅ unique size-5 Eq 677 magma magma#e549b5f8); the 21 sub-magmas form the lines of the projective plane PG(2, 4), with each point lying on 5 lines.\n\nDistinguishing feature: |Aut(M)| = 21 acting regularly on the 21 elements, with element orders {1, 3, 7} but NO order-21 element. So Aut(M) is the **non-abelian Frobenius group F_21 = Z_7 ⋊ Z_3** — NOT the cyclic Z_21 group. The 21 automorphisms break down as: 1 identity, 14 of order 3 (the Z_3 generators × Z_7 representatives), and 6 of order 7 (the Z_7-translations).\n\nContrast with the third size-21 PG(2, 4) magma magma#b1cfacfa, which has |Aut| = Z_21 cyclic (with order-21 elements present). The two cases correspond to the two non-isomorphic groups of order 21: Z_21 abelian vs. F_21 = Z_7 ⋊ Z_3 non-abelian. The fourth size-21 PG(2, 4) magma magma#b904cba0 is the most rigid: |Aut| = 1 (trivial).\n\nDisplay reorder presents elements as a 3×7 grid: rows are the 3 orbits of an order-7 automorphism σ_7, and within each row elements are ordered along the σ_7-cycle starting from the minimum-canonical-label element. Under this reorder the Cayley table has a row-shift symmetry: T_new[shift(x), shift(y)] = shift(T_new[x, y]) where shift increments column index mod 7 within each 7-block — directly reflecting the σ_7 cyclic action.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/21/4bd29022e5d9f444261306dd6af4078d3173b9f3915cf80ccf08aa4ae0f2ce98.txt"},{"canonical_hash":"b904cba009c70948d9608b90bc3c76e5cad39cc4bc1c4039215b1a9ab389626b","size":21,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,20,4,19,9,14,16,5,13,11,10,12,6,17,15,8,18,7","comment":"Size-21 = 3·7 idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the Steiner-S(2, 5, 21) = PG(2, 4) family. Every pair of distinct elements generates a 5-element sub-magma (≅ unique size-5 Eq 677 magma magma#e549b5f8); the 21 sub-magmas form the lines of the projective plane PG(2, 4), with each point lying on 5 lines.\n\nDistinguishing feature: |Aut(M)| = **1** (trivial). This is the MOST RIGID size-21 PG(2, 4) magma in the DB — no non-trivial symmetries at all. Compare with the other three size-21 PG(2, 4) magmas:\n  • magma#b1cfacfa: |Aut| = Z_21 cyclic (regular)\n  • magma#4bd29022: |Aut| = F_21 = Z_7 ⋊ Z_3 (non-abelian Frobenius)\n  • magma#50e6ad54: |Aut| = F_21 (another non-abelian Frobenius)\n  • magma#b904cba0 (this one): |Aut| = 1\n\nAll four magmas realize the same PG(2, 4) line structure but with progressively less algebraic symmetry — this one is at the extreme end, with no element distinguished from any other by any automorphism. Yet the magma operation isn't arbitrary: it must respect the PG(2, 4) Steiner system AND satisfy Eq 677.\n\nStructural uniformity despite trivial Aut: for EVERY element x, the cycle structure of L_x is (1, 2¹⁰) (= fixed-point-free involution on M \\ {x}, plus x fixed) and the cycle structure of R_x is (1, 4⁵) (= order-4 permutation with 5 cycles of 4 + x fixed). So while no automorphism swaps elements, every element 'looks the same' combinatorially.\n\nDisplay reorder uses an AG(2, 4) + line-at-infinity layout (= the standard 'embedding' of AG(2, 4) into PG(2, 4) by removing one line):\n  • Positions 0-4: a chosen line L_∞ (5 points). Specifically, the line through element 0 with min 2nd-smallest member.\n  • Positions 5-20: the remaining 16 affine points of AG(2, 4), laid out as a 4×4 grid using two chosen parallel classes (directions) of AG(2, 4) as the row and column coordinates. Each PG(2, 4) line not equal to L_∞ becomes an AG(2, 4) line of 4 points (sharing 1 'direction' point on L_∞).\n\nUnder this reorder the rendered Cayley table has a 5+16 partition visible: the top-left 5×5 corner involves the 'line at infinity', the lower-right 16×16 sub-block shows the affine-plane operation with 4×4 sub-structure from the parallel-class directions, and the L-shaped corner pieces (5×16, 16×5) reflect cross-region operations.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/21/b904cba009c70948d9608b90bc3c76e5cad39cc4bc1c4039215b1a9ab389626b.txt"},{"canonical_hash":"50e6ad5462414aff0d8592223cd82ba7befa1631fdfdb0691efa0212ca3dcfc7","size":21,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,5,18,10,19,16,13,1,6,3,20,4,11,8,2,7,12,9,15,14,17","comment":"Size-21 = 3·7 idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the Steiner-S(2, 5, 21) = PG(2, 4) family. Every pair of distinct elements generates a 5-element sub-magma (≅ unique size-5 Eq 677 magma magma#e549b5f8); the 21 sub-magmas form the lines of the projective plane PG(2, 4), with each point lying on 5 lines.\n\nDistinguishing feature: |Aut(M)| = 21 acting regularly on the 21 elements, with element orders {1, 3, 7} but NO order-21 element. So Aut(M) is the **non-abelian Frobenius group F_21 = Z_7 ⋊ Z_3** — NOT the cyclic Z_21 group. The 21 automorphisms break down as: 1 identity, 14 of order 3 (the Z_3 generators × Z_7 representatives), and 6 of order 7 (the Z_7-translations).\n\nContrast with the third size-21 PG(2, 4) magma magma#b1cfacfa, which has |Aut| = Z_21 cyclic (with order-21 elements present). The two cases correspond to the two non-isomorphic groups of order 21: Z_21 abelian vs. F_21 = Z_7 ⋊ Z_3 non-abelian. The fourth size-21 PG(2, 4) magma magma#b904cba0 is the most rigid: |Aut| = 1 (trivial).\n\nDisplay reorder presents elements as a 3×7 grid: rows are the 3 orbits of an order-7 automorphism σ_7, and within each row elements are ordered along the σ_7-cycle starting from the minimum-canonical-label element. Under this reorder the Cayley table has a row-shift symmetry: T_new[shift(x), shift(y)] = shift(T_new[x, y]) where shift increments column index mod 7 within each 7-block — directly reflecting the σ_7 cyclic action.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/21/50e6ad5462414aff0d8592223cd82ba7befa1631fdfdb0691efa0212ca3dcfc7.txt"},{"canonical_hash":"4aacf2e3f661d4e1f672f0ce67d5ef7b796dcc1af24b2f594b41843c25cc35b2","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"16,0,1,9,19,2,14,12,10,22,24,7,3,21,6,15,18,13,20,4,23,5,17,11,8","comment":"Size-25 idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. Every pair of distinct elements generates a 5-element sub-magma (≅ unique size-5 Eq 677 magma magma#e549b5f8); the 30 such sub-magmas are exactly the 30 lines of the affine plane AG(2, 5), partitioned into 6 parallel classes of 5 disjoint lines each — a Steiner system S(2, 5, 25).\n\nDistinguishing structural feature: |Aut(M)| = 48, acting on the 25 elements with orbit structure (1, 24) — there is a UNIQUE Aut-fixed element (canonical label 16 in the original labeling) and the other 24 elements form a single Aut-orbit. So this magma has a 'distinguished pivot' analogous to the size-76 pencil magma#875876e7, but at much smaller scale: 25 = 1 + 24 = 1 + 6·4 — one pivot + the 6 lines of AG(2, 5) through the pivot, each contributing 4 non-pivot elements.\n\nThe Aut group contains an order-24 element σ that fixes the pivot and acts as a single 24-cycle on the other 24 elements. Combined with σ²=24/2=12, etc., the structure (Z_24 acting transitively on 24-orbit, with the multiplicative stabilizer of an element being Z_2) is reminiscent of AGL(1, F_25)/Z_2 — exactly half the sharply 2-transitive group of order 600 that acts on the size-25 exceptional Zassenhaus near-field magma#09d21ec3. Compare also magma#d732efd1 (half-AG(2,5) non-RC) which has |Aut| = 300 (= 25 · 12), also half of the full near-field's 600.\n\nDisplay reorder: place the pivot at position 0, then enumerate the other 24 elements as σ⁰(x), σ¹(x), σ²(x), …, σ²³(x) for some starting x and the order-24 cyclic automorphism σ. Under this reorder the Cayley table shows clean diagonal banding from the cyclic σ-action: every row (except row 0) is a shift of the previous row by 1 in the cyclic index.\n\nNOT (Z/5)²-translation-invariant in any abelian-group sense: this magma has no fix-free order-5 magma automorphism, so its 25-element carrier doesn't admit a regular abelian translation subgroup. The 'symmetry' is concentrated in the multiplicative cyclic Z_24 around the fixed pivot rather than additive translations.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/4aacf2e3f661d4e1f672f0ce67d5ef7b796dcc1af24b2f594b41843c25cc35b2.txt"},{"canonical_hash":"05b4f26aadb27e70d9cccc9aae6f181d06ddc0a8fb0e1bd54823722ee586aaa3","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,17,14,11,1,6,19,12,9,2,7,16,13,10,3,5,8,15,18,20,21,23,24,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/05b4f26aadb27e70d9cccc9aae6f181d06ddc0a8fb0e1bd54823722ee586aaa3.txt"},{"canonical_hash":"0c721240e908f1c5beefe4404c42b70ef5cc4a89e25abbb39710463b74ae64f5","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,8,22,19,1,5,23,16,10,2,4,20,11,17,3,6,18,9,21,12,13,15,24,14","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/0c721240e908f1c5beefe4404c42b70ef5cc4a89e25abbb39710463b74ae64f5.txt"},{"canonical_hash":"053cceeb7cc19fb37507127dd6f4bf970764a9f0f3fa4c9357b2e9c714a512df","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,6,11,21,13,1,5,10,20,12,2,7,8,22,14,3,4,9,23,15,16,17,19,24,18","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/053cceeb7cc19fb37507127dd6f4bf970764a9f0f3fa4c9357b2e9c714a512df.txt"},{"canonical_hash":"2cef1f42375c5a42b4f42a93700cd4e457d5b51396a3bcfe4cbf056d3d5a7bf1","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,10,23,17,12,5,11,18,21,14,6,9,13,19,20,7,8,16,15,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/2cef1f42375c5a42b4f42a93700cd4e457d5b51396a3bcfe4cbf056d3d5a7bf1.txt"},{"canonical_hash":"ed5475f7885aff59f8210c696ee75398ba4d7de201c4ef1b0cc2e8eb32266101","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,10,23,19,14,5,9,21,12,18,6,11,13,20,17,7,8,16,15,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/ed5475f7885aff59f8210c696ee75398ba4d7de201c4ef1b0cc2e8eb32266101.txt"},{"canonical_hash":"04331ff119881466cdcd7af848c1f444fdbf911e07189f963bb89742d50d7717","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,11,22,19,12,1,9,14,16,23,2,10,15,20,18,3,8,17,21,13,4,5,7,24,6","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/04331ff119881466cdcd7af848c1f444fdbf911e07189f963bb89742d50d7717.txt"},{"canonical_hash":"fb2dc63b56d449bb828193c89b36eeaa059c3f4cce831381864b25dd9edc116d","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,17,21,12,1,6,13,20,18,2,5,14,19,23,3,4,16,15,22,8,9,11,24,10","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/fb2dc63b56d449bb828193c89b36eeaa059c3f4cce831381864b25dd9edc116d.txt"},{"canonical_hash":"05017728ce1cefb06a6d1e46164911659c237a992413d7d91ada358fa105ed1f","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/05017728ce1cefb06a6d1e46164911659c237a992413d7d91ada358fa105ed1f.txt"},{"canonical_hash":"9cd423b31d9bc95513f8fdaa05847ed9c6847645c3e60aa333f000be3a754c07","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,8,12,20,1,5,22,10,13,2,6,9,23,15,3,7,21,14,11,16,17,19,24,18","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/9cd423b31d9bc95513f8fdaa05847ed9c6847645c3e60aa333f000be3a754c07.txt"},{"canonical_hash":"35b3e0846ad5f5632c8e07398541e63ce047c1372d1ff6a25b242cbed5011806","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,11,14,18,23,5,10,13,17,22,6,8,15,19,20,7,9,12,16,21","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/35b3e0846ad5f5632c8e07398541e63ce047c1372d1ff6a25b242cbed5011806.txt"},{"canonical_hash":"208cb42fb32375e527d63cce28c63be67f1b02f576b71f876a6842a5210817c9","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,13,9,20,1,7,10,23,15,2,5,11,12,22,3,6,21,14,8,16,17,19,24,18","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/208cb42fb32375e527d63cce28c63be67f1b02f576b71f876a6842a5210817c9.txt"},{"canonical_hash":"8995d3d9b807033618d8b46d17ac395b6d36c4f75b6ddbab8a0cf265a8449c34","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,10,12,19,20,5,11,13,17,21,6,9,14,18,23,7,8,15,16,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/8995d3d9b807033618d8b46d17ac395b6d36c4f75b6ddbab8a0cf265a8449c34.txt"},{"canonical_hash":"82e4ef10c99d95b4f14a33222ea67af849b987e4aab82bd9681724bb8d9b1dab","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,16,14,10,1,6,19,12,9,2,4,17,13,11,3,5,18,15,8,20,21,23,24,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/82e4ef10c99d95b4f14a33222ea67af849b987e4aab82bd9681724bb8d9b1dab.txt"},{"canonical_hash":"095d4f1cdc8164ea49718a880e8392c0c9fdceec5507f3dfbaba29639e7dc53d","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,9,13,16,1,7,19,11,14,2,6,18,12,8,3,5,10,17,15,20,21,23,24,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/095d4f1cdc8164ea49718a880e8392c0c9fdceec5507f3dfbaba29639e7dc53d.txt"},{"canonical_hash":"0448d4b8198505fe4dc8c8866659dd5e4408a980c7eeb62900dec0e9e3ab1689","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,9,12,17,23,5,10,13,18,20,6,11,14,19,21,7,8,15,16,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/0448d4b8198505fe4dc8c8866659dd5e4408a980c7eeb62900dec0e9e3ab1689.txt"},{"canonical_hash":"db22b107c995d0971456662f5e7763687e83c0c56bd95222f1f8f0d3adddc608","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,9,13,16,1,7,19,11,14,2,6,18,12,8,3,5,10,17,15,20,21,23,24,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/db22b107c995d0971456662f5e7763687e83c0c56bd95222f1f8f0d3adddc608.txt"},{"canonical_hash":"4eb40a4b64be6de7c0e497dbbbf227e08ed991abafc2bd8361513bf63fb79299","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"12,5,23,16,8,0,3,2,24,1,6,22,10,17,14,13,18,11,21,4,9,15,20,19,7","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas are exactly the lines of the affine plane AG(2, 5); every pair of distinct elements lies on a unique line, forming a Steiner system S(2, 5, 25).\n\nDistinguishing structural feature: |Aut(M)| = 20 (the smallest Aut among the 29 AG(2, 5) line magmas in DB). Aut acts on the 25 elements with orbit structure (1, 4, 20):\n  • Singleton orbit {12}: a unique Aut-fixed element (the 'pivot').\n  • Size-4 orbit {5, 8, 16, 23}: 4 elements forming one Aut-orbit.\n  • Size-20 orbit: the remaining 20 elements forming one Aut-orbit.\n\nAut(M) contains an order-20 element σ with cycle structure (1, 4, 20) — fixes 12, acts as a 4-cycle on the size-4 orbit, and as a 20-cycle on the size-20 orbit. The structure |Aut| = 20 with this orbit pattern is reminiscent of AGL(1, F_5) (order 20) acting on F_5 ⊕ (something), but more rigid than the size-5 magma's natural Aut.\n\nCompare with magma#4aacf2e3 (|Aut| = 48, orbits (1, 24), cycle (1, 24)) and magma#09d21ec3 (|Aut| = 600 = AGL(1, F_25), sharply 2-transitive). This 4eb40a4b magma has even more rigid Aut than 4aacf2e3.\n\nDisplay reorder uses the Aut-orbit + σ-cycle structure:\n  • Position 0: the pivot (12).\n  • Positions 1-4: size-4 orbit in σ-cycle order (4-cycle of σ).\n  • Positions 5-24: size-20 orbit as a 4×5 sub-grid where rows are σ⁴-orbits (4 cosets of an order-5 subgroup) and columns enumerate positions within each row via σ.\n\nUnder this reorder the Cayley table shows a clean 'sub-block' structure: the upper-left 5×5 corner involves the pivot and size-4 orbit; the lower-right 20×20 block shows diagonal-banded structure from the σ-action on the 20-orbit. This is cleaner than the AG-grid (5×5 of 5×5 blocks) reorder for this specific magma because its small Aut group doesn't fully respect any AG(2, 5) parallel class as a 'symmetry axis'.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/4eb40a4b64be6de7c0e497dbbbf227e08ed991abafc2bd8361513bf63fb79299.txt"},{"canonical_hash":"8c5d7c2ac40d3269316c9b6c609da30ad020934ba59308d692b63a15d22fc149","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,16,13,10,1,6,19,12,9,2,4,17,14,11,3,5,18,15,8,20,21,23,24,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/8c5d7c2ac40d3269316c9b6c609da30ad020934ba59308d692b63a15d22fc149.txt"},{"canonical_hash":"5c7e06dbbfcd36916cace6b8a8d1f8502727c3ed86251d0a3f700a607fcccd35","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,8,22,19,1,5,10,16,23,2,4,18,20,9,3,6,21,11,17,12,13,15,24,14","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/5c7e06dbbfcd36916cace6b8a8d1f8502727c3ed86251d0a3f700a607fcccd35.txt"},{"canonical_hash":"0e57ccc089f48b1bf91c5f79c616de8cfd7873aef997748b233ef98352c72a12","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,8,12,20,1,5,22,10,13,2,6,9,23,15,3,7,21,14,11,16,17,19,24,18","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/0e57ccc089f48b1bf91c5f79c616de8cfd7873aef997748b233ef98352c72a12.txt"},{"canonical_hash":"10a51a1050aa0186b75cb663f1fc496e8b87966ef1571535e41cb4c162696a60","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,10,21,16,14,1,9,20,19,15,2,11,22,17,12,3,8,23,18,13,4,5,7,24,6","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/10a51a1050aa0186b75cb663f1fc496e8b87966ef1571535e41cb4c162696a60.txt"},{"canonical_hash":"d732efd172ca4d7b9967999fff8c2c19229e25d23884fce7dbc53f3cb456aad4","size":25,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,2,5,8,24,1,22,9,3,15,14,21,6,23,13,18,4,17,10,16,7,12,20,19,11","comment":"Size-25 'half-AG(2, 5)' magma — the first known sporadic non-right-cancellative solution to equation 677. Carrier = the 25 points of the affine plane AG(2, 5) (over the field F_5). The operation is encoded by the 15 lines coming from 3 of the 6 parallel classes of AG(2, 5); the other 3 parallel classes are not used. Every element is idempotent (x ◇ x = x). The magma is left-cancellative but not right-cancellative — for any fixed y, the column x ↦ x ◇ y has 5-fold fiber structure (5 elements collapsing to each value).\n\nFurther structural facts (added by analysis):\n  • Carrier is the additive group of GF(25) ≅ (Z/5)²: the magma is fully (Z/5)²-translation-invariant — verified by exhibiting two commuting order-5 fix-free magma automorphisms τ_1, τ_2 generating the translation subgroup.\n  • |Aut(M)| = 300 = 25 · 12, acting transitively on the 25 elements (single orbit). Multiplicative stabilizer of 0 has order 12 (most likely Z_12 from the element-order distribution {1, 2, 3, 4, 6, 12}). Compare with magma#09d21ec3, the size-25 exceptional Zassenhaus near-field, which has |Aut| = 600 = 25 · 24 = AGL(1, F_25) (mult group = SL(2, 3) of order 24 — twice the size of this magma's stabilizer). So this 'half-AG(2, 5)' magma has exactly HALF the automorphism group of the exceptional near-field at the same size, mirroring its use of half the AG(2, 5) parallel classes (3 of 6).\n  • Sub-magma sizes: exactly 15 size-5 sub-magmas (= 3 parallel classes × 5 lines each, half of AG(2, 5)'s 30 lines). All other pairs generate the entire 25-element magma. So this is genuinely a 'partial AG(2, 5)' realization at the magma level.\n\nThis magma serves as the 'nRC factor' in many composite magmas in the database: it appears as one factor in the family of direct products nRC-25(d732efd1) × F_p at sizes 125, 175, 225, 275, 325, 425, 475, etc.\n\nDisplay reorder presents elements as (i, j) ↦ τ_1^i τ_2^j(0) at index 5·i + j using the τ_1, τ_2 commuting order-5 automorphisms — the hidden additive translations in (Z/5)². Under this reorder the Cayley table is fully (Z/5)²-translation-invariant.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/d732efd172ca4d7b9967999fff8c2c19229e25d23884fce7dbc53f3cb456aad4.txt"},{"canonical_hash":"d7ba9c7f1fe3d06e2210af0dce342981cfc21db8c89ba8f3d7035e4c926fab7b","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,8,22,19,1,5,10,16,23,2,4,18,20,9,3,6,21,11,17,12,13,15,24,14","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/d7ba9c7f1fe3d06e2210af0dce342981cfc21db8c89ba8f3d7035e4c926fab7b.txt"},{"canonical_hash":"98cf34a4bdae8185058bdbb18608e30d182e449d7b445041ff7c187a1814c02c","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/98cf34a4bdae8185058bdbb18608e30d182e449d7b445041ff7c187a1814c02c.txt"},{"canonical_hash":"09d21ec32e467d63bed6450be01efa29ba770da06db0c6565a94a0c45a330e70","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,6,15,4,1,12,9,22,13,5,23,24,11,8,17,10,21,16,20,7,14,3,19,18","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. **The exceptional Zassenhaus near-field of order 5²** — the smallest member of the exceptional-near-field family.\n\nStructure:\n  • Additive carrier: (Z/5)² ≅ GF(25) (the additive group of F_25). The magma is fully (Z/5)²-translation-invariant — verified by exhibiting two commuting order-5 fix-free magma automorphisms τ_1, τ_2.\n  • Automorphism group: Aut(M) is the sharply 2-transitive group AGL(1, F_25) = (Z/5)² ⋊ SL(2, 3) of order 25 × 24 = 600 (= |F_25*|). For Zassenhaus's exceptional near-field at order p² = 25, the multiplicative group of order 24 is SL(2, 3) (the binary tetrahedral group). Aut acts transitively on the 25 elements.\n  • Operation: x ◇ y = x + f(y − x) on (Z/5)², where f is multiplication by a near-field element c of order 8 in the SL(2, 3) multiplicative group (L_0 has cycle structure (1, 8³): order 8, with 3 orbits of length 8 partitioning the 24 non-zero elements into 3 cosets of ⟨c⟩).\n\nDistinguishing features:\n  • EVERY pair of distinct elements generates the full 25-element magma (no proper sub-magmas of any size). This is uniquely different from the other 53 size-25 magmas: all the others have size-5 sub-magmas (AG(2, 5) family) or size-5 fibers (the F_5(2,4)×F_5 family) or partial-AG structure. This one has NO size-5 sub-magmas because the non-distributive near-field multiplication breaks the F_5-linearity required for size-5 lines to exist as sub-magmas.\n  • L_0 cycle structure (1, 8³): order 8, 3 cosets of an order-8 cyclic subgroup of the (non-commutative) multiplicative group SL(2, 3).\n  • In the (Z/5)² basis (chosen via τ_1, τ_2 commuting order-5 automorphisms): f is axis-additive (linear on each F_5-axis) but NOT globally F_5-linear — verified e.g. f(1,0) + f(0,1) = (4,3) + (2,2) = (1,0) ≠ (0,1) = f(1,1). This 'axis-additive but globally non-linear' fingerprint is the structural signature of near-field multiplication outside the prime subfield, identical to magma#5ebfbb80 (size 11², exceptional near-field of order 121) and magma#29114da6 (size 29², exceptional near-field of order 841).\n\nDisplay reorder presents elements as (i, j) ↦ τ_1^i τ_2^j(0) at index 5·i + j, where τ_1, τ_2 are the chosen commuting order-5 magma automorphisms (the hidden additive translations by '1' and '2' in (Z/5)²). Under this reorder the table is fully (Z/5)²-translation-invariant.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/09d21ec32e467d63bed6450be01efa29ba770da06db0c6565a94a0c45a330e70.txt"},{"canonical_hash":"624d766580f7686439e1b9a5219c68acfe092ba430ea67a11f381c5028a423ee","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/624d766580f7686439e1b9a5219c68acfe092ba430ea67a11f381c5028a423ee.txt"},{"canonical_hash":"0b78df8e4e9fde27ba30fe8bc712c3419a3dabee4ef97c455e2c972e74434628","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/0b78df8e4e9fde27ba30fe8bc712c3419a3dabee4ef97c455e2c972e74434628.txt"},{"canonical_hash":"0bab6d80761e3d2b6b6571d363ecd9c9bdd538758e81d256f93e9dcc7a2b8aa3","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/0bab6d80761e3d2b6b6571d363ecd9c9bdd538758e81d256f93e9dcc7a2b8aa3.txt"},{"canonical_hash":"6b293d3dd9fb5ff4c8ca99b0cb2e2ef204dd8c2fbbdb3cd862712b69cf3c9f1a","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/6b293d3dd9fb5ff4c8ca99b0cb2e2ef204dd8c2fbbdb3cd862712b69cf3c9f1a.txt"},{"canonical_hash":"f499417a2a7445ad9f0c51ee82bd70f8287e617ae8e51d57662622253f9f1192","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/f499417a2a7445ad9f0c51ee82bd70f8287e617ae8e51d57662622253f9f1192.txt"},{"canonical_hash":"1bd1d609a09b30097c151ba02239b1d42bdf4b94ccf7b3b7dcc1fd91fc58d2be","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/1bd1d609a09b30097c151ba02239b1d42bdf4b94ccf7b3b7dcc1fd91fc58d2be.txt"},{"canonical_hash":"011f266679d5012ddc6fb8a93866200462cdbeaadb2c1631b585faedf18b4c26","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/011f266679d5012ddc6fb8a93866200462cdbeaadb2c1631b585faedf18b4c26.txt"},{"canonical_hash":"cd8c22f6e9c6a41936eb5e1a69c63d5d570c9f8551822ee68def8219ab119099","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/cd8c22f6e9c6a41936eb5e1a69c63d5d570c9f8551822ee68def8219ab119099.txt"},{"canonical_hash":"25c170c25d31010d01ea1ba46853665c634b88515a2ed069ccaf83b78b2ed074","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/25c170c25d31010d01ea1ba46853665c634b88515a2ed069ccaf83b78b2ed074.txt"},{"canonical_hash":"6bb1106b8e24a8655dfb860c5a30a714c5306688ab0c374eace07bcf5f4050c4","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/6bb1106b8e24a8655dfb860c5a30a714c5306688ab0c374eace07bcf5f4050c4.txt"},{"canonical_hash":"a91948dae3ec350d6ccf5a91f2fb0a0158031eb6c93b83d02d41e1ddc7f6f793","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/a91948dae3ec350d6ccf5a91f2fb0a0158031eb6c93b83d02d41e1ddc7f6f793.txt"},{"canonical_hash":"5559ef707773c22cd3df3e725888c674cc0d59a18107bc217168548eab90171b","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,11,22,19,12,1,10,16,21,13,2,9,18,15,20,3,8,14,23,17,4,5,7,24,6","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/5559ef707773c22cd3df3e725888c674cc0d59a18107bc217168548eab90171b.txt"},{"canonical_hash":"4ddcf319cb4c8df91e51c07d961cca9cdfef2af9d37d18cb802df1e0e3d1dedd","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/4ddcf319cb4c8df91e51c07d961cca9cdfef2af9d37d18cb802df1e0e3d1dedd.txt"},{"canonical_hash":"f901c559a1615dd1e009e02f0f262302f105794d2ca410a9c456c150eb3536b9","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/f901c559a1615dd1e009e02f0f262302f105794d2ca410a9c456c150eb3536b9.txt"},{"canonical_hash":"8eb84c9c8fe59c06aef2cf4269ea981a1ba8fb6250cd52bf1d14afc79f3c4545","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/8eb84c9c8fe59c06aef2cf4269ea981a1ba8fb6250cd52bf1d14afc79f3c4545.txt"},{"canonical_hash":"1587d269527c09a9a3ea1658ddad4366d577cc8362914decea7094e4714a461e","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/1587d269527c09a9a3ea1658ddad4366d577cc8362914decea7094e4714a461e.txt"},{"canonical_hash":"4ce20570af1baca9e34b44041624827fdd323b5f1271852ef6749e03c20653fa","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/4ce20570af1baca9e34b44041624827fdd323b5f1271852ef6749e03c20653fa.txt"},{"canonical_hash":"eab35010758607055d3015887844d07eaa003d688f04794d8adc8a9e9d1442bc","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/eab35010758607055d3015887844d07eaa003d688f04794d8adc8a9e9d1442bc.txt"},{"canonical_hash":"b45707833fa439b2addf81067878b9403bdec922f3398e70d3db052bcbf7b41d","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/b45707833fa439b2addf81067878b9403bdec922f3398e70d3db052bcbf7b41d.txt"},{"canonical_hash":"01a71aee57f82e839da8b08c7bf3ae83011da1220dcadca4a9cfc46a154ebcc1","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/01a71aee57f82e839da8b08c7bf3ae83011da1220dcadca4a9cfc46a154ebcc1.txt"},{"canonical_hash":"c70bf961f0ae94eff919d930e473062db5e25e1d655e745c7126d24c86fd2e52","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/c70bf961f0ae94eff919d930e473062db5e25e1d655e745c7126d24c86fd2e52.txt"},{"canonical_hash":"bc8f5fe83ee72e49d594037387c3ccf3d097b4867543b485199370672d16ca1e","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,24,4,8,12,16,20,5,9,13,17,21,7,11,15,19,23,6,10,14,18,22","comment":"F_5(2, 4) base × F_5 fiber: 5 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/bc8f5fe83ee72e49d594037387c3ccf3d097b4867543b485199370672d16ca1e.txt"},{"canonical_hash":"a368146845d406f4362938f6262810a0cc16fecb3ce70dd4cca1fbe18e24c0c4","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,8,18,20,1,5,16,10,23,2,6,22,9,17,3,7,21,19,11,12,13,15,24,14","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/a368146845d406f4362938f6262810a0cc16fecb3ce70dd4cca1fbe18e24c0c4.txt"},{"canonical_hash":"36833d141f8560b5abcab4e2f05f1ccf00bec0c3daf655be8afb34dab1b9e717","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,8,21,17,12,5,11,18,14,23,6,10,15,16,22,7,9,13,20,19","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/36833d141f8560b5abcab4e2f05f1ccf00bec0c3daf655be8afb34dab1b9e717.txt"},{"canonical_hash":"e1896966e0b518d6302bf97f28748002359f8ddcc3d826423955c1b8ac5eba63","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,24,3,2,4,10,14,21,19,5,11,17,15,20,6,9,16,23,12,7,8,13,18,22","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/e1896966e0b518d6302bf97f28748002359f8ddcc3d826423955c1b8ac5eba63.txt"},{"canonical_hash":"41d78868d77e660f0d48a92baaeb156ea44077473724ed49cbc05c02730688ab","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,8,22,19,1,6,11,23,17,2,4,10,21,18,3,5,16,9,20,12,13,15,24,14","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:40","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/41d78868d77e660f0d48a92baaeb156ea44077473724ed49cbc05c02730688ab.txt"},{"canonical_hash":"f0ecd21d422c99c6010f30c11ad319f56483983e586009710c6cb2c151393ceb","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,11,22,19,12,1,9,13,23,16,2,10,18,15,21,3,8,20,14,17,4,5,7,24,6","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:40","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/f0ecd21d422c99c6010f30c11ad319f56483983e586009710c6cb2c151393ceb.txt"},{"canonical_hash":"d2ff72f88c4a81c62706f0cd20e6c71aefbc29a1fcaca875f7e35c29c2523b52","size":25,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,8,22,19,1,5,10,16,23,2,4,11,18,20,3,6,21,17,9,12,13,15,24,14","comment":"Size-25 = 5² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 5) line family. The 30 size-5 sub-magmas of this magma are exactly the lines of the affine plane AG(2, 5); every pair of distinct points lies on a unique line (so this realizes the Steiner system S(2, 5, 25)). Each line is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma over F_5, x ◇ y = 2x + 4y mod 5 — α = 4 is the only primitive 10th root of unity mod 5).\n\nThe 30 lines decompose into 6 parallel classes of 5 mutually disjoint lines each (covering the 25 elements). Each parallel class is one of the q + 1 = 6 'directions' of AG(2, 5).\n\nDisplay reorder uses an AG(2, 5) coordinate grid: pick two parallel classes C_h and C_v, sort each class's lines by minimum canonical label, then label each point as (i, j) at index 5·i + j where i is its line-index in C_h and j its line-index in C_v. Each pair of lines from different classes intersects in exactly one point, so this gives a bijection between elements and (Z/5) × (Z/5) coordinate positions. Under this reorder the Cayley table shows a clean 5×5 grid of 5×5 blocks: the 5 diagonal blocks are within-class C_h line operations (each block is the size-5 magma's Cayley table), and the 20 off-diagonal blocks reflect the cross-line operations.\n\nThere are 29 size-25 magmas in this AG(2, 5) line family currently in the DB. Of these, only 1 (magma#053cceeb, the F_5 × F_5 direct product with both factors using α=4) is fully (Z/5)²-translation-invariant; the other 28 share the same AG(2, 5) Steiner-system structure but their magma operations break the additive translation symmetry — they have rigid automorphism groups (typically order 24-120) with no order-5 fix-free element, so they are not 'linear' over F_5² in the additive sense.\n\nOther size-25 Eq 677 magma families in the DB (NOT in this family): (a) 23 'F_5(2, 4) base × F_5 fiber' fiber-bundle constructions with only 5 size-5 sub-magmas (different from the 30 here); (b) magma#d732efd1, a 'half-AG(2, 5)' sporadic non-product magma with 15 size-5 sub-magmas; (c) magma#09d21ec3, a sporadic non-product magma with NO size-5 sub-magmas at all.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/25/d2ff72f88c4a81c62706f0cd20e6c71aefbc29a1fcaca875f7e35c29c2523b52.txt"},{"canonical_hash":"9f34fd7dead4e1ea0f5f61fa37f1cc136f6f65725635fac6b38b00df5b4c0c9f","size":29,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,23,25,22,14,11,21,9,6,12,26,3,10,16,5,13,2,18,4,24,19,15,20,8,7,27,28,17","comment":"Tao Type II 2-piece translation-invariant magma at size 29.\n\nSize 29, prime, fully idempotent, RC. |Aut(M)| = 406 = 14 * 29.\n\n29 ≡ 9 (mod 10), so F_29 has no Phi_10 roots (no element of order 10) and there is no single-slope F_29 affine line magma at this size. But there IS a 2-piece \"Tao Type II piecewise\" construction over F_29:\n\nIn F_29-translation labeling (see suggested reorder, where x -> x+1 is an automorphism), the operation is x*y = x + f(y - x) mod 29 with\n  f(y) = 27 * y  if y is a quadratic residue mod 29\n  f(y) = 3 * y   if y is a non-residue mod 29\n(and f(0) = 0). 27 = 3^3 = -2 mod 29; both 3 and 27 are in F_29* but neither is a 10th root of unity (no such element exists in F_29*).\n\nQR(29) = {1, 4, 5, 6, 7, 9, 13, 16, 20, 22, 23, 24, 25, 28}\nNQR(29) = {2, 3, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 26, 27}\n\nThe Z_14 multiplicative stabilizer is precisely (F_29*)^2 = QR(29). It acts on F_29* preserving the QR/NQR split; squares acting on squares stay in squares, etc., so the slope function (which is constant on each of QR, NQR) is preserved by Z_14 multiplication. Combined with the regular Z_29 translation, |Aut| = 29 * 14 = 406.\n\nAut orbits: 1 single orbit covering all 29 idempotents (Aut is point-transitive). |Aut|/|orbit| = 406/29 = 14 = stab(0), matching the Z_14 multiplicative stabilizer.\n\nThis is a clean example of a Tao Type II piecewise construction over F_p for a prime p where no single-slope linear construction exists. The recipe:\n  - take H = (F_p*)^2 = QR(p), the index-2 subgroup\n  - find (alpha, beta) in F_p* such that the piecewise f (alpha on H, beta on F_p* \\ H) makes x + f(y-x) satisfy Eq 677\nFor p = 29 this admits the unique solution (alpha, beta) = (27, 3) up to swap.\n\nNo sub-magma structure: every pair of distinct elements generates the whole magma. Both L_x and R_x are involutive on the non-x part: cycle type 1 + 14 + 14.\n\nCompare: \n  - F_29^2 = size 841 linear magmas use Phi_10 roots from F_29^2 \\ F_29 (the irreducible factors of Phi_10 over F_29 -- since 29 has order 2 mod 10, Phi_10 splits into 2 irreducible quadratics over F_29 -- give magmas of size 841 = 29^2).\n  - This size-29 magma uses a fundamentally different recipe: a QR/NQR split with 2 slopes both in F_29*.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/29/9f34fd7dead4e1ea0f5f61fa37f1cc136f6f65725635fac6b38b00df5b4c0c9f.txt"},{"canonical_hash":"60f580e413a5832beb5a72905ae2661f74c504f82560d82cf9a68fbab2e14100","size":31,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,6,5,4,3,2,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,29,28,27,26,25,30","comment":"Constant-offset linear magma over F_31: x ◇ y = 5x + 27y + 28 (mod 31).\n\nSize 31, prime, fully NON-idempotent (no idempotents at all), right-cancellative. |Aut(M)| = 31 (only the Z_31 translation; no multiplicative stabilizer).\n\nThe operation is x ◇ y = 5x + 27y + 28 (mod 31), or equivalently x ◇ y = x + 27 * (y - x) + 28. Since 5 + 27 = 32 = 1 (mod 31), this falls into the affine-line family x ◇ y = a*x + (1-a)*y + c with a = 5, c = 28. The slope alpha = 27 is one of the four primitive 10th roots of unity in F_31* (the Phi_10 roots being {15, 23, 27, 29}); without the +28 constant offset this would be the same idempotent linear magma magma#543c5479 (which is x ◇ y = 5x + 27y).\n\nDiagonal: T(x, x) = (5 + 27) * x + 28 = x + 28 mod 31. So x ◇ x = x + 28, never x: zero idempotents.\n\nThis is the only non-fully-idempotent \"affine line + constant\" 677 magma at size 31 in the DB. The closest cousin is magma#3cb2b467 (x ◇ y = 5x + 9y), which is also non-idempotent but uses general (a, b) with a + b = 14 ≠ 1 (one idempotent at x = 0 only).\n\nCompare with the 4 fully idempotent linear F_31 magmas in the DB (one per Phi_10 root):\n  magma#7ba82cf6: x ◇ y = 17x + 15y (alpha = 15)\n  magma#543c5479: x ◇ y = 5x + 27y  (alpha = 27)\n  magma#fdf14b96: x ◇ y = 9x + 23y  (alpha = 23)\n  magma#7ee5b4b8: x ◇ y = 3x + 29y  (alpha = 29)\nEach has |Aut| = 930 = 30 * 31 = |AGL(1, 31)|.\n\nThis non-idempotent variant has only |Aut| = 31 (translation only) because the constant offset c = 28 breaks the multiplicative symmetry: multiplication by mu ∈ F_31* would satisfy mu * (5x + 27y + 28) = 5(mu x) + 27(mu y) + 28 only if 28*mu = 28, hence mu = 1.\n\nEq 677 verified algebraically: with f(z) = alpha * z + c (f(0) = c, so non-idempotent), the magma x ◇ y = x + f(y - x) satisfies Eq 677 iff alpha is a Phi_10 root in F_p AND c is arbitrary (any c gives Eq 677). The constant c shifts the magma \"in unison\" without breaking the equation.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/31/60f580e413a5832beb5a72905ae2661f74c504f82560d82cf9a68fbab2e14100.txt"},{"canonical_hash":"7ba82cf634363584caafe99d54dafc05130fde403f1ec210575a1bdb36a782cf","size":31,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,20,2,11,7,29,10,9,24,25,14,22,26,17,5,15,1,28,23,21,4,27,3,30,18,12,19,6,8,13,16","comment":"Linear magma over Z/31Z (the prime field F_31): x ◇ y = 17x + 15y (mod 31).","submitted_at":"2026-04-23 20:56:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/31/7ba82cf634363584caafe99d54dafc05130fde403f1ec210575a1bdb36a782cf.txt"},{"canonical_hash":"543c5479c1a00c109b39fc5b1531471842fc8538d9bccdad706827c746661dd9","size":31,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,21,5,12,7,13,20,18,29,2,19,9,27,4,8,10,23,17,22,15,11,26,25,14,28,16,30,6,3,24","comment":"Linear magma over Z/31Z (the prime field F_31): x ◇ y = 5x + 27y (mod 31).","submitted_at":"2026-04-23 20:56:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/31/543c5479c1a00c109b39fc5b1531471842fc8538d9bccdad706827c746661dd9.txt"},{"canonical_hash":"fdf14b96c1968d42a5ccded6c495baf14ad16d85724bb0f47e2c0bb18af6f4ab","size":31,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,28,13,21,29,4,15,23,30,14,7,18,11,12,22,10,25,26,8,27,17,20,24,19,5,2,3,6,9,16","comment":"Linear magma over Z/31Z (the prime field F_31): x ◇ y = 9x + 23y (mod 31).","submitted_at":"2026-04-23 20:56:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/31/fdf14b96c1968d42a5ccded6c495baf14ad16d85724bb0f47e2c0bb18af6f4ab.txt"},{"canonical_hash":"7ee5b4b80495c98c76e764353ccdbdf3c4acc91e5f6e0c34f9c09bd81abf40c8","size":31,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,12,8,13,22,24,14,20,17,25,11,4,21,6,19,26,10,2,5,29,9,7,28,23,27,16,15,3,30,18","comment":"Linear magma over Z/31Z (the prime field F_31): x ◇ y = 3x + 29y (mod 31).","submitted_at":"2026-04-23 20:56:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/31/7ee5b4b80495c98c76e764353ccdbdf3c4acc91e5f6e0c34f9c09bd81abf40c8.txt"},{"canonical_hash":"3cb2b467fe8954788af4626bf8f57b1dc786fc9556b614ab7f58614e7f7b6df8","size":31,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"30,0,17,16,5,9,4,25,23,3,27,29,22,6,13,26,11,28,21,7,15,12,18,8,10,19,24,20,1,2,14","comment":"Linear magma over Z/31Z (the prime field F_31): x ◇ y = 5x + 9y (mod 31).","submitted_at":"2026-04-23 20:56:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/31/3cb2b467fe8954788af4626bf8f57b1dc786fc9556b614ab7f58614e7f7b6df8.txt"},{"canonical_hash":"e6571cef468a5b957a96f550156000bf501aa6043ec9ef9a34135c5a6bf91ce2","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,12,18,22,32,1,6,10,15,16,21,33,3,5,9,14,19,23,31,24,25,26,27,28,29,34,2,7,11,13,17,20,30","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/e6571cef468a5b957a96f550156000bf501aa6043ec9ef9a34135c5a6bf91ce2.txt"},{"canonical_hash":"ab7b41b26d4b99ca4ecdbec5363c0af4be662cae6d9f607e0eb58caf2bd5f957","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,15,16,20,33,1,5,9,12,18,21,32,2,7,11,13,17,22,30,24,25,26,27,28,29,34,3,6,10,14,19,23,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/ab7b41b26d4b99ca4ecdbec5363c0af4be662cae6d9f607e0eb58caf2bd5f957.txt"},{"canonical_hash":"1f6a47f51140980acebe1a372e706bc78feb0908a3f2275dc4748d470b7f80dc","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"30,2,11,17,7,22,13,31,3,10,16,6,20,12,32,0,8,19,4,23,14,34,28,27,29,26,24,25,33,1,9,18,5,21,15","comment":"Direct product of two linear magmas: F_5 × F_7. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 4x₂ + 1y₂ (mod 7)).","submitted_at":"2026-04-23 20:56:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/1f6a47f51140980acebe1a372e706bc78feb0908a3f2275dc4748d470b7f80dc.txt"},{"canonical_hash":"5452d53e23f280b12d101c990bf556ffbec855a1aaadc544b1b7670c97c3a007","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"30,3,17,20,9,4,13,31,1,16,21,10,6,14,32,0,18,22,8,5,12,34,29,28,24,26,25,27,33,2,19,23,11,7,15","comment":"Direct product of two linear magmas: F_5 × F_7. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 4x₂ + 3y₂ (mod 7)).","submitted_at":"2026-04-23 20:56:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/5452d53e23f280b12d101c990bf556ffbec855a1aaadc544b1b7670c97c3a007.txt"},{"canonical_hash":"998f8dec2a8d83eb4d1cc5db7e0f31a8ff63ecfa7771a3096bff4d9e57d21982","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,10,14,18,22,30,1,6,8,13,17,21,32,3,5,9,12,16,20,33,2,7,11,15,19,23,31,24,25,26,27,28,29,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/998f8dec2a8d83eb4d1cc5db7e0f31a8ff63ecfa7771a3096bff4d9e57d21982.txt"},{"canonical_hash":"a297e0d68aa18948e12b8337dda1e4de2a46efa342b662a6af6d6fc3111778af","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,14,19,22,33,1,5,9,15,18,23,32,2,7,11,13,16,20,30,24,25,26,27,28,29,34,3,6,10,12,17,21,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/a297e0d68aa18948e12b8337dda1e4de2a46efa342b662a6af6d6fc3111778af.txt"},{"canonical_hash":"7c7b4a5d3753950984e669b04398eef6240938ad2b613e09fe6b144162e04cd0","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,8,14,18,22,33,1,6,10,12,17,21,30,3,4,9,13,16,20,31,2,7,11,15,19,23,32,24,25,26,27,28,29,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/7c7b4a5d3753950984e669b04398eef6240938ad2b613e09fe6b144162e04cd0.txt"},{"canonical_hash":"543c406d4f7934885312ba07fa4065e60e7c263117124d6c8f13ce271d7329b9","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,9,12,18,22,32,1,6,10,14,16,21,31,3,4,8,13,17,20,30,2,7,11,15,19,23,33,24,25,26,27,28,29,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/543c406d4f7934885312ba07fa4065e60e7c263117124d6c8f13ce271d7329b9.txt"},{"canonical_hash":"6c5f4bc923697a6a4fa7ccb54f3c3b79a402547a470aa3eb84106e1f6c9178df","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,15,16,20,30,1,5,9,13,18,22,32,3,7,11,14,19,23,33,2,6,10,12,17,21,31,24,25,26,27,28,29,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/6c5f4bc923697a6a4fa7ccb54f3c3b79a402547a470aa3eb84106e1f6c9178df.txt"},{"canonical_hash":"99d8d8c712e80bac403dac805fd8311b82bce0ff0c453740a6f6c79ff0b0fb12","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,13,19,20,30,1,5,9,12,17,22,32,3,7,11,15,18,23,33,2,6,10,14,16,21,31,24,25,26,27,28,29,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/99d8d8c712e80bac403dac805fd8311b82bce0ff0c453740a6f6c79ff0b0fb12.txt"},{"canonical_hash":"baf57268d2d90628bc6a1451408ead70e0d83e3d833cfa6d1ce49a5da5a36338","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,10,14,18,20,30,1,5,9,13,17,23,33,24,25,26,27,28,29,34,2,6,8,12,16,21,32,3,7,11,15,19,22,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/baf57268d2d90628bc6a1451408ead70e0d83e3d833cfa6d1ce49a5da5a36338.txt"},{"canonical_hash":"c689a91b3ffd7084c5c7eb7e7da23e74b4c3f1dab7b2d063b22c6a40044237ea","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,3,1,4,5,2,30,8,26,17,18,22,13,31,9,27,15,19,23,12,32,7,28,14,20,24,11,33,6,29,16,21,25,10,34","comment":"Twisted fiber bundle of shape 5 x 7.\n\nStructure: the 35 elements partition into 5 disjoint size-7 sub-magmas (the \"fibers\") via a congruence relation. Quotienting by the fibers yields a size-5 magma magma#e549b5f8, the unique Eq 677 magma at size 5 (the affine F_5 line magma, x*y = x + 2(y-x) mod 5).\n\nEach fiber is isomorphic to magma#7981e2df, the non-fully-idempotent size-7 magma (1 idempotent + 6 non-idempotents). The five global idempotents 30..34 are exactly the five fiber-idempotents (one per fiber), so the non-idempotent count is 5 of 35 (matching idem=False).\n\nIn the suggested reorder, the 35 elements are arranged as five consecutive 7-blocks (positions 0..6, 7..13, 14..20, 21..27, 28..34), one per fiber, with each block's idempotent placed at position 6 (last). The diagonal 7x7 blocks then expose the common fiber operation, and off-diagonal blocks show the bundle's twist.\n\nBundle is non-split: there is no size-5 sub-magma anywhere in M, in particular the 5 idempotents are not closed under the operation (e.g. T(30,31) = 16, not 34). The base operation Q on the 5 fibers permutes them, but the action restricted to the idempotent section fails to be a homomorphism on the nose.\n\nTwist structure: classifying off-diagonal \"fiber slice ops\" (the residue table p1,p2 -> (x*y) mod 7 for fixed fiber pair) gives just 4 distinct slice ops over the 25 base-pairs:\n  - 13 pairs share one op (including the 5 diagonal pairs)\n  - 4 pairs (0,j) for j>0 share another op\n  - 4 pairs (i,0) for i>0 share another\n  - 4 pairs ((1,3),(2,1),(3,4),(4,2)) share the last\nThis non-trivial twisting is why |Aut(M)| = 4 is small (a true direct product F_5 x M_7 would have |Aut(F_5)| * |Aut(M_7)| = 20 * |Aut(M_7)|).\n\nAut orbits: 7 singletons {0,1,2,3,4,5,30} = the special \"all-singletons\" fiber (the one through 30) + 7 size-4 orbits, one per residue-class of size-4 in each of the other 4 fibers. The 4 non-special fibers each form one size-4-orbit transversal (1 element per Aut orbit).\n\nCompare with the size-96 magma magma#b1cfacfa (6 disjoint size-16 petals, non-split) and size-127 / size-181 (single piece, Tao Type II). This size-35 magma is the smallest \"5-fiber x 7-fiber\" twisted bundle in the DB.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/c689a91b3ffd7084c5c7eb7e7da23e74b4c3f1dab7b2d063b22c6a40044237ea.txt"},{"canonical_hash":"d5b73a2567aa78772edc2d75f03495357b68a57129ff90f04af1b2c7548cac1b","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,9,13,17,21,32,1,4,8,12,16,23,30,24,25,26,27,28,29,34,2,6,10,14,18,20,31,3,7,11,15,19,22,33","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/d5b73a2567aa78772edc2d75f03495357b68a57129ff90f04af1b2c7548cac1b.txt"},{"canonical_hash":"26eaf65574572733ef049de603ecd83eb9e8526f898a554de9d553b00dc9ff1c","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"12,17,14,15,16,13,30,24,29,26,27,28,25,31,0,3,1,4,5,2,32,18,23,20,21,22,19,33,6,11,8,9,10,7,34","comment":"Twisted fiber bundle of shape 5 x 7 (fully twisted variant).\n\nSame skeleton as magma#c689a91b: the 35 elements partition into 5 disjoint size-7 sub-magmas via a congruence. Quotient is the size-5 affine F_5 line magma magma#e549b5f8 (unique Eq 677 magma at size 5). Each fiber is isomorphic to magma#7981e2df, the size-7 magma with exactly 1 idempotent. The 5 global idempotents 30..34 are exactly the 5 fiber-idempotents, one per fiber.\n\nIn the suggested reorder, the 35 elements are arranged as five consecutive 7-blocks (positions 0..6, 7..13, 14..20, 21..27, 28..34), one per fiber, with each block's idempotent placed at position 6. Diagonal 7x7 blocks reveal the common fiber operation; off-diagonal blocks reveal the bundle's twist.\n\nBundle is non-split: there is no size-5 sub-magma anywhere in M, so the 5 idempotents do not form a sub-magma (T(30,31) = 9, not 31).\n\nWhat distinguishes this from magma#c689a91b is the *twist class*. Classifying off-diagonal fiber slice ops (the residue table p1,p2 -> (x*y) mod 7 for fixed fiber pair):\n  - this magma: 21 distinct slice ops (5 diagonal pairs share one op; all 20 off-diagonal slices are pairwise distinct), so the twist is essentially \"fully scrambled\".\n  - magma#c689a91b: only 4 distinct slice ops (much more symmetric twist).\n\nReflecting the heavier twist, |Aut(M)| = 1 (trivial — only the identity automorphism), versus |Aut(magma#c689a91b)| = 4. Every element is a singleton Aut-orbit.\n\nR_0 cycle signature 1+3+3+4+12+12 and L_0 signature 7+14+14 match magma#c689a91b exactly, so the cycle-pattern fingerprint cannot distinguish the two; the discriminating invariants are the twist class and |Aut|.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/26eaf65574572733ef049de603ecd83eb9e8526f898a554de9d553b00dc9ff1c.txt"},{"canonical_hash":"5b34fd3d54a960c4913311640650d5e7c67e58a0347cd602c819bc4600c20f57","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,17,10,11,12,9,30,19,29,23,25,27,21,31,18,28,22,24,26,20,32,1,7,2,5,16,13,33,0,6,3,4,15,14,34","comment":"Twisted fiber bundle of shape 5 x 7 (intermediate-twist variant).\n\nSame skeleton as magma#c689a91b and magma#26eaf655: 35 elements partition into 5 disjoint size-7 sub-magmas via a congruence. Quotient is the unique size-5 Eq 677 magma magma#e549b5f8 (affine F_5 line). Each fiber is isomorphic to magma#7981e2df, the size-7 magma with exactly 1 idempotent; the 5 global idempotents 30..34 are the fiber-idempotents, one per fiber. No size-5 sub-magma anywhere (non-split bundle).\n\nIn the suggested reorder, the 35 elements are arranged as five consecutive 7-blocks (positions 0..6, 7..13, 14..20, 21..27, 28..34), one per fiber, with each block's idempotent at position 6.\n\nTwist class is intermediate between magma#c689a91b and magma#26eaf655. Classifying off-diagonal fiber slice ops (residue table p1,p2 -> (x*y) mod 7 for fixed fiber pair (f1,f2)):\n  - 11 distinct slice ops total\n  - 5 diagonal pairs share one op (the common fiber operation)\n  - All 20 off-diagonal slice ops occur in 10 pairs of 2: each pair of base-pairs shares a slice op\n\nThe pairing of base-pairs:\n  (0,1)~(0,2)   (0,3)~(0,4)   (1,0)~(2,0)   (1,2)~(2,1)\n  (1,3)~(2,4)   (1,4)~(2,3)   (3,0)~(4,0)   (3,1)~(4,2)\n  (3,2)~(4,1)   (3,4)~(4,3)\nThis pairing is induced by the involution on fibers (1<->2, 3<->4, fiber 0 fixed), which is a genuine automorphism of M.\n\n|Aut(M)| = 2. Aut orbits: 7 singletons (the 7 elements of fiber 0 -- this fiber is pointwise-fixed by the involution) + 14 size-2 orbits (the involution pairs corresponding elements across fibers 1<->2 and across 3<->4).\n\nComparison across the size-35 1+3+3+4+12+12 family seen so far:\n  magma#c689a91b: 4 slice ops, |Aut| = 4   (most symmetric twist)\n  this magma:    11 slice ops, |Aut| = 2   (one involution)\n  magma#26eaf655: 21 slice ops, |Aut| = 1  (fully scrambled twist)\n\n[text written by Claude]","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/5b34fd3d54a960c4913311640650d5e7c67e58a0347cd602c819bc4600c20f57.txt"},{"canonical_hash":"9eb5f84c893cfc8d4f8875dd0855ce17fa945abc84124fa832ed8609140d01b2","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,30,6,7,8,9,10,11,34,12,13,14,15,16,17,32,18,19,20,21,22,23,33,24,25,26,27,28,29,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/9eb5f84c893cfc8d4f8875dd0855ce17fa945abc84124fa832ed8609140d01b2.txt"},{"canonical_hash":"4d5e1d7c0bc8713731be0b8eac01db7bddd2845d8dd118b9bb864e63a058ce82","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,34,6,7,8,9,10,11,30,18,19,20,21,22,23,33,24,25,26,27,28,29,32,12,13,14,15,16,17,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/4d5e1d7c0bc8713731be0b8eac01db7bddd2845d8dd118b9bb864e63a058ce82.txt"},{"canonical_hash":"7ce654d389b42b1bf334fec493a4de1c23a02129dcfe2b8e0be8670e88478208","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,30,6,11,15,18,24,28,31,8,13,17,21,25,29,32,9,10,14,19,23,26,33,7,12,16,20,22,27,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/7ce654d389b42b1bf334fec493a4de1c23a02129dcfe2b8e0be8670e88478208.txt"},{"canonical_hash":"23b1fa4377c45404ba526594e00e445e45d186139e60fb56eb942b92e13b0391","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,32,6,7,8,9,10,11,33,24,25,26,27,28,29,34,18,19,20,21,22,23,30,12,13,14,15,16,17,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/23b1fa4377c45404ba526594e00e445e45d186139e60fb56eb942b92e13b0391.txt"},{"canonical_hash":"79fcb03c9bfc8bf293d09904ea702a05a9cd2eb25023a2ba96c4384bdf6126bf","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,34,6,9,11,13,15,17,33,19,21,23,25,27,29,31,18,20,22,24,26,28,30,7,8,10,12,14,16,32","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/79fcb03c9bfc8bf293d09904ea702a05a9cd2eb25023a2ba96c4384bdf6126bf.txt"},{"canonical_hash":"50a43b5517c93bde22b9524aeb7e979f4a400e135b4bcdb65506d6a716dff1c8","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,11,31,5,6,7,8,9,10,34,12,13,14,15,16,23,30,24,25,26,27,28,29,32,17,18,19,20,21,22,33","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/50a43b5517c93bde22b9524aeb7e979f4a400e135b4bcdb65506d6a716dff1c8.txt"},{"canonical_hash":"b3b6c29b36a9ffc285b203067cc7c7be36957efa60ab1193f85c9eed1653f95b","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,10,16,21,26,33,1,6,12,15,20,25,30,4,8,13,18,23,28,31,3,9,14,19,24,29,34,2,7,11,17,22,27,32","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/b3b6c29b36a9ffc285b203067cc7c7be36957efa60ab1193f85c9eed1653f95b.txt"},{"canonical_hash":"26534c69ada14720d9d39e9a7c01537810ba8f2f7b2df48113e4c3928fb026d7","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,31,6,7,8,9,10,11,34,18,19,20,21,22,23,30,12,13,14,15,16,17,32,24,25,26,27,28,29,33","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/26534c69ada14720d9d39e9a7c01537810ba8f2f7b2df48113e4c3928fb026d7.txt"},{"canonical_hash":"0b3769f778f8f422b259a10a8857d7986863da192e71cef1cce3a713816b41b5","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,6,11,15,23,27,32,1,7,12,17,21,25,31,4,5,10,16,22,26,30,2,8,13,18,20,28,33,3,9,14,19,24,29,34","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/0b3769f778f8f422b259a10a8857d7986863da192e71cef1cce3a713816b41b5.txt"},{"canonical_hash":"90d603a56bf87c7b7a76a4bf1abcf8543289f1eb4c1d0a7dd8a11072c1f2ed80","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,14,18,23,32,1,5,11,13,17,21,33,2,6,9,15,19,20,31,24,25,26,27,28,29,34,3,7,10,12,16,22,30","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/90d603a56bf87c7b7a76a4bf1abcf8543289f1eb4c1d0a7dd8a11072c1f2ed80.txt"},{"canonical_hash":"ce3fab54a4996781fd2a85c1449cd5f0d8ae79d083b78cebd6d5b0bcb0587c72","size":35,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,9,13,18,22,33,1,4,8,15,17,21,32,3,7,11,14,19,23,30,24,25,26,27,28,29,34,2,6,10,12,16,20,31","comment":"F_5(2, 4) base × F_7 fiber: 5 fibers of 7 (each = F_7 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:56:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/35/ce3fab54a4996781fd2a85c1449cd5f0d8ae79d083b78cebd6d5b0bcb0587c72.txt"},{"canonical_hash":"1210c3d67f88cb2755ace1fa21acb05f3423fab5f3fb0ca3a613f24fb22cf023","size":37,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"36,0,6,30,34,16,23,29,27,18,9,35,22,12,28,4,20,5,11,14,8,17,7,25,15,19,2,1,21,24,32,26,13,31,33,3,10","comment":"Linear magma over Z/37Z (the prime field F_37): x ◇ y = 26x + 2y (mod 37).","submitted_at":"2026-04-23 20:56:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/37/1210c3d67f88cb2755ace1fa21acb05f3423fab5f3fb0ca3a613f24fb22cf023.txt"},{"canonical_hash":"461ef7455634e2f25be11f11f23ba42d62ebe43d1b90ec5420b40027efc829b7","size":37,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"36,14,29,8,4,3,23,6,19,30,18,16,26,7,21,25,34,27,5,11,33,28,31,15,0,32,22,12,24,13,1,17,9,10,2,35,20","comment":"Linear magma over Z/37Z (the prime field F_37): x ◇ y = 26x + 24y (mod 37).","submitted_at":"2026-04-23 20:56:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/37/461ef7455634e2f25be11f11f23ba42d62ebe43d1b90ec5420b40027efc829b7.txt"},{"canonical_hash":"b7e8bf900acc08e5f60b3687543c1f96130d413ec34f406cbea87b23a80066c8","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,21,39,30,38,13,31,28,17,26,22,12,2,14,33,11,23,6,20,29,9,35,7,37,34,32,19,25,36,8,3,5,15,16,24,10,18,40,27,4","comment":"Steiner-line construction on the cyclic S(2, 5, 41) design.\n\nSize 41, fully idempotent, right-cancellative. Every pair of distinct elements lies in exactly one size-5 sub-magma, and there are 82 = 41*40/(5*4) such blocks, each point lying in 10 of them. Each block is isomorphic to magma#e549b5f8, the unique size-5 Eq 677 magma (the affine F_5 line).\n\n|Aut(M)| = 205 = 5 * 41, acting transitively on points. Aut has a regular Z_41 subgroup of translations, and the point-stabilizer is the Z_5 subgroup of F_41* generated by the order-5 element zeta = 10 (so {1, 10, 18, 16, 37} acts by multiplication). The structure is the Sharply 1-transitive piece of AGL(1, 41) restricted to a Z_5 multiplier group; equivalently Aut ~ Z_41 : Z_5.\n\nIn the suggested reorder, elements are labeled by F_41 = Z/41 in an order where translation x -> x+1 is an automorphism. The operation then takes the translation-invariant form x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41. Concretely f(y) = alpha(y) * y where alpha(y) takes only 4 values - the 4 roots of the cyclotomic polynomial Phi_10 in F_41:\n  Phi_10 roots = {4, 23, 25, 31} (these are the primitive 10th roots of unity in F_41*)\n  alpha is constant on each of 4 size-10 subsets that partition F_41*.\n\nEach size-10 \"slope class\" is a union of two Z_5-cosets in F_41*/<zeta>:\n  alpha=31: y in {1, 2, 10, 16, 18, 20, 32, 33, 36, 37}\n  alpha=4:  y in {4, 5, 8, 9, 21, 23, 25, 31, 39, 40}\n  alpha=25: y in {3, 6, 7, 13, 14, 17, 19, 26, 29, 30}\n  alpha=23: y in {11, 12, 15, 22, 24, 27, 28, 34, 35, 38}\nThis is a \"Tao Type II piecewise\" recipe: f is not multiplication by a single scalar, but each Z_5-coset gets its own primitive-10th-root slope. The four slopes are Galois-conjugate, and the assignment of slopes to cosets is what makes this Eq 677.\n\nBlock structure: the 82 blocks form 2 Aut-orbits (each of size 41), the orbits being the translate-classes of two base blocks under Z_41 (the standard difference family for a cyclic (41, 5, 1)-BIBD). The 10 blocks through 0 split as 2 Z_5-orbits of 5 blocks each.\n\nCompares with the F_p affine line magmas (size p, p ≡ 1 mod 10, e.g. p = 11, 31, 61) which are translation-invariant but with f(y) = alpha*y a single linear map; those are also Steiner-line magmas, but their S(2, 5, p) is \"linear\" - this size-41 magma uses a more general Tao Type II f and gives a (likely) inequivalent design.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:57:07","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/b7e8bf900acc08e5f60b3687543c1f96130d413ec34f406cbea87b23a80066c8.txt"},{"canonical_hash":"d32b07ca31049c672f273f1263a4018f94e1733b8b7fb07b48828ac9e2e0d0f0","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,9,27,19,5,39,34,28,11,24,6,8,40,25,35,36,38,22,18,15,16,31,13,14,10,26,21,30,37,29,3,7,23,33,20,12,4,2,32,17","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry.\n\nSize 41, fully idempotent, RC. Like magma#b7e8bf90, this is a Steiner-line magma: 82 = 41*40/(5*4) size-5 sub-magmas covering each pair exactly once, each block isomorphic to magma#e549b5f8 (the F_5 affine line). But this magma uses a *different* Steiner design - only 11 of the 82 blocks coincide with those of magma#b7e8bf90.\n\n|Aut(M)| = 41 (versus 205 for magma#b7e8bf90). The full Aut group is just the cyclic Z_41 of translations; there is no multiplicative stabilizer. As a result, only one Aut orbit (all 41 points), and the 82 blocks split as exactly 2 Aut-orbits of 41 blocks each (the cyclic BIBD's 2 base-block translate classes).\n\nIn the suggested reorder, elements are labeled by F_41 so that translation x -> x+1 is an automorphism. The operation is x*y = x + f(y - x) mod 41, where f is a non-linear permutation of F_41 with f(0) = 0.\n\nSlope analysis: writing f(y) = alpha(y) * y, the slope function takes 12 distinct values:\n  Phi_10-root slopes (the four primitive 10th roots of unity in F_41*): {4, 23, 25, 31}, each occurring on a size-2 subset\n    alpha=4  on {21, 31}    alpha=23 on {35, 38}\n    alpha=25 on {13, 26}    alpha=31 on {1, 2}\n  Non-Phi_10 slopes (8 values), each occurring on a size-4 subset:\n    alpha=11 on {4, 8, 9, 25}     alpha=13 on {10, 20, 33, 37}\n    alpha=15 on {3, 6, 17, 29}    alpha=17 on {11, 12, 22, 24}\n    alpha=19 on {7, 14, 19, 30}   alpha=27 on {15, 27, 28, 34}\n    alpha=29 on {5, 23, 39, 40}   alpha=38 on {16, 18, 32, 36}\nTotals: 4*2 + 8*4 = 40 = |F_41*|. So 8 elements get a Phi_10-root slope; the other 32 use non-root slopes - meaning f is not a \"linear-on-cosets\" function as in magma#b7e8bf90. It's a genuinely Tao-Type-II non-linear permutation of F_41 satisfying Eq 677 only because of compatibility conditions on the f values across blocks.\n\nThe four Phi_10-root slopes appearing on 2-element subsets is a striking pattern - it suggests a partial structure where some pairs of differences are \"fully aligned\" with the abstract block magma, while most differences carry a separate slope.\n\nComparison within size 41:\n  magma#345a4ec9, magma#385ad4434a17, magma#a7a4546c, magma#ef76453c -- the four F_41 affine line magmas (one per Phi_10 root, single-slope linear over F_41), |Aut| = 1640 = 40 * 41.\n  magma#b7e8bf90 -- Tao Type II piecewise with 4 Phi_10-root slopes on Z_5-cosets, |Aut| = 205.\n  this magma#d32b07ca -- Tao Type II with 12 slopes, |Aut| = 41 (only translation).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:57:37","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/d32b07ca31049c672f273f1263a4018f94e1733b8b7fb07b48828ac9e2e0d0f0.txt"},{"canonical_hash":"c0b238e3e43ad60c2fb2ad83956bb18e6473d948c371d36a33c22d21b848a92c","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,8,39,35,28,5,24,18,21,29,20,27,2,14,16,15,22,17,19,11,37,12,34,6,32,23,10,38,31,9,40,36,26,7,4,13,30,3,25,33","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry (Type A slope pattern).\n\nSize 41, fully idempotent, RC. 82 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8), every pair of distinct elements lies in exactly one block. |Aut(M)| = 41 (only translations Z_41, no multiplicative stabilizer). 1 point-orbit; 2 block-orbits of 41 blocks (cyclic BIBD difference family with 2 base blocks).\n\nIn the suggested reorder, F_41 labeling makes translation x -> x+1 an automorphism. The operation is x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41.\n\nSlope analysis (alpha(y) = f(y)/y on F_41*):\n  Phi_10-root slopes {4, 23, 25, 31} each occur on 2-element subsets (total 8 elements)\n  Eight non-Phi_10 slopes {11, 13, 15, 17, 19, 27, 29, 38} each occur on 4-element subsets (total 32 elements)\n\nThis \"Type A\" slope multiset (4*2 + 8*4 = 40) is shared with magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0 -- 5 distinct Eq 677 magmas at size 41 that all have this exact slope-class-size pattern but use different assignments of slope values to F_41* subsets, giving 5 inequivalent iso classes.\n\nCompare with magma#b7e8bf90 (Type \"all-Phi\": only Phi_10 slopes, each on size-10 set, |Aut| = 205) and magma#e3521249 / magma#8b36eeff (Type B: Phi-slopes on size-6, non-Phi on size-2, |Aut| = 41).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:05","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/c0b238e3e43ad60c2fb2ad83956bb18e6473d948c371d36a33c22d21b848a92c.txt"},{"canonical_hash":"e35212498674cd8f46b935dedf3868e48522f1a7c087363e82ed72736c418825","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,38,29,19,10,23,20,18,8,28,15,30,26,7,31,34,2,12,25,13,5,16,40,11,33,6,1,35,21,37,14,36,22,4,39,32,24,27,17,9,3","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry (Type B slope pattern).\n\nSize 41, fully idempotent, RC. 82 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8), every pair of distinct elements lies in exactly one block. |Aut(M)| = 41 (only translations Z_41, no multiplicative stabilizer). 1 point-orbit; 2 block-orbits of 41 blocks (cyclic BIBD difference family with 2 base blocks).\n\nIn the suggested reorder, F_41 labeling makes translation x -> x+1 an automorphism. The operation is x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41.\n\nSlope analysis (alpha(y) = f(y)/y on F_41*):\n  Phi_10-root slopes {4, 23, 25, 31} each occur on 6-element subsets (total 24 elements)\n  Eight non-Phi_10 slopes {11, 13, 15, 17, 19, 27, 29, 38} each occur on 2-element subsets (total 16 elements)\n\nThis \"Type B\" slope multiset (4*6 + 8*2 = 40) is shared with magma#8b36eeff. So 2 of the 7 translation-only size-41 Steiner-line magmas in the DB have this pattern; the other 5 (magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0) have a complementary \"Type A\" pattern (4*2 + 8*4 = 40).\n\nCompare with magma#b7e8bf90 (Type \"all-Phi\": only Phi_10 slopes, each on size-10 set, |Aut| = 205, fully Z_5-symmetric).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/e35212498674cd8f46b935dedf3868e48522f1a7c087363e82ed72736c418825.txt"},{"canonical_hash":"345a4ec93ae3fa1bba61287462b80fafef9122504ff6dfa9db613820ec27a058","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,18,36,40,16,38,21,20,10,3,29,2,26,32,17,25,13,11,15,24,27,8,19,14,34,39,28,7,4,35,31,33,5,37,12,6,22,9,23,30","comment":"Linear magma over Z/41Z (the prime field F_41): x ◇ y = 38x + 4y (mod 41).","submitted_at":"2026-04-23 20:58:10","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/345a4ec93ae3fa1bba61287462b80fafef9122504ff6dfa9db613820ec27a058.txt"},{"canonical_hash":"a7a4546c9486046dcc5acd5575f01b4c24a896f79b113664f1757764ce2631cc","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,39,27,15,37,17,3,30,20,23,19,16,26,7,21,33,11,31,35,5,4,10,6,18,29,36,38,13,24,8,40,12,28,9,34,32,25,22,2,14","comment":"Linear magma over Z/41Z (the prime field F_41): x ◇ y = 11x + 31y (mod 41).","submitted_at":"2026-04-23 20:58:11","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/a7a4546c9486046dcc5acd5575f01b4c24a896f79b113664f1757764ce2631cc.txt"},{"canonical_hash":"385ad4434a17e4ee02410b1a1320c40d185319baaa8a6621777c525b1a493044","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,26,6,21,20,29,36,17,13,35,7,39,4,18,34,11,5,2,32,3,30,28,40,8,10,23,12,22,25,31,14,38,24,19,27,15,33,37,16,9","comment":"Linear magma over Z/41Z (the prime field F_41): x ◇ y = 19x + 23y (mod 41).","submitted_at":"2026-04-23 20:58:13","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/385ad4434a17e4ee02410b1a1320c40d185319baaa8a6621777c525b1a493044.txt"},{"canonical_hash":"ef76453c64493eb6da934811a9073a1178e611fb169ec134b8e052376b4964c2","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,8,25,10,30,5,28,21,20,17,29,3,7,31,36,34,26,35,13,2,32,19,38,4,40,24,18,39,12,22,33,15,6,14,16,11,27,23,9,37","comment":"Linear magma over Z/41Z (the prime field F_41): x ◇ y = 17x + 25y (mod 41).","submitted_at":"2026-04-23 20:58:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/ef76453c64493eb6da934811a9073a1178e611fb169ec134b8e052376b4964c2.txt"},{"canonical_hash":"8b36eeffa27a4c5929eeb3f9cf2546a9af598b6d9e8556a4ccabca66eae91685","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,21,38,3,36,30,4,5,8,35,40,12,18,32,14,22,11,7,17,37,33,13,25,27,39,9,24,16,2,28,10,31,19,26,23,6,20,29,34,15","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry (Type B slope pattern).\n\nSize 41, fully idempotent, RC. 82 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8), every pair of distinct elements lies in exactly one block. |Aut(M)| = 41 (only translations Z_41, no multiplicative stabilizer). 1 point-orbit; 2 block-orbits of 41 blocks (cyclic BIBD difference family with 2 base blocks).\n\nIn the suggested reorder, F_41 labeling makes translation x -> x+1 an automorphism. The operation is x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41.\n\nSlope analysis (alpha(y) = f(y)/y on F_41*):\n  Phi_10-root slopes {4, 23, 25, 31} each occur on 6-element subsets (total 24 elements)\n  Eight non-Phi_10 slopes {11, 13, 15, 17, 19, 27, 29, 38} each occur on 2-element subsets (total 16 elements)\n\nThis \"Type B\" slope multiset (4*6 + 8*2 = 40) is shared with magma#e3521249. So 2 of the 7 translation-only size-41 Steiner-line magmas in the DB have this pattern; the other 5 (magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0) have a complementary \"Type A\" pattern (4*2 + 8*4 = 40).\n\nCompare with magma#b7e8bf90 (Type \"all-Phi\": only Phi_10 slopes, each on size-10 set, |Aut| = 205, fully Z_5-symmetric).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:17","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/8b36eeffa27a4c5929eeb3f9cf2546a9af598b6d9e8556a4ccabca66eae91685.txt"},{"canonical_hash":"10305dec2cdc4766d69507bafc0c943147752dd4be3df3d7a01e611b00a620b5","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,14,37,23,17,4,6,13,39,24,25,18,32,19,3,10,16,31,2,35,7,33,8,15,40,38,30,11,26,29,5,21,34,20,27,9,22,28,12,36","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry (Type A slope pattern).\n\nSize 41, fully idempotent, RC. 82 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8), every pair of distinct elements lies in exactly one block. |Aut(M)| = 41 (only translations Z_41, no multiplicative stabilizer). 1 point-orbit; 2 block-orbits of 41 blocks (cyclic BIBD difference family with 2 base blocks).\n\nIn the suggested reorder, F_41 labeling makes translation x -> x+1 an automorphism. The operation is x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41.\n\nSlope analysis (alpha(y) = f(y)/y on F_41*):\n  Phi_10-root slopes {4, 23, 25, 31} each occur on 2-element subsets (total 8 elements)\n  Eight non-Phi_10 slopes {11, 13, 15, 17, 19, 27, 29, 38} each occur on 4-element subsets (total 32 elements)\n\nThis \"Type A\" slope multiset (4*2 + 8*4 = 40) is shared with magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0 -- 5 distinct Eq 677 magmas at size 41 that all have this exact slope-class-size pattern but use different assignments of slope values to F_41* subsets, giving 5 inequivalent iso classes.\n\nCompare with magma#b7e8bf90 (Type \"all-Phi\": only Phi_10 slopes, each on size-10 set, |Aut| = 205) and magma#e3521249 / magma#8b36eeff (Type B: Phi-slopes on size-6, non-Phi on size-2, |Aut| = 41).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/10305dec2cdc4766d69507bafc0c943147752dd4be3df3d7a01e611b00a620b5.txt"},{"canonical_hash":"8f879c028af0b7dd5b97ef584edd6ea9d00137efc70be997ffc3b44c1cecf621","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,15,34,5,32,10,4,6,22,36,14,8,3,9,24,28,13,18,12,7,31,25,19,35,26,27,20,37,33,29,2,16,11,23,39,30,21,40,38,17","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry (Type A slope pattern).\n\nSize 41, fully idempotent, RC. 82 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8), every pair of distinct elements lies in exactly one block. |Aut(M)| = 41 (only translations Z_41, no multiplicative stabilizer). 1 point-orbit; 2 block-orbits of 41 blocks (cyclic BIBD difference family with 2 base blocks).\n\nIn the suggested reorder, F_41 labeling makes translation x -> x+1 an automorphism. The operation is x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41.\n\nSlope analysis (alpha(y) = f(y)/y on F_41*):\n  Phi_10-root slopes {4, 23, 25, 31} each occur on 2-element subsets (total 8 elements)\n  Eight non-Phi_10 slopes {11, 13, 15, 17, 19, 27, 29, 38} each occur on 4-element subsets (total 32 elements)\n\nThis \"Type A\" slope multiset (4*2 + 8*4 = 40) is shared with magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0 -- 5 distinct Eq 677 magmas at size 41 that all have this exact slope-class-size pattern but use different assignments of slope values to F_41* subsets, giving 5 inequivalent iso classes.\n\nCompare with magma#b7e8bf90 (Type \"all-Phi\": only Phi_10 slopes, each on size-10 set, |Aut| = 205) and magma#e3521249 / magma#8b36eeff (Type B: Phi-slopes on size-6, non-Phi on size-2, |Aut| = 41).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/8f879c028af0b7dd5b97ef584edd6ea9d00137efc70be997ffc3b44c1cecf621.txt"},{"canonical_hash":"c754a6c0451a80d188121cd83903ec4ce55426ae156f8221428f2cab0c91ac50","size":41,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,37,20,40,11,27,22,8,16,38,2,25,15,23,10,33,34,14,39,32,24,29,5,36,7,26,35,19,3,18,4,21,9,30,28,17,12,31,13,6","comment":"Steiner-line magma on a (41, 5, 1)-BIBD with only translation symmetry (Type A slope pattern).\n\nSize 41, fully idempotent, RC. 82 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8), every pair of distinct elements lies in exactly one block. |Aut(M)| = 41 (only translations Z_41, no multiplicative stabilizer). 1 point-orbit; 2 block-orbits of 41 blocks (cyclic BIBD difference family with 2 base blocks).\n\nIn the suggested reorder, F_41 labeling makes translation x -> x+1 an automorphism. The operation is x*y = x + f(y - x) mod 41 with f a non-linear permutation of F_41.\n\nSlope analysis (alpha(y) = f(y)/y on F_41*):\n  Phi_10-root slopes {4, 23, 25, 31} each occur on 2-element subsets (total 8 elements)\n  Eight non-Phi_10 slopes {11, 13, 15, 17, 19, 27, 29, 38} each occur on 4-element subsets (total 32 elements)\n\nThis \"Type A\" slope multiset (4*2 + 8*4 = 40) is shared with magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0 -- 5 distinct Eq 677 magmas at size 41 that all have this exact slope-class-size pattern but use different assignments of slope values to F_41* subsets, giving 5 inequivalent iso classes.\n\nCompare with magma#b7e8bf90 (Type \"all-Phi\": only Phi_10 slopes, each on size-10 set, |Aut| = 205) and magma#e3521249 / magma#8b36eeff (Type B: Phi-slopes on size-6, non-Phi on size-2, |Aut| = 41).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/41/c754a6c0451a80d188121cd83903ec4ce55426ae156f8221428f2cab0c91ac50.txt"},{"canonical_hash":"9486457571c37201341237f72897af52b1d875b125f566fb97df4399b275152d","size":43,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"42,0,6,19,38,13,14,24,1,27,22,7,23,37,33,35,5,25,36,11,17,9,39,10,18,29,32,2,28,26,30,16,41,15,34,40,31,21,20,8,12,3,4","comment":"Linear magma over Z/43Z (the prime field F_43): x ◇ y = 36x + 14y (mod 43).","submitted_at":"2026-04-23 20:58:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/43/9486457571c37201341237f72897af52b1d875b125f566fb97df4399b275152d.txt"},{"canonical_hash":"cfebc87a95d3692e8ba0cf4cb6b8a86c6928d3841d0867e9fecb0d542ed3307f","size":43,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"42,0,27,29,12,11,14,7,39,16,38,30,1,4,34,40,24,10,2,5,23,36,15,3,26,22,31,41,19,13,25,20,9,17,37,18,28,35,32,33,8,6,21","comment":"Linear magma over Z/43Z (the prime field F_43): x ◇ y = 6x + 15y (mod 43).","submitted_at":"2026-04-23 20:58:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/43/cfebc87a95d3692e8ba0cf4cb6b8a86c6928d3841d0867e9fecb0d542ed3307f.txt"},{"canonical_hash":"ede195276bb355a7217fa1cc7c325b11ba49b3d1155fd8091013a4b2a19e35c8","size":43,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"42,0,27,1,12,29,26,19,15,2,10,24,13,22,34,28,30,16,25,35,17,18,39,38,14,8,37,3,5,41,11,20,9,23,31,36,40,7,4,21,32,6,33","comment":"Linear magma over Z/43Z (the prime field F_43): x ◇ y = 36x + 22y (mod 43).","submitted_at":"2026-04-23 20:58:22","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/43/ede195276bb355a7217fa1cc7c325b11ba49b3d1155fd8091013a4b2a19e35c8.txt"},{"canonical_hash":"a4ffed3770afd3b5ebd05400108a7000f4ead32dd63e69c0fc284614f9ff0457","size":43,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"42,0,21,8,4,7,28,40,24,15,27,5,11,19,16,14,1,17,35,9,10,3,25,32,31,41,39,22,36,38,34,33,20,12,37,2,18,13,29,26,30,6,23","comment":"Linear magma over Z/43Z (the prime field F_43): x ◇ y = 6x + 34y (mod 43).","submitted_at":"2026-04-23 20:58:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/43/a4ffed3770afd3b5ebd05400108a7000f4ead32dd63e69c0fc284614f9ff0457.txt"},{"canonical_hash":"9ac61f33e0de3061260327cd1f8ec493e58b27cc56b59ca78e22c7e08c8ddabf","size":45,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"40,0,5,7,2,1,3,4,6,41,8,25,33,12,36,17,21,29,42,9,24,32,13,37,16,20,28,44,11,27,34,15,38,19,23,31,43,10,26,35,14,39,18,22,30","comment":"Size-45 (= 5 × 9) right-cancellative magma decomposing as a TWISTED fiber bundle: F_5(2,4) base × F_9(3,7) fiber. The 45 elements partition into 5 fibers of 9 elements (an F_5-quotient congruence), and each fiber is itself a sub-magma isomorphic to the F_9 linear magma F_9(3,7). However, unlike the direct product F_5 × F_9, the cross-fiber multiplication is twisted by a non-trivial cocycle — so the magma is NOT isomorphic to the direct product. The database contains 5 iso classes of size 45 sharing this F_5(2,4) base × F_9(3,7) fiber structure: one direct product (57ccc920) and 4 inequivalent non-trivial twists; this magma is one of the 4 twists.","submitted_at":"2026-04-23 20:58:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/45/9ac61f33e0de3061260327cd1f8ec493e58b27cc56b59ca78e22c7e08c8ddabf.txt"},{"canonical_hash":"57ccc920f3a4ae4bbffe4b3ea9285a0b0b067889bdceee076361c43900c3431e","size":45,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"40,3,19,15,20,11,28,24,7,41,0,16,12,22,8,30,26,4,42,1,17,13,21,9,29,25,5,44,33,36,35,37,39,32,38,34,43,2,18,14,23,10,31,27,6","comment":"Size-45 (= 5 × 9) magma: the direct product F_5(2,4) × F_9(3,7). The 45 elements partition into 5 fibers of 9, every fiber is an F_9(3,7) sub-magma, and the cross-fiber multiplication is the trivial (direct-product) cocycle. F_9 is the field of order 9 = 3², and (3,7) gives one of the two F_9-linear magmas satisfying equation 677. The database has 4 other size-45 magmas (9ac61f33, 05aba89c, a97cd359, fec06f1f) with the same F_5 base × F_9 fiber structure but non-trivial twists.","submitted_at":"2026-04-23 20:58:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/45/57ccc920f3a4ae4bbffe4b3ea9285a0b0b067889bdceee076361c43900c3431e.txt"},{"canonical_hash":"05aba89c8fda3d45fa6b247c3cfa1978c014a8edff02986eef8d4cfb39f715ed","size":45,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"40,0,5,7,2,1,3,4,6,43,8,12,14,9,15,10,11,13,41,16,20,22,17,23,18,19,21,44,32,36,38,33,39,34,35,37,42,24,28,30,25,31,26,27,29","comment":"Size-45 (= 5 × 9) right-cancellative magma decomposing as a TWISTED fiber bundle: F_5(2,4) base × F_9(3,7) fiber. The 45 elements partition into 5 fibers of 9 elements (an F_5-quotient congruence), and each fiber is itself a sub-magma isomorphic to the F_9 linear magma F_9(3,7). However, unlike the direct product F_5 × F_9, the cross-fiber multiplication is twisted by a non-trivial cocycle — so the magma is NOT isomorphic to the direct product. The database contains 5 iso classes of size 45 sharing this F_5(2,4) base × F_9(3,7) fiber structure: one direct product (57ccc920) and 4 inequivalent non-trivial twists; this magma is one of the 4 twists.","submitted_at":"2026-04-23 20:58:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/45/05aba89c8fda3d45fa6b247c3cfa1978c014a8edff02986eef8d4cfb39f715ed.txt"},{"canonical_hash":"a97cd359209ca8128895583745774fa637e4d6ff9668d716e70c1186faf8de63","size":45,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"44,0,5,7,2,1,3,4,6,41,8,12,14,9,15,10,11,13,42,16,20,22,17,23,18,19,21,40,32,36,38,33,39,34,35,37,43,24,28,30,25,31,26,27,29","comment":"Size-45 (= 5 × 9) right-cancellative magma decomposing as a TWISTED fiber bundle: F_5(2,4) base × F_9(3,7) fiber. The 45 elements partition into 5 fibers of 9 elements (an F_5-quotient congruence), and each fiber is itself a sub-magma isomorphic to the F_9 linear magma F_9(3,7). However, unlike the direct product F_5 × F_9, the cross-fiber multiplication is twisted by a non-trivial cocycle — so the magma is NOT isomorphic to the direct product. The database contains 5 iso classes of size 45 sharing this F_5(2,4) base × F_9(3,7) fiber structure: one direct product (57ccc920) and 4 inequivalent non-trivial twists; this magma is one of the 4 twists.","submitted_at":"2026-04-23 20:58:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/45/a97cd359209ca8128895583745774fa637e4d6ff9668d716e70c1186faf8de63.txt"},{"canonical_hash":"fec06f1f4e8fb8a75710f5bc1d50e294877f11815b0f1ef2fd4a7890098a78e1","size":45,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"44,0,32,33,1,31,2,3,4,40,5,9,10,6,35,7,8,34,43,11,36,16,12,17,13,14,15,42,25,29,30,26,39,27,28,38,41,18,21,23,19,24,37,20,22","comment":"Size-45 (= 5 × 9) right-cancellative magma decomposing as a TWISTED fiber bundle: F_5(2,4) base × F_9(3,7) fiber. The 45 elements partition into 5 fibers of 9 elements (an F_5-quotient congruence), and each fiber is itself a sub-magma isomorphic to the F_9 linear magma F_9(3,7). However, unlike the direct product F_5 × F_9, the cross-fiber multiplication is twisted by a non-trivial cocycle — so the magma is NOT isomorphic to the direct product. The database contains 5 iso classes of size 45 sharing this F_5(2,4) base × F_9(3,7) fiber structure: one direct product (57ccc920) and 4 inequivalent non-trivial twists; this magma is one of the 4 twists.","submitted_at":"2026-04-23 20:58:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/45/fec06f1f4e8fb8a75710f5bc1d50e294877f11815b0f1ef2fd4a7890098a78e1.txt"},{"canonical_hash":"3d9ea61f4ac8ad5b1b47ed51fe6742da3b2f6d6bdf7a08716863169482908deb","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,0,33,5,3,31,18,34,15,40,29,7,41,38,4,20,28,11,10,8,46,1,26,14,43,19,35,25,47,23,37,21,45,16,24,2,44,6,12,13,30,22,32,36,39,9,27,42,17","comment":"Linear magma over the extension field F_49 = F_7[α]/⟨α² - 3⟩.\n\nOperation: x ◇ y = a·x + b·y in F_49 with (a, b) = (2, 1 + α). Here β = 1 + α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_49, and α_coef = -β³ - β - 1 = 2 (in F_49). This is Pace Nielsen's Type-2 non-fully-idempotent linear 677 magma family.\n\nF_49 is the proper degree-2 extension of F_7; do NOT confuse with the ring Z/49Z (which has zero divisors and is NOT a field). Note that the size-49 family in the DB includes two distinct constructions: this one (over F_49) and others (magma#bd9c4bf0, magma#a9267aad) over the ring Z/49Z.\n\nSize 49, not fully idempotent, right-cancellative.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/3d9ea61f4ac8ad5b1b47ed51fe6742da3b2f6d6bdf7a08716863169482908deb.txt"},{"canonical_hash":"8937c71c1ef192ba79af42af3840d5d23ef43e0f80f552069f678faab4a4adfe","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,0,3,2,5,1,4,6,18,44,36,24,30,12,8,26,20,32,46,14,38,7,31,37,19,13,25,45,10,42,28,16,22,40,34,11,41,17,43,35,23,29,9,15,33,27,39,47,21","comment":"Direct product of two linear magmas: F_7 × F_7. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 4x₂ + 1y₂ (mod 7)).","submitted_at":"2026-04-23 20:58:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/8937c71c1ef192ba79af42af3840d5d23ef43e0f80f552069f678faab4a4adfe.txt"},{"canonical_hash":"3c5f0d7eb14153db0dff1cac065e10f9f6418fc970ad8c9c0e61f635d0e398ae","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,36,13,23,6,3,31,22,39,15,25,8,5,35,18,38,14,24,7,4,30,17,41,11,27,10,0,32,20,37,12,28,34,2,29,21,40,16,26,9,1,33,19","comment":"Direct product of two linear magmas: F_7 × F_7. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 4x₂ + 3y₂ (mod 7)).","submitted_at":"2026-04-23 20:58:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/3c5f0d7eb14153db0dff1cac065e10f9f6418fc970ad8c9c0e61f635d0e398ae.txt"},{"canonical_hash":"614a739af0e4003cdd734d42abd90c6c9465e902bff8bf806e9ef96e5dd47cd3","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,0,5,6,3,2,4,1,30,21,8,16,45,31,39,14,28,43,19,35,12,40,44,7,29,36,15,20,37,23,18,33,26,10,42,41,9,32,22,46,25,17,38,34,47,13,11,24,27","comment":"Direct product of two linear magmas: F_7 × F_7. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 3y₁ (mod 7), 4x₂ + 3y₂ (mod 7)).","submitted_at":"2026-04-23 20:58:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/614a739af0e4003cdd734d42abd90c6c9465e902bff8bf806e9ef96e5dd47cd3.txt"},{"canonical_hash":"bd9c4bf04842e2985c41b595e9243858f92359259c97b118f4c0aa0eb8ec7ca0","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,34,33,9,24,20,1,42,39,29,11,22,17,0,43,41,32,13,27,14,2,47,38,28,8,25,18,3,44,37,31,10,23,15,4,45,36,40,12,21,19,5,46,35,30,7,26,16,6","comment":"Linear magma over the ring Z/49Z: x ◇ y = 18x + 8y (mod 49).\n\nNOTE: Z/49Z is the ring of integers mod 49, NOT a field — since 49 = 7² is not prime, Z/49Z has zero divisors (e.g. 7·7 = 0 mod 49). The genuine field F_49 = GF(7²) exists as a separate object (and gives different size-49 Eq 677 magmas, e.g. magma#3d9ea61f); this construction uses ring arithmetic mod 49 instead. Bernhard Reinke flagged this distinction.\n\nCoefficients (18, 8) satisfy the Eq 677 polynomial conditions over the RING Z/49Z (verified: 8·(18 + 8·18·8) = 1 and 18 + 8³ + 8²·18² = 0 mod 49).\n\nSize 49, not fully idempotent, right-cancellative.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:32","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/bd9c4bf04842e2985c41b595e9243858f92359259c97b118f4c0aa0eb8ec7ca0.txt"},{"canonical_hash":"a9267aade1a1ca38e866601f513e4cbf640498155d05f73c82f7db0c3027d5fe","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,0,12,26,41,21,10,45,14,5,39,36,28,24,42,34,32,33,23,35,4,44,20,25,1,29,8,37,47,40,18,6,16,15,17,46,7,11,19,3,22,31,43,27,38,13,9,2,30","comment":"Linear magma over the ring Z/49Z: x ◇ y = 18x + 10y (mod 49).\n\nNOTE: Z/49Z is the ring of integers mod 49, NOT a field — since 49 = 7² is not prime, Z/49Z has zero divisors (e.g. 7·7 = 0 mod 49). The genuine field F_49 = GF(7²) exists as a separate object (and gives different size-49 Eq 677 magmas, e.g. magma#3d9ea61f); this construction uses ring arithmetic mod 49 instead.\n\nCoefficients (18, 10) satisfy the Eq 677 polynomial conditions over the ring Z/49Z.\n\nSize 49, not fully idempotent, right-cancellative. Companion to magma#bd9c4bf0 (also Z/49Z with coefficients (18, 8)).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/a9267aade1a1ca38e866601f513e4cbf640498155d05f73c82f7db0c3027d5fe.txt"},{"canonical_hash":"979e13db929ed8d28a9dc1e7b61512b2acf5f3c3cdc6a5b92a17db0016d4f766","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"23,24,25,26,27,28,29,30,31,32,33,35,0,5,6,9,13,34,17,18,19,20,21,22,1,4,8,11,12,16,2,3,7,10,14,15,36,37,41,38,39,40,42,43,47,44,45,46,48","comment":"6 fibers of 6 (L_x-fixed sets) + S2 (F_7) + S1 (F_7) + idempotent 48. Size-49 magma with two F_7(4,1) sub-magmas sharing a common idempotent, plus 6 fibers of 6 anchored to the first sub-magma.","submitted_at":"2026-04-23 20:58:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/979e13db929ed8d28a9dc1e7b61512b2acf5f3c3cdc6a5b92a17db0016d4f766.txt"},{"canonical_hash":"0d104541999f3c03dc6265618ea99bf8b14ed79e9753b076747dd2057b6d1584","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,43,47,44,45,46,1,41,3,0,33,4,2,11,9,7,5,10,8,6,40,38,36,34,39,37,35,25,23,21,19,24,22,20,32,30,28,26,31,29,27,18,16,14,12,17,15,13","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 1) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 1). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/0d104541999f3c03dc6265618ea99bf8b14ed79e9753b076747dd2057b6d1584.txt"},{"canonical_hash":"4aaf07b3164e0ec8a91341f1b4df55884c9ac582f58184cd39664483c1cdea77","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"42,43,44,45,46,47,48,0,1,2,3,4,5,6,14,15,16,17,18,19,20,7,8,9,10,11,12,13,21,22,23,24,25,26,27,35,36,37,38,39,40,41,28,29,30,31,32,33,34","comment":"F_7(4,1) base × F_7-fiber-cocycle. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 20:58:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/4aaf07b3164e0ec8a91341f1b4df55884c9ac582f58184cd39664483c1cdea77.txt"},{"canonical_hash":"10eb36578df4912f5e1def5de951577a1eda7de635d47e05dbe4bbc2db9722bd","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,36,37,38,39,40,41,42,43,44,45,46,47,30,31,32,33,34,35,48","comment":"Size-49 \"pivot + 7 petals\" magma — 1 size-7 sub-magma + 7 size-6 Aut-orbits.\n\nSize 49, exactly 1 idempotent (element 48), right-cancellative. |Aut(M)| = 6 with 14 Aut-orbits:\n- 7 singletons: {30}, {31}, {32}, {33}, {34}, {35}, {48} — the elements of the unique size-7 sub-magma\n- 7 size-6 orbits: {0..5}, {6..11}, {12..17}, {18..23}, {24..29}, {36..41}, {42..47} — the 7 \"petals\"\n\nSub-magma structure: exactly ONE proper non-singleton sub-magma exists, the size-7 set {30, 31, 32, 33, 34, 35, 48}, isomorphic to magma#7981e2df (the size-7 Eq 677 magma with exactly 1 idempotent). Every pair of distinct elements (x, y) with at least one element outside the pivot generates the full magma — i.e., no size-7 sub-magma is \"shared\" between petals, unlike the AG(2, 7) pencil magma#1b32837d which has 8 size-7 sub-magmas through a common pivot.\n\nThe 7 petals exactly coincide with the size-6 Aut-orbits. The pivot's 7 elements are exactly the L_48-fixed points (where T(48, y) = y), and they form the size-7 sub-magma containing the unique idempotent 48.\n\nSo 49 = 7 (pivot) + 7 × 6 (petals) = 7 × 7 in the multiplicative sense, but NOT factored through any AG(2, 7) line structure — this is a different kind of \"size-49 quotient by F_7-acting-on-something\" construction. The Aut-orbit structure (7 fixed singletons + 7 transitively permuted size-6 sets) suggests a cyclic Z_6 action on each petal, with the 7 petals collectively permuted as a single Aut-orbit at a higher level — though |Aut| = 6 (not 7 × 6 = 42), so the petals themselves are NOT exchanged by Aut. Each petal is fixed setwise, with Aut acting on the 6 elements within each petal.\n\nIn the suggested reorder, positions 0..41 contain the 7 petals (each 6 consecutive cells, in canonical-label order), and positions 42..48 contain the pivot (with idempotent 48 last). Diagonal 6×6 blocks at positions 5k..5k+5 reveal within-petal structure; the last 7×7 sub-table is the pivot sub-magma; off-diagonal blocks capture cross-petal cross-pivot operations.\n\nCompare:\n  magma#1b32837d (size 49, AG(2,7) pencil): 8 size-7 lines through a common pivot, |Aut| = 252\n  magma#fa885ee6 (size 49 AG(2,7)-like): 8 size-7 sub-magmas, non-RC\n  this magma: ONLY 1 size-7 sub-magma + 7 petals of 6, |Aut| = 6, RC\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/10eb36578df4912f5e1def5de951577a1eda7de635d47e05dbe4bbc2db9722bd.txt"},{"canonical_hash":"530ee4afe55c1a4eef644c73b62c4e17dec64da2dfce3ba779281604aa8d1ae7","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,14,21,29,34,37,0,6,13,18,24,33,41,3,9,12,20,27,35,40,5,7,16,22,25,32,36,2,11,17,23,28,31,38,1,8,15,19,26,30,39,4,10","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 3) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/530ee4afe55c1a4eef644c73b62c4e17dec64da2dfce3ba779281604aa8d1ae7.txt"},{"canonical_hash":"68e1384937134c63af129f5ece64a7c008537a590ceb711a2736724a4179b727","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,0,7,13,19,25,31,37,1,5,11,17,23,29,35,6,12,18,24,30,36,41,3,9,15,21,27,33,39,2,8,14,20,26,32,38,4,10,16,22,28,34,40","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 3) base × F_7(4, 3) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/68e1384937134c63af129f5ece64a7c008537a590ceb711a2736724a4179b727.txt"},{"canonical_hash":"a12f6f3db78f610b44a941f732c49ec176e692d9ab77ce3eeab5e60cadbd9675","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,0,1,2,3,4,5,6,28,29,30,31,32,33,34,35,36,37,38,39,40,41,14,15,16,17,18,19,20,7,8,9,10,11,12,13,21,22,23,24,25,26,27","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 3) base × F_7(4, 3) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/a12f6f3db78f610b44a941f732c49ec176e692d9ab77ce3eeab5e60cadbd9675.txt"},{"canonical_hash":"17308306cc5b8d9c61349d35b814f80cb209655c7344fd42c277638cc87a50af","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,31,34,27,0,36,17,8,10,5,35,13,26,21,39,19,38,6,18,32,9,1,12,24,20,41,3,15,33,7,4,30,16,25,22,37,11,29,2,28,23,40,14","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 3) fiber. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence). One fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). In addition there is exactly one extra 7-element sub-magma, a transversal that hits each fiber in exactly one element. The 2 size-7 sub-magmas (1 closed fiber + 1 transversal) form a small AG(2,7)-pencil fragment. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:40","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/17308306cc5b8d9c61349d35b814f80cb209655c7344fd42c277638cc87a50af.txt"},{"canonical_hash":"0f61935b4db30f484ad547e361777e867ee1b016fc2a1a79c60017913a4e9023","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,0,1,36,4,3,5,2,12,16,13,15,38,14,17,6,9,11,7,8,10,37,24,40,28,26,25,29,27,30,35,32,41,33,31,34,18,20,21,22,23,39,19","comment":"Size-49 (= 7²) right-cancellative magma. Has 8 distinct 7-element sub-magmas, all passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (F_7 quotient with base ≅ F_7(4, 1)) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4, 3)); the other 7 sub-magmas through the idempotent are transversals, each hitting all 7 fibers in exactly one element. The 8 sub-magmas correspond to the 8 lines through the origin in AG(2,7).","submitted_at":"2026-04-23 20:58:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/0f61935b4db30f484ad547e361777e867ee1b016fc2a1a79c60017913a4e9023.txt"},{"canonical_hash":"508cfe4539f15cff6cc738c716e9b22f5619d645dfed26166728e0e9f83cc4c8","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,36,37,41,38,39,40,2,6,7,35,0,5,47,3,46,9,1,8,29,10,33,28,4,43,27,34,26,30,15,11,45,14,12,13,20,18,19,31,16,17,42,32,25,21,44,24,22,23","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 1) fiber. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence). One fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 1). In addition there is exactly one extra 7-element sub-magma, a transversal that hits each fiber in exactly one element. The 2 size-7 sub-magmas (1 closed fiber + 1 transversal) form a small AG(2,7)-pencil fragment. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/508cfe4539f15cff6cc738c716e9b22f5619d645dfed26166728e0e9f83cc4c8.txt"},{"canonical_hash":"390e6c431321564796ff2264907445439dc1a68da78d4e9b911647156f9137cc","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,0,3,2,5,1,4,6,24,30,18,44,36,12,8,46,26,38,32,14,20,7,31,45,13,25,19,37,10,34,42,16,28,22,40,11,43,29,41,35,17,23,9,27,33,21,47,39,15","comment":"Size-49 (= 7²) right-cancellative magma. Has 8 distinct 7-element sub-magmas, all passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (F_7 quotient with base ≅ F_7(4, 1)) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4, 1)); the other 7 sub-magmas through the idempotent are transversals, each hitting all 7 fibers in exactly one element. The 8 sub-magmas correspond to the 8 lines through the origin in AG(2,7).","submitted_at":"2026-04-23 20:58:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/390e6c431321564796ff2264907445439dc1a68da78d4e9b911647156f9137cc.txt"},{"canonical_hash":"1b32837d48cf824298e002ad9b32e9e636c12c5307101a2c12e0bb572f0348c9","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,6,12,19,24,32,1,7,13,18,25,31,2,9,15,21,27,33,3,10,16,22,28,34,4,11,17,23,29,35,5,8,14,20,26,30,36,37,38,39,40,41,42,43,44,45,46,47,48","comment":"Size-49 \"pencil\" magma — 8 size-7 sub-magmas all sharing a unique idempotent, in 2 iso classes (7+1).\n\nSize 49 = 7^2. Exactly 1 idempotent (element 48 in canonical labels), 48 non-idempotents.\n\n|Aut(M)| = 252 = 4 * 63 = 6 * 42 acting in 3 orbits:\n- {48} (the lone idempotent, fixed by all Aut)\n- 1 orbit of size 6 (the non-pivot part of the \"special\" line)\n- 1 orbit of size 42 (the non-pivot parts of the other 7 lines, joined into a single transitive action)\n\nThere are 8 distinct size-7 sub-magmas in M (\"lines through the origin\"), each containing element 48 plus 6 other elements. Together with 48 they partition the 49 elements as 1 pivot + 8 lines * 6 non-pivots = 1 + 48 = 49. So this is an \"8-line pencil through the unique idempotent\" structure analogous to AG(2, 7)-lines-through-origin (which is the geometric source, although the magma is NOT a faithful AG(2,7)-line construction - see below).\n\nThe 8 lines split into 2 iso classes (NOT all the same, contrary to a literal AG(2,7) interpretation):\n- 7 lines (the 42-orbit ones): each iso to magma#7981e2df, the size-7 Eq 677 magma with exactly 1 idempotent. Lines (in canonical labels):\n    [0, 6, 12, 19, 24, 32, 48], [1, 7, 13, 18, 25, 31, 48], [2, 9, 15, 21, 27, 33, 48], \n    [3, 10, 16, 22, 28, 34, 48], [4, 11, 17, 23, 29, 35, 48], [5, 8, 14, 20, 26, 30, 48], \n    [36, 37, 38, 39, 40, 41, 48]\n- 1 \"special\" line (the 6-orbit one): iso to magma#baf8b55c, the *other* size-7 Eq 677 iso class:\n    [42, 43, 44, 45, 46, 47, 48]\nBoth iso classes have exactly 1 idempotent (in each sub-magma, the global idempotent 48 is the unique idempotent), so the lines all \"share the unique idempotent\". But the two size-7 iso classes are non-isomorphic as magmas, so the pencil is INHOMOGENEOUS - 7 lines of one type + 1 line of another.\n\nIn the suggested reorder, the 49 elements are arranged as 8 consecutive 6-element blocks (positions 0..5, 6..11, ..., 42..47) one per line, with the unique idempotent 48 at position 48 (the very last). The diagonal 6x6 blocks reveal each line's operation on its 6 non-pivot elements.\n\nThe \"AG(2, 7)-pencil\" description (in the original comment) captures the geometric intuition: AG(2,7) has 49 points and 8 lines through the origin (one per direction). Here, the magma has the same combinatorial incidence pattern - 8 lines through a single point - but with an asymmetry that makes one line iso-distinct from the other 7, consistent with |Aut| = 252 < |AGL(2, 7)| = 2,016 (the full affine group of AG(2,7)). So the magma is a *twisted* AG(2,7) pencil, not the canonical one.\n\nThe original comment said \"8 size-7 F_7(4,3) sub-magmas all... corresponding to the 8 lines through the origin\" - the line-through-origin geometric picture is correct, but the claim that all 8 lines are iso to F_7(4,3) is incorrect: 7 are iso to magma#7981e2df, 1 to magma#baf8b55c (the special line {42..47, 48}).\n\n[text written by Claude]","submitted_at":"2026-04-23 20:58:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/1b32837d48cf824298e002ad9b32e9e636c12c5307101a2c12e0bb572f0348c9.txt"},{"canonical_hash":"fa885ee6c3df774cdb6f92bab42105d2b77f2283399d1303376327ddba8c4e2f","size":49,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"48,42,45,44,47,43,46,0,1,2,3,4,5,41,24,25,26,27,28,29,40,30,31,32,33,34,35,36,12,13,14,15,16,17,38,6,7,8,9,10,11,37,18,19,20,21,22,23,39","comment":"Size-49 (= 7²) non-right-cancellative magma. Has 8 distinct 7-element sub-magmas, all passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (F_7 quotient with base ≅ F_7(4, 3)) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4, 1)); the other 7 sub-magmas through the idempotent are transversals, each hitting all 7 fibers in exactly one element. The 8 sub-magmas correspond to the 8 lines through the origin in AG(2,7).","submitted_at":"2026-04-23 20:58:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/fa885ee6c3df774cdb6f92bab42105d2b77f2283399d1303376327ddba8c4e2f.txt"},{"canonical_hash":"4d61b716a1d5a148a41f900773c0f0b235022db6e9e7292d428fc8c43f88ef27","size":49,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"48,0,4,5,2,1,3,6,7,8,9,10,11,42,30,31,32,33,34,35,45,36,37,38,39,40,41,46,18,19,20,21,22,23,43,12,13,14,15,16,17,47,24,25,26,27,28,29,44","comment":"Size-49 (= 7²) non-right-cancellative magma with a unique idempotent. Has 8 distinct 7-element sub-magmas, all isomorphic to F_7(4,3), and ALL passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (an F_7 quotient) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4,3)); the other 7 sub-magmas are transversals, each hitting all 7 fibers in exactly one element. The base operation on the 7 fibers is also iso to F_7. Differs from the AG(2,7)-pencil magma 1b32837d at the same size: both have 8 sub-magmas through the unique idempotent and the same pencil-of-lines combinatorics, but they are NOT isomorphic — they are two inequivalent realizations of an AG(2,7)-pencil structure as a 677 magma.","submitted_at":"2026-04-23 20:58:49","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/4d61b716a1d5a148a41f900773c0f0b235022db6e9e7292d428fc8c43f88ef27.txt"},{"canonical_hash":"d6c9c43daeec81402e0ce4478ca60ba4ddd1bb7c0269582ebc81aec95b198a83","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,45,44,47,43,46,0,1,2,3,4,5,41,24,25,26,27,28,29,40,30,31,32,33,34,35,36,12,13,14,15,16,17,38,6,7,8,9,10,11,37,18,19,20,21,22,23,39","comment":"Size-49 (= 7²) right-cancellative magma. Has 8 distinct 7-element sub-magmas, all passing through the unique idempotent — an AG(2,7)-pencil-like configuration. The 49 elements admit a 7-class congruence (F_7 quotient with base ≅ F_7(4, 3)) where exactly ONE fiber is itself a sub-magma (the fiber containing the idempotent, ≅ F_7(4, 1)); the other 7 sub-magmas through the idempotent are transversals, each hitting all 7 fibers in exactly one element. The 8 sub-magmas correspond to the 8 lines through the origin in AG(2,7).","submitted_at":"2026-04-23 20:58:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/d6c9c43daeec81402e0ce4478ca60ba4ddd1bb7c0269582ebc81aec95b198a83.txt"},{"canonical_hash":"831590d70812e68344934b9268cd25bdf4ddf964844fda821d01b992ba0d33d8","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,0,1,2,3,4,5,36,12,13,14,15,16,17,41,30,31,32,33,34,35,37,24,25,26,27,28,29,39,18,19,20,21,22,23,38,6,7,8,9,10,11,40","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 3) base × F_7(4, 3) fiber. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence). One fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). In addition there is exactly one extra 7-element sub-magma, a transversal that hits each fiber in exactly one element. The 2 size-7 sub-magmas (1 closed fiber + 1 transversal) form a small AG(2,7)-pencil fragment. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/831590d70812e68344934b9268cd25bdf4ddf964844fda821d01b992ba0d33d8.txt"},{"canonical_hash":"053a3e61d34d944daefe569417a0a208db032ad589aae5d37defc34bfef2514f","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,24,12,0,30,18,6,36,14,8,2,38,32,26,20,37,19,1,25,7,31,13,10,28,4,22,40,16,34,35,41,5,11,17,23,29,21,33,3,15,27,39,9","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 3) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/053a3e61d34d944daefe569417a0a208db032ad589aae5d37defc34bfef2514f.txt"},{"canonical_hash":"767749918ef64050d3572cb1ee9f41abdbf2428164d3752c8a7f1af434993fee","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,43,47,44,45,46,11,27,39,17,30,21,0,6,29,41,16,31,23,2,8,24,37,13,34,20,3,10,28,40,15,35,22,4,7,25,36,12,33,19,1,9,26,38,14,32,18,5","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 1) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 1). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/767749918ef64050d3572cb1ee9f41abdbf2428164d3752c8a7f1af434993fee.txt"},{"canonical_hash":"f593f6fd6af22628aac56132e8a404f0f5495474f221e7cb9f730b3899344421","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,43,47,44,45,46,1,32,30,0,33,31,41,8,6,4,2,7,5,3,40,38,36,34,39,37,35,22,20,18,16,21,19,17,29,27,25,23,28,26,24,15,13,11,9,14,12,10","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 1) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 1). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/f593f6fd6af22628aac56132e8a404f0f5495474f221e7cb9f730b3899344421.txt"},{"canonical_hash":"667d627aa2fe665380ef708eb31c815311af7a00df4bfaefa28ed785f5a7bc57","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,14,32,0,8,38,26,20,34,28,3,22,10,16,40,27,15,2,39,21,33,9,24,12,5,36,18,30,6,31,25,1,19,7,13,37,17,29,4,11,35,41,23","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 1) base × F_7(4, 3) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/667d627aa2fe665380ef708eb31c815311af7a00df4bfaefa28ed785f5a7bc57.txt"},{"canonical_hash":"ae5baeb35d4cd775115bda8c52a567f461417c9dc4f1ea7de693ce9eac021400","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,47,43,45,44,46,0,7,12,19,25,34,36,2,8,15,21,26,32,39,3,11,16,22,28,33,40,4,10,17,23,29,31,41,1,9,14,20,27,35,38,5,6,13,18,24,30,37","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 3) base × F_7(4, 3) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 3). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/ae5baeb35d4cd775115bda8c52a567f461417c9dc4f1ea7de693ce9eac021400.txt"},{"canonical_hash":"d50b3565f55696fb14ff77cb5b87148a39c99833e06e009f0d6349acb1e2c81d","size":49,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,7,13,19,25,31,37,1,5,11,17,23,29,35,2,8,14,20,26,32,38,3,9,15,21,27,33,39,4,10,16,22,28,34,40,6,12,18,24,30,36,41,48,42,47,43,45,44,46","comment":"Non-right-cancellative size-49 magma: a 7-element F_7 sub-magma (linear over F_7) plus 6 fibers of 7 elements partitioning the remaining 42 elements.","submitted_at":"2026-04-23 20:58:54","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/d50b3565f55696fb14ff77cb5b87148a39c99833e06e009f0d6349acb1e2c81d.txt"},{"canonical_hash":"b91b0b41763b44835ed91cbafd865ef9782d8e4ad54d80f28b30d51e5744c8f2","size":49,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"48,42,43,47,44,45,46,0,7,14,21,28,35,41,5,11,18,19,26,33,40,1,6,12,13,20,27,34,3,9,16,23,30,31,38,2,8,15,22,29,36,37,4,10,17,24,25,32,39","comment":"Size-49 (= 7²) non-right-cancellative fiber bundle: F_7(4, 3) base × F_7(4, 1) fiber. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence); only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 1). The other 6 fibers are non-closed congruence classes. Left-cancellative but not right-cancellative; unique idempotent.","submitted_at":"2026-04-23 20:58:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/b91b0b41763b44835ed91cbafd865ef9782d8e4ad54d80f28b30d51e5744c8f2.txt"},{"canonical_hash":"100ca3593871874365e5cf9089c9e3084e490c2e5279a34a3329c18f7ddc7505","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"48,42,43,47,44,45,46,0,7,14,21,28,35,41,5,11,18,19,26,33,40,1,6,12,13,20,27,34,3,9,16,23,30,31,38,2,8,15,22,29,36,37,4,10,17,24,25,32,39","comment":"Size-49 (= 7²) right-cancellative fiber bundle: F_7(4, 3) base × F_7(4, 1) fiber, in the \"twisted\" Family B variant. The 49 elements partition into 7 fibers of 7 (an F_7-quotient congruence), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, ≅ F_7(4, 1). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 20:58:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/49/100ca3593871874365e5cf9089c9e3084e490c2e5279a34a3329c18f7ddc7505.txt"},{"canonical_hash":"7aca021e3f8365b6920d8e7566922b4337108c018a11c518b82d5794186ce2cf","size":49,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"44,43,42,46,45,47,48,2,1,0,3,4,5,41,24,25,26,28,27,29,40,32,33,31,30,34,35,36,12,14,13,17,15,16,38,6,7,8,10,9,11,37,20,19,18,21,22,23,39","comment":"Order-49 (=7^2) non-right-cancellative eq677 magma of fiber-bundle type. It carries a congruence with 7 classes of size 7; the quotient is the order-7 magma F_7(4,3), and the 7 classes are order-7 fibers. Being non-right-cancellative, some right multiplications collapse a fiber to a point (this is what breaks cancellativity). It has a single idempotent. The display reorder uses (base, fiber) coordinates with the base in canonical F_7 order, so the Cayley table shows a clean 7x7 block super-grid, each block being the fiber action over a pair of base points. See the size-49 notes for the broader taxonomy. [text written by Claude]","submitted_at":"2026-05-26 08:58:43","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/7aca021e3f8365b6920d8e7566922b4337108c018a11c518b82d5794186ce2cf.txt"},{"canonical_hash":"4f522dd0c698a0cadde9f0460b9542b0617e28d190d733554840c3f3be82182d","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"43,48,28,5,36,21,7,35,14,33,3,19,26,40,11,12,23,16,0,24,9,31,38,30,15,1,22,29,37,8,4,6,27,13,41,34,20,10,32,17,25,39,18,2,42,47,46,44,45","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/4f522dd0c698a0cadde9f0460b9542b0617e28d190d733554840c3f3be82182d.txt"},{"canonical_hash":"446d3b0cda5b02b89a916d398d2a9c05f9f007e64908e04cd5773c040a58fbd1","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"41,32,10,1,19,11,46,33,0,20,28,36,17,14,13,15,12,16,48,34,6,21,37,2,29,47,44,9,26,5,40,18,31,7,22,24,3,38,35,42,4,23,25,39,43,30,8,27,45","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:48","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/446d3b0cda5b02b89a916d398d2a9c05f9f007e64908e04cd5773c040a58fbd1.txt"},{"canonical_hash":"5346793d1fbda4ee4448a10ef4a9a64ecb28717882fd439372965693c3708129","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"45,44,43,47,42,46,48,14,21,28,0,7,35,36,16,3,38,9,31,24,23,30,29,37,15,8,22,2,26,11,5,19,33,12,40,27,20,34,6,41,1,13,39,32,10,18,17,25,4","comment":"Order-49 (=7^2) right-cancellative eq677 magma of fiber-bundle type. It carries a congruence with 7 classes of size 7; the quotient is the order-7 magma F_7(4,1), and the 7 classes are order-7 fibers. It has a single idempotent. The display reorder uses (base, fiber) coordinates with the base in canonical F_7 order, so the Cayley table shows a clean 7x7 block super-grid, each block being the fiber action over a pair of base points. See the size-49 notes for the broader taxonomy. [text written by Claude]","submitted_at":"2026-05-26 10:26:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/5346793d1fbda4ee4448a10ef4a9a64ecb28717882fd439372965693c3708129.txt"},{"canonical_hash":"57bc3b9f50cd3924d004798c81d067f9bcceeb3de5093b724879033a8820f4e2","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"44,46,42,47,48,45,43,0,5,36,3,4,2,1,16,15,13,38,12,14,17,7,8,9,6,10,11,37,29,24,25,28,26,27,40,35,33,41,31,30,34,32,21,18,22,23,19,20,39","comment":"Order-49 (=7^2) right-cancellative eq677 magma of fiber-bundle type. It carries a congruence with 7 classes of size 7; the quotient is the order-7 magma F_7(4,1), and the 7 classes are order-7 fibers. It has a single idempotent. The display reorder uses (base, fiber) coordinates with the base in canonical F_7 order, so the Cayley table shows a clean 7x7 block super-grid, each block being the fiber action over a pair of base points. See the size-49 notes for the broader taxonomy. [text written by Claude]","submitted_at":"2026-05-26 10:26:51","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/57bc3b9f50cd3924d004798c81d067f9bcceeb3de5093b724879033a8820f4e2.txt"},{"canonical_hash":"923ca9b2cfa6ac8860e9ac94734cff220fa182589f737c357e66e3576fac1df0","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"5,36,0,4,2,6,8,7,11,41,9,10,17,37,12,13,14,16,15,19,38,20,22,18,23,21,26,25,24,29,28,39,27,32,30,34,40,35,33,31,48,47,46,45,42,44,43,1,3","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:53","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/923ca9b2cfa6ac8860e9ac94734cff220fa182589f737c357e66e3576fac1df0.txt"},{"canonical_hash":"45a22380c70952d861e1efcdc02795a882cb5106e7ec51cbfed6a94645403359","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"10,24,17,25,32,39,3,12,1,34,0,27,20,13,2,33,18,11,19,26,40,4,9,38,31,23,16,30,8,29,37,15,36,5,22,35,7,14,21,6,28,41,48,44,42,45,43,47,46","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:55","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/45a22380c70952d861e1efcdc02795a882cb5106e7ec51cbfed6a94645403359.txt"},{"canonical_hash":"9bace1a4ea5e67bdb28ff50c5b736760fa1d1a20697147d60336695350fe3bc6","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,18,26,5,20,1,34,12,13,27,21,6,35,28,41,14,7,39,3,17,32,24,10,25,8,37,36,0,15,22,29,16,30,31,9,23,38,2,19,33,40,11,48,43,46,45,42,47,44","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:56","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/9bace1a4ea5e67bdb28ff50c5b736760fa1d1a20697147d60336695350fe3bc6.txt"},{"canonical_hash":"f5e7c8aa2901e341ebad9df9f6395da463c8d806eecea448ebf9306b9d1fba29","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,0,3,2,1,7,10,6,9,41,11,8,12,37,14,17,13,15,16,23,38,19,21,20,18,22,29,26,28,24,25,39,27,31,40,30,32,35,34,33,48,45,43,44,42,47,46,36,5","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:58","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/f5e7c8aa2901e341ebad9df9f6395da463c8d806eecea448ebf9306b9d1fba29.txt"},{"canonical_hash":"6cb28689ab2975911ef74d685890294bc998a977a4d99fc76c4d540feee2bb84","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"1,0,2,5,4,10,11,8,38,9,7,6,15,12,39,13,14,17,16,19,40,22,21,23,20,18,25,24,27,26,36,28,29,33,35,34,31,41,30,32,47,42,43,44,45,46,48,37,3","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:26:59","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/6cb28689ab2975911ef74d685890294bc998a977a4d99fc76c4d540feee2bb84.txt"},{"canonical_hash":"6432c2bb4b2daa03f9bc94e194afc247e005c217a4ec8d098457d81a35ae5df2","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"2,1,0,3,5,4,10,39,9,7,8,11,6,15,12,13,14,16,40,17,48,29,26,24,27,25,28,36,34,35,37,31,30,33,32,22,23,19,18,21,20,41,42,46,44,43,47,45,38","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,1) and 1 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:02","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/6432c2bb4b2daa03f9bc94e194afc247e005c217a4ec8d098457d81a35ae5df2.txt"},{"canonical_hash":"dd887de0dd0982c52b2b161aa9c952d5ac294a345db8f5b74864cae2a3ddcda7","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"3,0,5,4,38,6,11,39,10,7,8,9,12,17,15,14,40,13,16,23,20,19,22,18,41,21,24,27,25,26,36,29,28,35,33,32,31,37,34,30,45,46,44,47,43,42,48,2,1","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,1) and 1 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:03","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/dd887de0dd0982c52b2b161aa9c952d5ac294a345db8f5b74864cae2a3ddcda7.txt"},{"canonical_hash":"0a971d42da4069bcfdfa944a177c8c6d6f51bf859a8e1d3e5ca6a3b381aec830","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"34,3,42,21,26,37,48,10,6,11,7,8,9,14,31,29,18,45,1,40,19,15,24,5,46,41,32,38,27,43,35,2,12,22,30,28,0,39,44,23,13,47,25,33,20,16,4,36,17","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:05","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/0a971d42da4069bcfdfa944a177c8c6d6f51bf859a8e1d3e5ca6a3b381aec830.txt"},{"canonical_hash":"314d451a70bfa5342e635f4f3dd8699b37f0289bb35b11e9783246bab1b46016","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"9,26,36,34,19,0,17,24,15,7,40,5,32,23,2,35,10,20,37,27,12,30,13,3,38,11,28,21,1,41,33,25,18,16,8,14,4,22,39,29,6,31,48,46,44,47,43,42,45","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:07","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/314d451a70bfa5342e635f4f3dd8699b37f0289bb35b11e9783246bab1b46016.txt"},{"canonical_hash":"d2e79a8b10c3255a00e23cee4240cff8739978fa33d79ae47e4bfc8dafb7c2c7","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,2,3,0,1,5,48,25,44,15,32,7,20,41,22,34,29,17,9,37,46,42,39,18,13,30,11,27,14,31,19,6,40,43,26,16,36,45,8,33,21,24,10,38,12,47,23,35,28","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:08","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/d2e79a8b10c3255a00e23cee4240cff8739978fa33d79ae47e4bfc8dafb7c2c7.txt"},{"canonical_hash":"5bc425f6a7f2773aba5b5a16dc763ea485467f4da3e31d5b1a843e867b9ae075","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"37,2,0,3,11,9,6,7,10,8,38,12,15,13,17,39,16,14,19,40,21,23,18,20,22,29,26,24,25,27,41,28,30,33,31,35,36,34,32,1,4,5,48,46,44,47,42,43,45","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,1) and 1 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:10","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/5bc425f6a7f2773aba5b5a16dc763ea485467f4da3e31d5b1a843e867b9ae075.txt"},{"canonical_hash":"1851038ff6baafa7797a0deb2f970c9d34c17d02f2513567651f2f74f1c95056","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"37,0,1,5,9,8,7,10,6,38,11,39,16,15,12,13,14,17,18,20,40,19,21,22,23,25,27,26,28,24,29,41,32,36,34,33,35,30,31,47,46,44,45,43,42,48,4,2,3","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,1) and 1 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:11","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/1851038ff6baafa7797a0deb2f970c9d34c17d02f2513567651f2f74f1c95056.txt"},{"canonical_hash":"33ce16d8e28625a160759e238c551021da233dfe0e44356183ebb7099afdd413","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"42,45,44,48,47,43,46,0,3,1,2,5,4,41,26,25,24,27,28,40,29,35,34,32,30,36,33,31,15,17,13,14,12,38,16,10,8,11,7,6,9,37,20,23,22,39,19,21,18","comment":"Order-49 (=7^2) right-cancellative eq677 magma of fiber-bundle type. It carries a congruence with 7 classes of size 7; the quotient is the order-7 magma F_7(4,3), and the 7 classes are order-7 fibers. It has a single idempotent. The display reorder uses (base, fiber) coordinates with the base in canonical F_7 order, so the Cayley table shows a clean 7x7 block super-grid, each block being the fiber action over a pair of base points. See the size-49 notes for the broader taxonomy. [text written by Claude]","submitted_at":"2026-05-26 10:27:13","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/33ce16d8e28625a160759e238c551021da233dfe0e44356183ebb7099afdd413.txt"},{"canonical_hash":"0102f7d796c22250137ffd2ddf6930ec6d09f5082a96b36cc2f8abc535fe8043","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"46,43,42,44,45,47,48,25,19,7,0,37,31,13,5,35,17,1,23,29,11,30,36,24,12,41,18,6,33,27,39,9,21,3,15,2,32,14,38,20,26,8,22,40,4,10,16,28,34","comment":"Order-49 (=7^2) right-cancellative eq677 magma of fiber-bundle type. It carries a congruence with 7 classes of size 7; the quotient is the order-7 magma F_7(4,3), and the 7 classes are order-7 fibers. It has a single idempotent. The display reorder uses (base, fiber) coordinates with the base in canonical F_7 order, so the Cayley table shows a clean 7x7 block super-grid, each block being the fiber action over a pair of base points. See the size-49 notes for the broader taxonomy. [text written by Claude]","submitted_at":"2026-05-26 10:27:15","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/0102f7d796c22250137ffd2ddf6930ec6d09f5082a96b36cc2f8abc535fe8043.txt"},{"canonical_hash":"870ca0f0fa4c8c9b71a879b834b6df1dc549b00e4d7dbdaa883eb8024cf2d963","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"3,0,2,5,1,4,41,9,37,7,11,16,15,12,38,14,13,17,18,21,20,22,23,39,19,27,24,25,28,40,26,29,30,36,35,33,34,32,31,8,10,6,43,44,47,45,46,42,48","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:16","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/870ca0f0fa4c8c9b71a879b834b6df1dc549b00e4d7dbdaa883eb8024cf2d963.txt"},{"canonical_hash":"65674b90d692e4767d43eefbfb9909fa346cb01c34cb8f922095683b112582a8","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,2,4,1,9,38,6,7,11,8,10,17,39,15,13,14,16,12,18,20,23,21,19,40,22,24,28,25,27,29,26,41,31,34,36,32,33,30,35,48,45,47,44,43,42,46,3,37,5","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,1) and 1 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:19","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/65674b90d692e4767d43eefbfb9909fa346cb01c34cb8f922095683b112582a8.txt"},{"canonical_hash":"3df8a36ca3b05aa08e401c6a1f0ce9c09ce4825d8a005bfaa41708b8a926f4cd","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,3,1,37,5,8,38,6,9,10,7,11,15,17,13,12,14,39,16,20,23,21,19,40,22,18,29,24,28,27,26,41,25,35,31,33,36,34,32,30,48,47,44,43,45,46,42,0,2","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,1) and 1 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:20","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/3df8a36ca3b05aa08e401c6a1f0ce9c09ce4825d8a005bfaa41708b8a926f4cd.txt"},{"canonical_hash":"5f7a89f2bbf384946086b0c6b240119c8baea38cbbf588fce80a12275b7de2fa","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"39,43,35,20,9,1,16,41,6,46,32,23,13,3,38,33,37,4,18,47,7,14,5,15,42,34,8,19,36,48,24,28,29,26,25,27,40,0,44,30,10,17,21,2,31,45,12,11,22","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:22","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/5f7a89f2bbf384946086b0c6b240119c8baea38cbbf588fce80a12275b7de2fa.txt"},{"canonical_hash":"40b041b0d9e4117c64e398f175e71db904288bc259e6c638e3212204f13040e5","size":49,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"5,2,3,0,48,1,4,7,6,9,8,10,11,42,30,45,34,31,33,32,35,36,39,37,38,41,46,40,18,21,19,20,23,43,22,12,47,16,13,15,14,17,25,24,27,26,28,29,44","comment":"Order-49 (=7^2) non-right-cancellative eq677 magma of fiber-bundle type. It carries a congruence with 7 classes of size 7; the quotient is the order-7 magma F_7(4,3), and the 7 classes are order-7 fibers. Being non-right-cancellative, some right multiplications collapse a fiber to a point (this is what breaks cancellativity). It has a single idempotent. The display reorder uses (base, fiber) coordinates with the base in canonical F_7 order, so the Cayley table shows a clean 7x7 block super-grid, each block being the fiber action over a pair of base points. See the size-49 notes for the broader taxonomy. [text written by Claude]","submitted_at":"2026-05-26 10:27:24","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/40b041b0d9e4117c64e398f175e71db904288bc259e6c638e3212204f13040e5.txt"},{"canonical_hash":"78e1b2d45ef77b2d33b6ea30cd891df8dc6dced8d2f4f450cdea72e3263e9f0a","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"39,25,32,17,4,24,10,33,5,19,40,11,18,26,31,16,3,30,38,23,9,1,20,12,6,27,13,34,29,15,8,37,22,2,36,14,7,21,0,41,28,35,48,42,47,43,45,44,46","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:25","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/78e1b2d45ef77b2d33b6ea30cd891df8dc6dced8d2f4f450cdea72e3263e9f0a.txt"},{"canonical_hash":"3d311818c711eb957c5e868ec0cdeef6b146ba20fc63ef44a349c33ef03f1d7f","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,19,17,35,27,10,37,30,22,40,14,32,7,4,18,36,38,2,28,20,11,6,33,15,23,25,5,8,13,29,21,31,3,12,39,16,26,24,34,1,9,41,48,43,46,45,47,44,42","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:27","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/3d311818c711eb957c5e868ec0cdeef6b146ba20fc63ef44a349c33ef03f1d7f.txt"},{"canonical_hash":"7113308fa15f6cd99050a6c890dd34d678142161d1b13b87ca77cf609610a98e","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"34,2,46,0,38,22,12,25,33,17,13,15,18,16,14,48,42,6,32,21,37,30,11,47,10,20,5,31,29,41,43,4,1,19,9,36,28,44,3,35,24,40,27,8,45,7,39,26,23","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:28","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/7113308fa15f6cd99050a6c890dd34d678142161d1b13b87ca77cf609610a98e.txt"},{"canonical_hash":"b3572d59f88b8e3e895d1710ef9573f86792fc48c74104c3a0105897e290d1cc","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"43,42,19,33,9,29,1,17,0,31,7,5,23,25,15,39,12,36,22,14,38,26,4,16,30,40,32,24,8,6,13,11,35,37,3,27,21,20,18,41,2,28,34,10,48,47,45,44,46","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are all 8 of type F_7(4,3). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:30","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/b3572d59f88b8e3e895d1710ef9573f86792fc48c74104c3a0105897e290d1cc.txt"},{"canonical_hash":"73638003f60ba7ba23ef82e3d7be5adda5484104e8787c589d3354d130099355","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,3,2,7,11,38,6,8,10,9,16,17,12,13,14,39,15,20,23,22,18,19,21,40,26,25,29,24,36,28,27,35,31,30,33,32,34,41,43,42,44,46,45,47,48,1,5,37","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:31","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/73638003f60ba7ba23ef82e3d7be5adda5484104e8787c589d3354d130099355.txt"},{"canonical_hash":"dd73fb5e7d2886565f4750055fa04c9c8ec33efabeea12964e33f554e59479cb","size":49,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,2,1,4,41,7,11,6,9,8,37,10,18,20,22,21,39,19,23,38,17,13,16,12,14,15,30,31,32,33,35,36,34,26,24,28,29,25,27,40,48,47,44,45,42,46,43,3","comment":"Order-49 (=7^2) right-cancellative eq677 magma of 'pencil' type. It is simple (no nontrivial congruence): any two elements generate either a shared order-7 sub-magma or the whole magma. There are exactly 8 order-7 sub-magmas, all passing through one common element -- the unique idempotent -- which partitions the other 48 elements into 8 'petals' of 6. This is the incidence pattern of the 8 lines through a point of the affine plane AG(2,7). As order-7 magmas the 8 lines are 7 of type F_7(4,3) and 1 of type F_7(4,1). Although this looks like the arrangement of the 8 one-dimensional subspaces of a linear magma over F_49, it is NOT isomorphic to any linear F_49 magma and is not even affine over its lines -- a genuinely twisted construction. With no congruence to exploit, the display reorder was obtained by minimizing a Cayley-image smoothness measure rather than from algebraic coordinates. One of 24 pairwise non-isomorphic order-49 pencils; see the size-49 notes. [text written by Claude]","submitted_at":"2026-05-26 10:27:33","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/49/dd73fb5e7d2886565f4750055fa04c9c8ec33efabeea12964e33f554e59479cb.txt"},{"canonical_hash":"8584ee107238610abf080b50686e707ca6d8fc8f0362ec6e641802178bf0dc39","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,50,12,25,46,16,38,34,42,8,5,9,35,17,26,51,1,43,39,47,13,15,19,45,7,28,41,11,53,49,37,3,10,14,40,2,27,36,6,48,44,52,18,33,32,21,30,54,22,29,24,20,23,31","comment":"Direct product of two linear magmas: F_5 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 4x₂ + 8y₂ (mod 11)).","submitted_at":"2026-04-23 20:58:56","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/8584ee107238610abf080b50686e707ca6d8fc8f0362ec6e641802178bf0dc39.txt"},{"canonical_hash":"b44f1eb845c070da04b6823b0358d2fa6555e1c0d290fe39936791794d370e40","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,46,12,32,42,16,34,50,38,8,10,14,36,2,30,52,6,44,40,48,18,35,39,1,47,33,17,51,9,5,13,43,21,25,22,23,54,28,27,20,26,24,29,45,49,11,37,31,7,41,19,15,3,53","comment":"Direct product of two linear magmas: F_5 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 10x₂ + 2y₂ (mod 11)).","submitted_at":"2026-04-23 20:58:56","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/b44f1eb845c070da04b6823b0358d2fa6555e1c0d290fe39936791794d370e40.txt"},{"canonical_hash":"e48ea93aeb8fbed3d4b41e777c9ddf102aa6903f9f084f8c2aad69ea9ed79542","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,12,11,9,2,10,54,4,13,3,14,30,40,44,52,26,48,5,18,36,22,19,15,45,49,37,31,53,6,23,41,27,29,25,35,39,47,21,43,8,33,51,17,24,20,50,34,42,16,38,7,28,46,32","comment":"Direct product of two linear magmas: F_5 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 5x₂ + 7y₂ (mod 11)).","submitted_at":"2026-04-23 20:58:58","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/e48ea93aeb8fbed3d4b41e777c9ddf102aa6903f9f084f8c2aad69ea9ed79542.txt"},{"canonical_hash":"798efd474269d937c90a3cdc31b7814719f23be2475239b8b41d28a4dfac2c8c","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,4,5,6,7,28,29,54,8,12,16,20,24,32,34,38,42,46,50,9,13,17,21,25,33,35,39,43,47,51,11,15,19,23,27,31,37,41,45,49,53,10,14,18,22,26,30,36,40,44,48,52","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:00","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/798efd474269d937c90a3cdc31b7814719f23be2475239b8b41d28a4dfac2c8c.txt"},{"canonical_hash":"a369b77d3127e65f9dfd279d244ae9a14cfb03b2c6dc10328990cc599034e03d","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,8,28,5,4,54,3,6,27,7,13,34,46,30,21,38,52,17,42,9,25,35,14,26,10,43,18,53,39,22,31,47,33,16,49,12,41,20,51,37,24,29,45,15,36,48,32,23,40,50,19,44,11,1","comment":"Direct product of two linear magmas: F_5 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 6x₂ + 6y₂ (mod 11)).","submitted_at":"2026-04-23 20:59:00","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/a369b77d3127e65f9dfd279d244ae9a14cfb03b2c6dc10328990cc599034e03d.txt"},{"canonical_hash":"52d549ff40e2efe253920577848a2f2161900601d06807c463d362e2d8732e15","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,4,5,6,7,12,13,54,8,14,18,22,26,30,36,40,44,48,52,9,15,19,23,27,31,37,41,45,49,53,11,17,21,25,29,33,35,39,43,47,51,10,16,20,24,28,32,34,38,42,46,50","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:02","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/52d549ff40e2efe253920577848a2f2161900601d06807c463d362e2d8732e15.txt"},{"canonical_hash":"8766aa961234effb2addc4bcb812f6903246799eae10da8dfc12ef87d8cbde6d","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,9,13,17,21,25,34,38,42,46,50,1,10,14,18,22,26,35,39,43,47,51,3,12,16,20,24,28,37,41,45,49,53,2,11,15,19,23,27,36,40,44,48,52,4,5,6,7,8,29,30,31,32,33,54","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:05","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/8766aa961234effb2addc4bcb812f6903246799eae10da8dfc12ef87d8cbde6d.txt"},{"canonical_hash":"00962f278671d3dcce33ef52f643a2563bbd0666650ed306f81f071447051b2b","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,4,5,10,11,32,33,54,6,15,19,23,27,31,37,41,45,49,53,7,12,16,20,24,28,34,38,42,46,50,9,14,18,22,26,30,36,40,44,48,52,8,13,17,21,25,29,35,39,43,47,51","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:06","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/00962f278671d3dcce33ef52f643a2563bbd0666650ed306f81f071447051b2b.txt"},{"canonical_hash":"ad16915a758fdd906f800eee247a97bebaf0f76515e67b02d83e09980a6b3c9d","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,4,25,26,27,28,29,54,5,9,13,17,21,32,34,38,42,46,50,6,10,14,18,22,33,35,39,43,47,51,8,12,16,20,24,31,37,41,45,49,53,7,11,15,19,23,30,36,40,44,48,52","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:06","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/ad16915a758fdd906f800eee247a97bebaf0f76515e67b02d83e09980a6b3c9d.txt"},{"canonical_hash":"212032b69655cb00346d1ecb5e16bb8c46bf4d24feef634271bab1b7b3cf69bd","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,5,9,13,17,21,35,39,43,47,51,1,6,10,14,18,22,36,40,44,48,52,3,4,8,12,16,20,34,38,42,46,50,2,7,11,15,19,23,37,41,45,49,53,24,25,26,27,28,29,30,31,32,33,54","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/212032b69655cb00346d1ecb5e16bb8c46bf4d24feef634271bab1b7b3cf69bd.txt"},{"canonical_hash":"938ac244cd91cf849a1264ab9aeba5b08b8b7b32676abf0e5d342eb89807a51a","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,16,20,24,28,32,34,38,42,46,50,1,17,21,25,29,33,35,39,43,47,51,3,15,19,23,27,31,37,41,45,49,53,2,14,18,22,26,30,36,40,44,48,52,4,5,6,7,8,9,10,11,12,13,54","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:11","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/938ac244cd91cf849a1264ab9aeba5b08b8b7b32676abf0e5d342eb89807a51a.txt"},{"canonical_hash":"be0a62af0535a752ae1daa3c1b100a9821a6f6ba6b7c47f956eed2c34a70ce3a","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,4,9,10,11,12,13,54,5,16,20,24,28,32,34,38,42,46,50,6,17,21,25,29,33,35,39,43,47,51,8,15,19,23,27,31,37,41,45,49,53,7,14,18,22,26,30,36,40,44,48,52","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/be0a62af0535a752ae1daa3c1b100a9821a6f6ba6b7c47f956eed2c34a70ce3a.txt"},{"canonical_hash":"744887827cf5a928a08a07e3f0c3c46a46f9a1022fd9d61c4f67fa565be521f0","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,4,25,26,27,28,29,54,5,9,13,17,21,32,34,38,42,46,50,6,10,14,18,22,33,35,39,43,47,51,8,12,16,20,24,31,37,41,45,49,53,7,11,15,19,23,30,36,40,44,48,52","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 20:59:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/744887827cf5a928a08a07e3f0c3c46a46f9a1022fd9d61c4f67fa565be521f0.txt"},{"canonical_hash":"6d38d946299b25fa3f70243da87ca558821822f74f9043eaddfba0a9272b6ac6","size":55,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,2,3,49,4,5,6,7,48,32,33,34,35,54,20,21,22,23,51,12,13,14,15,44,28,29,30,31,53,8,9,10,11,45,36,37,38,39,47,16,17,18,19,52,24,25,26,27,50,40,41,42,43,46","comment":"Twisted (NOT direct) fiber bundle: F_11(10, 2) base × F_5 fiber.\n\nSize 55 = 5 * 11. Fully idempotent. Left-cancellative but NOT right-cancellative -- this is the key indicator that the bundle is non-trivial: a direct product of two RC magmas would itself be RC.\n\nStructure: the 55 elements partition into 11 disjoint size-5 sub-magmas (the \"fibers\"); the fiber partition is a congruence. Quotienting by the fibers gives a size-11 magma = magma#15fbff50 (the linear F_11 magma x ◇ y = 10x + 2y mod 11, which is right-cancellative). Each fiber is isomorphic to magma#e549b5f8 (the F_5 affine line, also RC).\n\nBut the bundle is TWISTED: a true direct product F_11(10,2) × F_5 (Tao G × M product) would satisfy T((x1, x2), (y1, y2)) = (T_F11(x1, y1), T_F5(x2, y2)), making the whole magma a quasigroup since both factors are. Here, in the suggested reorder (11 consecutive 5-blocks), the diagonal 5×5 blocks correctly show the F_5 fiber operation, and the off-diagonal blocks reflect the base operation -- but the fiber operation embedded in off-diagonal blocks differs from a constant action across (f1, f2) pairs, breaking right-cancellation.\n\nIn addition to the 11 size-5 fiber sub-magmas, there is exactly 1 size-11 sub-magma in M (a \"section\" of the bundle, an embedded copy of F_11(10, 2) hitting each fiber in exactly one point). The full sub-magma lattice: 1 size-11, 11 size-5, plus singletons and M itself.\n\nThe construction is the \"Tao Type II fiber bundle\" or \"twisted G × M\" recipe at sizes that are products of two primes admitting Eq 677 linear magmas (5 and 11 both ≡ 1 or 5 mod 20). Compare with the various size-65 (= 5*13) bundles in the DB.\n\n[text written by Claude]","submitted_at":"2026-04-23 20:59:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/6d38d946299b25fa3f70243da87ca558821822f74f9043eaddfba0a9272b6ac6.txt"},{"canonical_hash":"c3a63dd57243e895a64de8cecd280358a09e7d61091c167d346240d72ce2a73b","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,5,12,15,18,21,24,27,34,37,40,1,3,7,10,13,20,26,29,32,35,42,2,6,9,16,19,22,25,28,31,38,41,44,45,46,47,48,49,50,51,52,53,54,4,8,11,14,17,23,30,33,36,39,43","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:19:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/c3a63dd57243e895a64de8cecd280358a09e7d61091c167d346240d72ce2a73b.txt"},{"canonical_hash":"d914e39808eb8ebc75b1374967cc8f943a657269fc101095cec0baa4b4f2fa33","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,8,11,14,17,23,30,33,36,39,43,1,4,7,10,13,20,26,29,32,35,42,44,45,46,47,48,49,50,51,52,53,54,2,5,12,15,18,21,24,27,34,37,40,3,6,9,16,19,22,25,28,31,38,41","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:19:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/d914e39808eb8ebc75b1374967cc8f943a657269fc101095cec0baa4b4f2fa33.txt"},{"canonical_hash":"b762573ff743eecbabe99c391b9af8690466b8ea92a0fcc7953951c1b38b8924","size":55,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,5,12,15,18,21,24,27,34,37,40,1,3,7,10,13,20,26,29,32,35,42,2,6,9,16,19,22,25,28,31,38,41,44,45,46,47,48,49,50,51,52,53,54,4,8,11,14,17,23,30,33,36,39,43","comment":"F_5(2, 4) base × F_11 fiber: 5 fibers of 11 (each = F_11 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:19:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/55/b762573ff743eecbabe99c391b9af8690466b8ea92a0fcc7953951c1b38b8924.txt"},{"canonical_hash":"f2d8c865ef19ddeb3586c5e0c70736a75bdf8ec0a3800b79887e7edd09fba180","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,33,16,8,58,56,32,25,11,34,12,53,44,15,27,52,19,6,9,13,7,37,43,39,36,49,22,57,45,14,23,42,4,41,55,2,26,28,38,46,3,31,30,51,17,35,20,40,24,29,18,60,48,59,54,10,50,5,47,21","comment":"Linear magma over Z/61Z (the prime field F_61): x ◇ y = 10x + 52y (mod 61).","submitted_at":"2026-04-23 20:59:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/f2d8c865ef19ddeb3586c5e0c70736a75bdf8ec0a3800b79887e7edd09fba180.txt"},{"canonical_hash":"d5df0d93f68f095457a2d141ec2d9203138dbbd6c547f4edaa7340b3c0b68172","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,52,3,15,20,47,54,57,41,35,5,11,27,24,17,50,45,33,22,31,30,32,49,23,10,34,56,46,14,51,59,18,39,25,43,28,8,12,37,6,60,36,7,42,38,58,13,55,9,48,29,21,44,16,26,4,40,53,19,2","comment":"Linear magma over Z/61Z (the prime field F_61): x ◇ y = 21x + 41y (mod 61).","submitted_at":"2026-04-23 20:59:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/d5df0d93f68f095457a2d141ec2d9203138dbbd6c547f4edaa7340b3c0b68172.txt"},{"canonical_hash":"82a4911ca956aa0b19b916c56909ecfa3b9d878ae0cee4d823390f761682e741","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,22,57,33,26,59,42,16,5,43,2,50,4,14,10,39,55,18,15,17,23,8,28,36,41,54,60,24,11,6,58,38,53,47,45,48,25,9,40,44,34,20,32,13,35,46,12,29,56,3,27,52,31,30,21,49,7,37,19,51","comment":"Linear magma over Z/61Z (the prime field F_61): x ◇ y = 35x + 27y (mod 61).","submitted_at":"2026-04-23 20:59:33","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/82a4911ca956aa0b19b916c56909ecfa3b9d878ae0cee4d823390f761682e741.txt"},{"canonical_hash":"e70931b6f8e204fe7241ce539775d6cad92bb3da4733d8231fe2cbdcb0380d85","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,34,60,28,7,6,19,15,18,56,41,17,37,25,40,32,30,36,53,22,39,2,49,29,4,20,52,57,11,38,9,33,48,54,27,3,44,5,51,58,14,10,35,55,8,45,16,59,42,24,26,46,31,43,23,47,50,12,21,13","comment":"Linear magma over Z/61Z (the prime field F_61): x ◇ y = 59x + 3y (mod 61).","submitted_at":"2026-04-23 20:59:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/e70931b6f8e204fe7241ce539775d6cad92bb3da4733d8231fe2cbdcb0380d85.txt"},{"canonical_hash":"d51ca85e32d7d6406eaf3f1f85392c21d620d77306cf300360c9f340410aecb5","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,47,14,59,60,9,43,7,57,10,37,12,45,40,48,4,29,50,2,26,27,32,58,8,25,49,31,35,15,28,41,54,19,22,13,20,42,30,24,39,44,36,23,5,18,3,55,53,38,56,11,52,46,51,17,6,34,16,33,21","comment":"Translation-only Steiner-line magma on a cyclic S(2, 5, 61) design.\n\nSize 61, fully idempotent, RC. 183 = 61*60/(5*4) size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8); every pair of distinct elements lies in exactly one block; each element is in 15 blocks.\n\n|Aut(M)| = 61 - only the Z_61 translation subgroup; no multiplicative stabilizer at any point. The 183 blocks split as 3 Aut-orbits of 61 each (cyclic BIBD with 3 base blocks under Z_61, since 183 = 3*61).\n\nIn the suggested reorder, F_61 labeling makes translation x -> x+1 an automorphism. Operation: x*y = x + f(y - x) mod 61, where f is a non-linear permutation with f(0) = 0.\n\nSlope analysis (alpha(y) = f(y)/y on F_61*): 34 distinct slope values, far less symmetric than the size-41 analogs. Phi_10 roots in F_61 = {3, 27, 41, 52} (the primitive 10th roots of unity). The slope multiset:\n  4 Phi_10-root slopes appear on only 6 of the 60 nonzero elements (class sizes 1, 1, 2, 2)\n  30 non-Phi_10 slopes appear on the remaining 54 elements (class sizes ranging 1 to 5)\nThe chaotic slope structure reflects the lack of higher symmetry: with only Aut = Z_61, the cyclic BIBD's difference family carries no extra multiplicative regularity, so the slope function is \"as generic as possible\" subject to the 677 constraint.\n\nContext: 36 size-61 Eq 677 magmas in the DB, split as\n  4 linear F_61 affine line magmas (one per Phi_10 root, |Aut| = 3660 = |AGL(1, 61)|),\n  1 magma#0bcf3cca with Z_15 multiplicative stabilizer (|Aut| = 915 = 15*61),\n  1 magma#05fbff2c with Z_3 multiplicative stabilizer (|Aut| = 183 = 3*61),\n  30 translation-only Steiner-line magmas (this one is one of them), |Aut| = 61.\n\nCompared to size 41: at size 41 there were only 8 Steiner-line magmas total (1 Z_5-symmetric + 7 translation-only), with a tidy 12-value slope set common to all. At size 61, 60 = 4*15 has more divisors than 40 = 8*5, giving Aut subgroups of orders 1, 3, 15, 60 (vs. 1, 5, 40 at size 41), hence many more variant types and a richer slope landscape.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:19:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/d51ca85e32d7d6406eaf3f1f85392c21d620d77306cf300360c9f340410aecb5.txt"},{"canonical_hash":"4689cfed4bb4bc23cd30c27b2540306efe0b80bcdcaf19a20e54fb619ff0c5fe","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,20,45,10,46,50,3,11,41,48,30,42,13,23,15,4,33,9,32,51,39,16,53,37,40,24,7,44,27,43,56,47,17,55,5,6,36,14,29,8,18,60,52,49,21,34,25,19,54,59,57,12,2,38,31,35,58,22,26,28","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:33","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/4689cfed4bb4bc23cd30c27b2540306efe0b80bcdcaf19a20e54fb619ff0c5fe.txt"},{"canonical_hash":"5064faf2efb9ff902dfa8cacade7196503afd65cf5a836aa68b757cc0ba355f2","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,52,42,17,34,3,36,20,27,45,5,12,8,18,22,11,9,51,6,25,58,10,59,46,21,14,26,39,35,50,33,44,31,13,19,57,24,54,43,37,49,2,4,32,7,23,16,48,28,56,38,29,30,53,41,47,55,60,40,15","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/5064faf2efb9ff902dfa8cacade7196503afd65cf5a836aa68b757cc0ba355f2.txt"},{"canonical_hash":"fe5421e4e8a32d9111ae08268aa2e72179e111b4ca7abd5ee52522e4f3f4ee2e","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,42,6,2,34,20,51,9,52,54,4,16,60,14,33,19,13,40,31,37,47,53,46,49,18,15,27,24,50,28,25,11,57,22,30,5,41,35,58,26,38,21,7,23,32,45,3,48,39,56,36,8,44,29,59,55,43,10,17,12","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:37","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/fe5421e4e8a32d9111ae08268aa2e72179e111b4ca7abd5ee52522e4f3f4ee2e.txt"},{"canonical_hash":"03b5a3568c5ba89da125a80407e0915e5b7eaffae37f71619b72ab6420fdb676","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,22,49,47,55,8,25,44,19,16,34,5,13,53,59,36,10,42,11,3,58,9,23,12,51,15,37,35,60,6,43,39,24,40,45,14,21,18,38,29,41,31,46,2,30,52,54,32,4,48,57,28,17,26,56,50,33,7,20,27","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/03b5a3568c5ba89da125a80407e0915e5b7eaffae37f71619b72ab6420fdb676.txt"},{"canonical_hash":"03138da91e25052845fc0e4ac81b63807546da4bc918a9a76590d6137ba622de","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,44,50,35,30,38,3,56,36,17,2,18,29,26,15,13,27,37,40,41,49,14,20,46,52,60,8,34,4,42,58,53,10,24,21,55,11,6,39,47,12,32,23,19,43,7,25,48,16,51,54,9,57,28,59,22,31,45,5,33","comment":"Steiner-type magma: every pair of distinct elements lies in exactly one 5-element sub-magma, and these sub-magmas form the blocks of a Steiner system S(2,5,n).","submitted_at":"2026-04-23 21:19:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/03138da91e25052845fc0e4ac81b63807546da4bc918a9a76590d6137ba622de.txt"},{"canonical_hash":"9ead2b476c2bdd8520f60fd7863ed3cee0eaa181ad5624699f3e603a513b1ea5","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,20,13,2,14,37,24,17,6,4,35,58,60,8,28,57,11,43,21,52,32,7,30,36,56,9,49,45,46,38,55,47,16,48,18,25,54,42,12,41,44,23,19,15,50,3,33,40,29,26,51,34,39,31,5,22,27,59,10,53","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/9ead2b476c2bdd8520f60fd7863ed3cee0eaa181ad5624699f3e603a513b1ea5.txt"},{"canonical_hash":"1a41aeda4f8fd79533ccd70ff523114d70a84014a61bb93b72e8eeda04e65e90","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,32,40,42,39,54,22,31,8,35,38,34,57,20,19,13,55,9,30,21,59,7,56,18,25,45,15,24,47,49,5,10,50,33,52,37,28,16,11,27,44,2,53,26,60,46,29,41,51,48,17,4,14,23,12,58,3,6,36,43","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/1a41aeda4f8fd79533ccd70ff523114d70a84014a61bb93b72e8eeda04e65e90.txt"},{"canonical_hash":"09a525dc5c4006d1a4ad789b4f20de96b39a0407c55b521ebc9dc0f67a28f199","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,10,26,15,51,38,55,13,32,31,21,50,14,39,46,56,41,4,34,49,35,33,40,9,16,30,12,2,52,29,17,25,23,42,28,45,58,27,5,11,43,18,37,8,53,44,59,47,60,57,6,7,20,54,48,24,19,22,3,36","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4) (the unique F_5 linear satisfying eq677). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). Not isomorphic to any F_61-linear magma — those are 82a4911c, d5df0d93, e70931b6, f2d8c865. Same family as the existing Steiner S(2,5,61) magma 03138da9 in the database.","submitted_at":"2026-04-23 21:19:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/09a525dc5c4006d1a4ad789b4f20de96b39a0407c55b521ebc9dc0f67a28f199.txt"},{"canonical_hash":"4706da12746a98bb04f275c62a522a35559c80874bcb2c711ef61d01ef4e7956","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,13,11,30,53,41,16,17,24,3,44,29,21,43,31,58,60,7,42,27,10,26,15,19,39,59,5,38,2,36,47,32,56,4,46,18,14,33,22,50,12,28,8,40,57,6,25,51,52,54,48,34,49,20,37,35,45,9,55,23","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/4706da12746a98bb04f275c62a522a35559c80874bcb2c711ef61d01ef4e7956.txt"},{"canonical_hash":"f3c3816472baadd25245de7e6c90a2fddbbdeba139b7d0e689fa8bb84bd183b0","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,32,23,56,15,26,20,11,53,18,7,41,55,5,42,34,31,16,51,17,21,35,37,13,28,6,60,43,48,10,44,22,52,29,59,50,57,54,14,12,36,8,9,58,47,3,38,19,2,25,46,39,4,40,30,45,49,24,33,27","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/f3c3816472baadd25245de7e6c90a2fddbbdeba139b7d0e689fa8bb84bd183b0.txt"},{"canonical_hash":"3f913a91790e319928103cd329fba1403347104b9e8bd1f4c83e132299d253c8","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,12,26,9,4,24,57,60,31,7,53,15,52,19,59,28,3,18,22,20,33,49,43,58,29,46,23,50,47,8,44,51,27,14,6,21,41,54,35,16,37,34,40,32,10,25,42,5,13,2,55,39,36,48,17,45,56,30,11,38","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:19:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/3f913a91790e319928103cd329fba1403347104b9e8bd1f4c83e132299d253c8.txt"},{"canonical_hash":"05fbff2cbfe3711de697b9352e1668424e4f986c475611652b7c984992c68aff","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,12,27,13,4,59,25,29,45,56,14,2,54,17,7,20,3,5,46,23,48,47,10,34,41,30,31,19,37,24,53,55,58,18,49,16,9,28,6,26,51,32,60,40,8,57,44,52,39,50,38,11,22,35,43,21,15,36,33,42","comment":"Z_3-symmetric Steiner-line magma at size 61.\n\nSize 61, fully idempotent, RC. 183 size-5 sub-magmas (= F_5 affine line magma#e549b5f8). Every pair lies in exactly one block; each element in 15 blocks.\n\n|Aut(M)| = 183 = 3 * 61. Aut is Z_61 : Z_3: regular Z_61 acting by translation, and Z_3 = {1, 13, 47} (= the order-3 subgroup of F_61*, since 60 = 4*15 = 12*5 = 20*3, the order-3 subgroup is {1, 13, 47} where 13^3 = 47^3 = 1 mod 61). The Z_3 acts by multiplication.\n\nIn the F_61 translation labeling (suggested reorder), the operation is x*y = x + f(y - x) where f is c-equivariant for c in {1, 13, 47}: f(13y) = 13 f(y) and f(47y) = 47 f(y). Equivalently, the slope function alpha(y) = f(y)/y is constant on the 20 Z_3-orbits of size 3 that partition F_61* = {1, ..., 60}.\n\nSlope analysis: alpha takes 16 distinct values across the 20 Z_3-orbits, all non-Phi_10 roots (i.e., NONE of {3, 27, 41, 52} appear as slopes!):\n  alpha in {4, 6, 7, 8, 10, 17, 18, 19, 23, 29, 35, 40, 45, 46, 51, 55}\n  4 slopes occur on 2 Z_3-orbits each (size-6 slope classes)\n  12 slopes occur on 1 Z_3-orbit each (size-3 slope classes)\nThis is structurally unusual: a translation-invariant magma whose slope function avoids all Phi_10 roots. The 16 chosen slopes satisfy a non-trivial Eq 677 functional equation jointly with the Z_3 equivariance.\n\nCompared to magma#0bcf3cca (the Z_15-symmetric variant): magma#0bcf3cca uses ONLY Phi_10-root slopes; this magma uses ONLY non-Phi_10-root slopes. The two represent opposite extremes of how the Z_61-translation structure can interact with multiplicative symmetry.\n\nAmong the 36 size-61 Eq 677 magmas: 4 linear (|Aut|=3660), 1 with Z_15 stabilizer (magma#0bcf3cca, |Aut|=915), this one with Z_3 stabilizer (|Aut|=183), and 30 with only translation symmetry (|Aut|=61).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:19:56","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/05fbff2cbfe3711de697b9352e1668424e4f986c475611652b7c984992c68aff.txt"},{"canonical_hash":"2426bbe0d2878d01a935bde77346bd813af42339ce250a95c2f327aad53574eb","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,9,12,59,47,58,60,45,16,17,27,48,56,46,15,19,10,22,26,43,28,50,52,7,37,13,38,36,6,25,33,20,8,39,32,53,42,51,5,14,2,40,34,24,29,11,57,44,30,18,49,41,54,35,4,23,31,55,3,21","comment":"Translation-only Steiner-line magma at size 61, \"half-Phi-tribe\" slope pattern.\n\nSize 61, fully idempotent, RC. 183 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8). |Aut(M)| = 61 (only Z_61 translation).\n\nIn the F_61 translation labeling, x*y = x + f(y - x). Slope alpha(y) = f(y)/y takes 12 distinct values:\n  4 Phi_10 root slopes {3, 27, 41, 52}, each on a size-7 subset (28 elements total)\n  8 non-Phi_10 slopes {7, 10, 21, 30, 32, 35, 55, 59}, each on a size-4 subset (32 elements total)\n\nThe 8 non-Phi slopes form 4 inverse pairs in F_61*: {7,35}, {10,55}, {21,32}, {30,59}.\n\nThis (Phi-sum=28) fingerprint is shared by exactly 2 magmas in the DB: this one and magma#ec9ec6f6. Both belong to the same \"Phi+inverse-pair tribe\" as magma#0bcf3cca (Phi-sum=60), magma#e87f6bb9 (Phi-sum=44). All four magmas use the same 12-element slope value set {3, 7, 10, 21, 27, 30, 32, 35, 41, 52, 55, 59} = (4 Phi_10 roots) union (8 non-Phi inverse-paired extras). They differ in how those 12 values are assigned to the 60 elements of F_61*.\n\nThe other ~26 translation-only Steiner-line magmas at size 61 use larger and more chaotic slope-value sets.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:19:58","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/2426bbe0d2878d01a935bde77346bd813af42339ce250a95c2f327aad53574eb.txt"},{"canonical_hash":"9aee6a69115859cdf001ba9bb3af50f19d3f4bc9c1ee9237cc073fc8ee231fa3","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,22,3,29,24,42,39,30,48,57,58,53,60,18,54,16,33,49,20,25,47,35,56,43,55,19,28,45,14,40,27,50,12,2,4,34,26,13,46,10,8,38,9,59,44,52,17,23,31,37,7,15,11,51,6,21,36,32,41,5","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:01","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/9aee6a69115859cdf001ba9bb3af50f19d3f4bc9c1ee9237cc073fc8ee231fa3.txt"},{"canonical_hash":"b175c0f43b21da014cc71111bc9d7015ab000b5b8cb3df961e4cb4a98380d4cf","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,22,23,6,43,47,48,4,18,41,49,44,32,53,10,24,45,42,28,55,16,5,3,11,60,25,21,50,35,31,36,46,52,12,14,39,57,29,17,54,56,19,33,38,30,34,8,27,9,26,37,2,7,20,59,51,15,58,13,40","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:04","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/b175c0f43b21da014cc71111bc9d7015ab000b5b8cb3df961e4cb4a98380d4cf.txt"},{"canonical_hash":"e87f6bb9ba969573393484affe37922297c8a96cc7555bbbc348b2ae2ed49b3d","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,41,33,8,14,53,2,10,39,16,55,24,59,47,42,11,35,30,36,20,7,29,50,37,27,19,9,52,12,28,40,45,13,46,44,17,56,23,4,22,60,6,51,48,32,43,21,5,57,49,26,15,34,38,31,25,54,18,3,58","comment":"Translation-only Steiner-line magma at size 61, \"near-Z_15-symmetric\" slope pattern.\n\nSize 61, fully idempotent, RC. 183 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8). |Aut(M)| = 61 (only Z_61 translation, no multiplicative stabilizer).\n\nIn the F_61 translation labeling, x*y = x + f(y - x) with f a non-linear permutation. Slope alpha(y) = f(y)/y takes 12 distinct values in F_61* on the 60 non-zero residues:\n  4 Phi_10 root slopes {3, 27, 41, 52}, each on a size-11 subset (44 elements total)\n  8 non-Phi_10 slopes {7, 10, 21, 30, 32, 35, 55, 59}, each on a size-2 subset (16 elements total)\n\nThe 8 non-Phi slopes form 4 inverse pairs in F_61*: {7, 35}, {10, 55}, {21, 32}, {30, 59} (each pair multiplies to 1 mod 61). The 4 Phi_10 roots also pair as {3, 41} and {27, 52}.\n\nThis magma is the unique Phi-sum=44 variant in the DB. It is the \"closest approximation\" to the fully Z_15-symmetric magma#0bcf3cca (which has Phi-sum = 60) among the translation-only Steiner-line magmas at size 61: of the 60 nonzero residues, 44 receive Phi_10-root slopes and only 16 deviate. The 16 deviating elements are sprinkled across F_61* as 8 inverse pairs.\n\nCompare with magma#2426bbe0, magma#ec9ec6f6 (the Phi-sum=28 pair: 4 Phi-slopes on size-7 + 8 non-Phi on size-4) - sharing the same 12-element slope value set. These four magmas (including this one) form a \"tribe\" using the unique 12-value slope set {3, 7, 10, 21, 27, 30, 32, 35, 41, 52, 55, 59} (= 4 Phi_10 roots + 8 inverse-paired extras).\n\nThe other ~26 translation-only Steiner-line magmas at size 61 use larger, more chaotic slope-value sets (typically 20-34 distinct values).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:06","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/e87f6bb9ba969573393484affe37922297c8a96cc7555bbbc348b2ae2ed49b3d.txt"},{"canonical_hash":"b8ecd85435377cb9d2fecfd7bc1ebb7a97553c424d83c7fba1b6a66479a59321","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,19,25,29,20,15,9,34,4,31,6,38,10,57,28,14,18,60,27,32,11,2,39,52,13,37,35,21,54,22,40,55,49,50,16,24,23,45,17,26,42,59,41,44,30,3,5,8,47,43,48,46,36,12,51,33,56,58,53,7","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:08","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/b8ecd85435377cb9d2fecfd7bc1ebb7a97553c424d83c7fba1b6a66479a59321.txt"},{"canonical_hash":"fc63e2bd6cd94fe49b2d51d39cf1a76badc08b24ac8f870093097593494fa256","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,9,29,58,20,14,27,43,18,13,5,51,22,30,60,59,26,53,11,7,39,34,47,8,46,40,42,49,28,56,54,50,32,33,52,23,48,24,16,55,41,21,3,25,36,45,19,35,17,2,15,44,37,12,38,4,31,57,6,10","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:11","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/fc63e2bd6cd94fe49b2d51d39cf1a76badc08b24ac8f870093097593494fa256.txt"},{"canonical_hash":"d8c966e4d19c1748943024fc8d085234fc62285c3bda30f20419e41ae7326d9a","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,4,58,7,51,33,55,15,22,60,11,30,44,57,39,13,3,31,20,8,2,27,19,43,26,23,9,6,52,21,10,46,5,12,18,28,40,16,14,48,29,50,54,25,37,47,38,49,41,34,32,42,36,59,56,53,17,24,45,35","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/d8c966e4d19c1748943024fc8d085234fc62285c3bda30f20419e41ae7326d9a.txt"},{"canonical_hash":"ec9ec6f628572f7e4e02ea4feebb657ae8ff71916239d89e655729ae0397f987","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,15,54,46,39,43,2,44,34,27,23,13,56,48,25,45,52,18,41,28,9,17,6,22,24,32,47,12,37,16,35,50,38,51,49,40,57,31,10,30,60,8,7,4,53,20,29,11,58,5,42,36,55,26,19,21,33,14,3,59","comment":"Translation-only Steiner-line magma at size 61, \"half-Phi-tribe\" slope pattern.\n\nSize 61, fully idempotent, RC. 183 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8). |Aut(M)| = 61 (only Z_61 translation).\n\nIn the F_61 translation labeling, x*y = x + f(y - x). Slope alpha(y) = f(y)/y takes 12 distinct values:\n  4 Phi_10 root slopes {3, 27, 41, 52}, each on a size-7 subset (28 elements total)\n  8 non-Phi_10 slopes {7, 10, 21, 30, 32, 35, 55, 59}, each on a size-4 subset (32 elements total)\n\nThe 8 non-Phi slopes form 4 inverse pairs in F_61*: {7,35}, {10,55}, {21,32}, {30,59}.\n\nThis (Phi-sum=28) fingerprint is shared by exactly 2 magmas in the DB: this one and magma#2426bbe0. Both belong to the same \"Phi+inverse-pair tribe\" as magma#0bcf3cca (Phi-sum=60), magma#e87f6bb9 (Phi-sum=44). All four magmas use the same 12-element slope value set {3, 7, 10, 21, 27, 30, 32, 35, 41, 52, 55, 59} = (4 Phi_10 roots) union (8 non-Phi inverse-paired extras). They differ in how those 12 values are assigned to the 60 elements of F_61*.\n\nThe other ~26 translation-only Steiner-line magmas at size 61 use larger and more chaotic slope-value sets.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:16","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/ec9ec6f628572f7e4e02ea4feebb657ae8ff71916239d89e655729ae0397f987.txt"},{"canonical_hash":"343090d1aa23a5ec1732c81bd3a2921ef36f3db43b2121d0d14767fc3f3fa179","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,22,43,60,18,44,41,19,49,11,27,6,52,53,9,2,55,38,42,17,12,21,29,47,28,36,15,26,54,56,7,14,4,24,51,23,57,46,25,34,10,50,30,20,39,45,37,8,35,33,5,3,32,58,40,16,31,13,48,59","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:18","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/343090d1aa23a5ec1732c81bd3a2921ef36f3db43b2121d0d14767fc3f3fa179.txt"},{"canonical_hash":"2e8995b35c2f059349bca5ab1f1c01c7aeb5e4fea64e5c830b6093dcf29f66bb","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,19,38,24,53,23,11,22,34,25,32,13,58,40,20,52,48,60,7,9,35,37,31,18,55,14,8,54,44,10,45,16,3,57,50,4,2,46,30,56,47,41,43,26,28,39,36,59,27,49,5,12,29,51,6,21,15,17,33,42","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:21","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/2e8995b35c2f059349bca5ab1f1c01c7aeb5e4fea64e5c830b6093dcf29f66bb.txt"},{"canonical_hash":"be4a14bddbeb724f0ff30600f68bf166b4f710992addfb372353c168fea8611b","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,18,53,19,51,2,22,46,7,11,28,49,59,23,29,24,36,43,27,14,55,48,12,21,42,45,4,32,52,54,25,10,50,44,60,6,20,57,15,47,5,16,37,38,34,41,9,40,39,56,8,17,3,58,26,33,30,35,13,31","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/be4a14bddbeb724f0ff30600f68bf166b4f710992addfb372353c168fea8611b.txt"},{"canonical_hash":"e1aef7169f2675f0eba4c0ac28de86191fef20e49964d073021640400e402995","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,44,7,22,33,18,50,56,29,32,40,60,14,48,39,53,2,24,3,11,17,30,42,15,37,20,27,43,13,41,12,23,45,8,59,4,46,58,52,9,21,54,28,6,19,38,31,57,10,36,26,55,16,34,35,49,51,5,25,47","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/e1aef7169f2675f0eba4c0ac28de86191fef20e49964d073021640400e402995.txt"},{"canonical_hash":"1bdfe90eff0047ea6200fee85ed2eb02a5b13c73d44937de4d05b3d7f4e78e69","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,45,26,20,22,43,35,19,27,10,32,55,13,24,44,3,25,30,54,23,52,50,4,36,58,49,6,33,34,8,53,59,14,56,42,11,17,29,12,2,9,40,51,60,5,16,15,21,28,38,47,31,46,41,37,18,57,39,48,7","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/1bdfe90eff0047ea6200fee85ed2eb02a5b13c73d44937de4d05b3d7f4e78e69.txt"},{"canonical_hash":"2fd6ffbaec2d58f44601af97d8f84048b4ec43eaeb681a15caba4123389994fb","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,31,13,32,8,38,27,14,60,33,18,52,47,6,4,23,12,34,30,43,10,41,7,9,44,22,3,45,50,29,37,28,48,55,15,35,20,57,21,24,5,16,59,56,51,11,25,49,19,46,39,58,42,54,36,2,26,53,17,40","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:32","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/2fd6ffbaec2d58f44601af97d8f84048b4ec43eaeb681a15caba4123389994fb.txt"},{"canonical_hash":"8b9a92d13745d7e076940966d071d559d96dce4e031aa2ebb2424c447087c978","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,6,24,18,48,19,32,54,27,23,25,43,10,4,21,8,42,44,50,58,37,53,45,59,39,34,7,11,33,28,57,38,22,31,41,16,15,49,20,56,60,36,40,55,2,26,47,13,46,29,30,3,51,35,9,52,14,12,17,5","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/8b9a92d13745d7e076940966d071d559d96dce4e031aa2ebb2424c447087c978.txt"},{"canonical_hash":"ebea3e11487c6655e73ecb3497d2a5e85d65a8de229650fc24ef9501d9991759","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,7,23,8,60,53,35,59,10,54,21,16,32,3,29,48,50,9,55,4,49,46,57,41,45,27,36,25,19,51,42,17,20,24,33,31,39,28,6,44,13,58,22,30,34,5,18,43,56,2,40,15,12,11,52,26,14,38,47,37","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/ebea3e11487c6655e73ecb3497d2a5e85d65a8de229650fc24ef9501d9991759.txt"},{"canonical_hash":"b8dc6b8872614b853eebdb68c614577f96303fefda33f88e0122f63c856347dc","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,34,20,60,31,16,22,28,13,44,37,48,10,8,47,3,11,42,21,29,59,4,35,7,18,49,58,38,9,55,33,56,19,39,15,41,53,43,36,25,46,12,6,50,32,51,17,45,27,24,5,2,26,52,23,30,40,57,14,54","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/b8dc6b8872614b853eebdb68c614577f96303fefda33f88e0122f63c856347dc.txt"},{"canonical_hash":"c27cf8c7f8876d33337d813add63a796ec747bb90458db90feaa0653d9006583","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,18,31,5,21,19,47,43,55,15,28,42,6,23,51,48,12,3,10,13,34,14,57,53,8,27,17,33,44,59,35,7,60,20,58,26,29,25,41,38,16,2,37,32,39,56,40,50,24,4,22,52,54,46,9,36,49,30,11,45","comment":"Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.","submitted_at":"2026-04-23 21:20:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/61/c27cf8c7f8876d33337d813add63a796ec747bb90458db90feaa0653d9006583.txt"},{"canonical_hash":"0bcf3cca3be57625671ff27dc41a0c8250ad2b8ff8c5d52d4bb3b1212cb4f322","size":61,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,15,11,18,44,36,2,21,25,13,51,31,9,54,56,43,37,40,41,59,12,4,24,23,42,6,55,50,10,58,38,32,48,7,14,30,22,16,47,29,3,8,49,52,5,57,26,28,53,34,27,33,35,20,39,17,46,19,60,45","comment":"The most symmetric Eq 677 Steiner-line magma at size 61.\n\nSize 61, fully idempotent, RC. 183 size-5 sub-magmas (each = the F_5 affine line magma#e549b5f8). Every pair of distinct elements lies in exactly one block; each element is in 15 blocks.\n\n|Aut(M)| = 915 = 15 * 61. Aut is the Frobenius-style group Z_61 : Z_15: the regular Z_61 acts by translation, and the point-stabilizer is the order-15 subgroup of F_61* = {1, 9, 12, 13, 15, 16, 20, 22, 25, 34, 42, 47, 56, 57, 58} (= (F_61*)^4, the unique cyclic subgroup of order 15), acting by multiplication.\n\nIn the suggested reorder, F_61 labeling makes translation x -> x+1 an automorphism. The operation is then x*y = x + f(y - x) mod 61 with f(y) = alpha(y) * y, where alpha takes each of the 4 Phi_10 roots {3, 27, 41, 52} on exactly one coset of (F_61*)^4 in F_61*. Specifically (in the chosen F_61 labeling):\n  coset 0 (= (F_61*)^4 itself, containing 1):  alpha = 41\n  coset 1 (containing 2):                       alpha = 52\n  coset 2 (containing 3):                       alpha = 3\n  coset 3 (containing 6):                       alpha = 27\nEach Phi_10 root is assigned to exactly one of the 4 (F_61*)^4-cosets, and the slope class sizes are 15+15+15+15 = 60 (= |F_61*|).\n\nThis is the analog of magma#b7e8bf90 at size 41, with the same recipe: take the unique multiplicative subgroup of (F_q*)^4 in F_q* (q ≡ 1 mod 10), assign the 4 Phi_10 roots to its 4 cosets, and define f(y) = alpha(coset of y) * y. The compatibility conditions for Eq 677 force a specific assignment of Phi_10 roots to cosets (essentially unique up to Galois conjugation).\n\nAmong the 36 size-61 Eq 677 magmas, this is the unique one with |Aut| = 915. The Z_15 stabilizer is the highest non-trivial multiplicative stabilizer; the only other multi-stabilizer magma at size 61 is magma#05fbff2c with Z_3 stabilizer (|Aut| = 183). The other 30 Steiner-line magmas have only Z_61 translation symmetry (|Aut| = 61). And the 4 linear F_61 magmas have |Aut| = 3660.\n\n[text written by Claude]","submitted_at":"2026-05-12 08:53:00","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/61/0bcf3cca3be57625671ff27dc41a0c8250ad2b8ff8c5d52d4bb3b1212cb4f322.txt"},{"canonical_hash":"cc548f7353efc76265ce438f2caa716a3ad7190b8a251735121a3a48e0d4a4e1","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,54,59,58,60,57,55,61,56,48,11,2,12,10,9,46,5,3,49,19,1,20,18,17,42,6,4,53,15,0,16,14,13,47,7,8,50,33,30,34,32,31,44,28,29,51,37,41,38,36,35,45,39,40,52,23,27,24,22,21,43,25,26","comment":"Direct product of two linear magmas: F_7(4,1) × F_9.","submitted_at":"2026-04-23 21:20:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/cc548f7353efc76265ce438f2caa716a3ad7190b8a251735121a3a48e0d4a4e1.txt"},{"canonical_hash":"ffd9f7c3b502fd1625d93f6a29d155b17cd2a096a045bfa5ec565b7742bf2deb","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,48,52,51,53,50,49,54,55,56,43,11,36,30,17,24,5,42,61,15,3,28,22,9,40,2,34,57,41,29,10,4,35,47,23,16,59,7,0,20,38,45,32,13,26,58,25,37,18,12,19,6,31,44,60,33,21,46,1,27,14,39,8","comment":"Direct product of two linear magmas: F_7(4,3) × F_9.","submitted_at":"2026-04-23 21:20:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/ffd9f7c3b502fd1625d93f6a29d155b17cd2a096a045bfa5ec565b7742bf2deb.txt"},{"canonical_hash":"832468c3d44940b64768c63ac8e098aa45eb6fe656142a411cf4217d78340d56","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,54,59,61,56,55,57,58,60,12,32,38,26,50,0,45,6,20,15,35,40,28,48,4,47,9,19,14,33,39,27,49,1,44,8,18,17,31,37,25,52,2,42,11,23,13,30,36,24,51,5,43,7,21,16,34,41,29,53,3,46,10,22","comment":"Size-63 (= 7 × 9) right-cancellative fiber bundle: F_7(4, 1) base × F_9(3, 7) fiber, in the \"twisted\" Family B variant. The 63 elements partition into 7 fibers of 9 (a non-trivial congruence with F_7 quotient), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, which is isomorphic to F_9(3, 7) (a linear magma over the field F_9 = F_3²). The other 6 fibers are congruence classes that are NOT closed under ◇. The full magma is a quasigroup (LC + RC) with a unique idempotent. Analogous to the size-77 F_7 × F_11 family-B and size-91 F_7 × F_13 family-B magmas in the database.","submitted_at":"2026-04-23 21:20:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/832468c3d44940b64768c63ac8e098aa45eb6fe656142a411cf4217d78340d56.txt"},{"canonical_hash":"42d78fdb27ce9af377b1ab245df9d9443d767b536cb3712e40b6f43e6babb0d8","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,0,4,6,1,7,2,3,5,8,18,22,29,32,43,44,55,57,12,17,20,31,33,42,45,54,58,9,16,23,26,37,39,48,51,60,10,19,21,30,34,41,46,53,56,13,15,24,28,35,40,49,50,61,11,14,25,27,36,38,47,52,59","comment":"Size-63 (= 7 × 9) right-cancellative fiber bundle: F_7(4, 3) base × F_9(3, 7) fiber, in the \"twisted\" Family B variant. The 63 elements partition into 7 fibers of 9 (a non-trivial congruence with F_7 quotient), but only ONE fiber is itself a sub-magma — the fiber at the F_7-idempotent coset, isomorphic to F_9(3, 7). The other 6 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 21:20:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/42d78fdb27ce9af377b1ab245df9d9443d767b536cb3712e40b6f43e6babb0d8.txt"},{"canonical_hash":"abfcc2525483f7084fdf58ede34fe0a68ce576a3898bcf3bdbbec627d325e49b","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,40,41,44,42,43,45,24,51,9,57,0,34,22,28,46,12,60,6,37,17,29,49,10,61,3,33,21,26,52,15,56,5,32,16,31,50,8,54,7,35,20,27,53,14,55,1,36,18,25,47,13,58,4,38,23,30,48,11,59,2,39,19","comment":"Size-63 (= 9 × 7) right-cancellative fiber bundle: F_9(3, 7) base × F_7(4, 1) fiber, in the \"twisted\" Family B variant. The 63 elements partition into 9 fibers of 7 (a non-trivial congruence with F_9 quotient over the extension field F_9 = F_3²), but only ONE fiber is itself a sub-magma — the fiber at the F_9-idempotent coset, isomorphic to F_7(4, 1). The other 8 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 21:20:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/abfcc2525483f7084fdf58ede34fe0a68ce576a3898bcf3bdbbec627d325e49b.txt"},{"canonical_hash":"e83035650a112a4626b8c7ce1675cd9b58ab3b164a3e70252b4d03aa47124247","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,56,61,57,59,58,60,13,19,42,32,0,48,30,8,16,46,35,3,53,31,14,20,45,33,2,55,24,10,21,41,38,7,50,27,11,22,40,34,4,49,28,15,18,47,36,1,51,29,9,23,44,37,6,52,26,12,17,43,39,5,54,25","comment":"Size-63 (= 9 × 7) right-cancellative fiber bundle: F_9(3,7) base × F_7(4,3) fiber, in the \"twisted\" Family B variant. The 63 elements partition into 9 fibers of 7 (a non-trivial congruence with F_9 quotient over the extension field F_9 = F_3²), but only ONE fiber is itself a sub-magma — the fiber at the F_9-idempotent coset, isomorphic to F_7(4,3). The other 8 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent. The database contains 3 inequivalent (non-isomorphic) Family B twists with this same F_9(3,7) × F_7(4,3) skeleton: e8303565, aa98186d, and a24a85fe — they share the same fiber-bundle structure but differ by non-trivial cocycle twists across fibers.","submitted_at":"2026-04-23 21:20:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/e83035650a112a4626b8c7ce1675cd9b58ab3b164a3e70252b4d03aa47124247.txt"},{"canonical_hash":"9b3f61babba7023b3ac27b5449355faf40f8519d426ff548bf5e28048942c25e","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,60,24,1,16,41,3,8,17,4,35,29,5,34,45,7,54,12,9,33,36,11,46,27,13,55,25,15,39,47,19,57,31,20,23,21,26,58,37,38,56,43,40,2,52,32,6,62,22,10,50,42,14,51,61,18,53,30,28,48,59,44,49","comment":"Size-63 non-idempotent right-cancellative magma satisfying Eq 677 and Eq 255. A genuinely sporadic structure — neither a fiber-bundle / direct product, nor a translation-invariant magma in any abelian group sense.\n\nAut(M) has order 48 and acts on the 63 elements with 4 orbits of sizes (1, 6, 8, 48):\n\n  • Orbit {62}: a single fixed element — the unique idempotent of M (verified directly).\n  • Orbit {48, 49, 50, 51, 52, 53}: six elements. Together with 62, they form a unique 7-element sub-magma isomorphic to magma#7981e2df (the linear F_7 magma x ◇ y = 4x + y mod 7).\n  • Orbit {54, 55, 56, 57, 58, 59, 60, 61}: eight elements. Together with 62, they form a unique 9-element sub-magma isomorphic to magma#2925dc18 (the linear Z/9Z magma x ◇ y = x + 3y mod 9).\n  • Orbit {0, 1, …, 47}: 48 elements (the 'free' / off-axis points), acted on REGULARLY by Aut(M) — orbit size equals |Aut|, so the action there is a faithful regular representation.\n\nSub-magma counts: there are EXACTLY one size-7 sub-magma and EXACTLY one size-9 sub-magma (besides the trivial size-1 sub-magma {62}). Every other pair (out of 1896 of the C(63, 2) = 1953 pairs) generates the full 63-element magma — i.e. the magma is 'almost everywhere 2-generated'.\n\nWhy this is NOT an F_7 × F_9 direct product: a direct product would have 7 + 9 = 16 axes (7 rows + 9 columns) as sub-magmas of size 9 and 7 respectively. We observe only 1 + 1 = 2 such sub-magmas, so this is not a product structure.\n\nR_0 = T[·, 0] has uniform cycle structure (3²¹) — order 3, with 21 orbits of length 3. The R_0 cycles decompose by Aut-orbit composition as follows: 8 cycles entirely in the 48-orbit; 6 mixed (F_9 element + 2 free); 4 mixed (F_7 element + 2 free); 2 mixed (F_7 + F_9 + free) — these are the 'bridge' cycles linking the two special sub-magmas; 1 mixed (2 free + idempotent 62). Total 8+6+4+2+1 = 21 ✓. So R_0 mixes elements across all four Aut-orbits.\n\nL_0 = T[0, ·] has mixed cycle structure (1, 6, 8, 24, 24) — orders 1, 6, 8, 24 mixed. Compare to R_0's uniform order 3: the magma has highly asymmetric left vs right behaviour.\n\nS map (x ↦ x ◇ x): not a permutation. Only one S-fixed point (the unique idempotent 62). The existing display_reorder organizes elements by the 21 R_0 cycles (with the 7 'S-anchored' cycles — those whose elements eventually map to 62 under iterated S — placed together).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/9b3f61babba7023b3ac27b5449355faf40f8519d426ff548bf5e28048942c25e.txt"},{"canonical_hash":"aa98186d6c35a24d1477133f874cd8b977e362969f96407f1551154b079ab268","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,56,61,57,59,58,60,40,0,29,15,22,36,52,46,18,4,32,25,49,11,9,16,30,50,7,8,23,39,14,53,28,35,1,21,47,51,43,44,45,42,41,38,27,20,54,2,13,34,37,55,33,19,12,26,3,6,31,10,5,48,17,24","comment":"Size-63 (= 9 × 7) right-cancellative fiber bundle: F_9(3,7) base × F_7(4,3) fiber, in the \"twisted\" Family B variant. The 63 elements partition into 9 fibers of 7 (a non-trivial congruence with F_9 quotient over the extension field F_9 = F_3²), but only ONE fiber is itself a sub-magma — the fiber at the F_9-idempotent coset, isomorphic to F_7(4,3). The other 8 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent. The database contains 3 inequivalent (non-isomorphic) Family B twists with this same F_9(3,7) × F_7(4,3) skeleton: e8303565, aa98186d, and a24a85fe — they share the same fiber-bundle structure but differ by non-trivial cocycle twists across fibers.","submitted_at":"2026-04-23 21:20:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/aa98186d6c35a24d1477133f874cd8b977e362969f96407f1551154b079ab268.txt"},{"canonical_hash":"a24a85feef58ddab4c391c9a1de4c871b079971f7b4143c6d1225a457f6447d5","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,56,61,57,59,58,60,25,16,41,50,39,0,14,26,21,45,54,38,4,10,31,19,40,49,36,2,9,30,20,42,51,37,1,8,27,22,47,48,33,7,11,28,23,43,52,32,6,12,24,18,46,53,35,5,15,29,17,44,55,34,3,13","comment":"Size-63 (= 9 × 7) right-cancellative fiber bundle: F_9(3,7) base × F_7(4,3) fiber, in the \"twisted\" Family B variant. The 63 elements partition into 9 fibers of 7 (a non-trivial congruence with F_9 quotient over the extension field F_9 = F_3²), but only ONE fiber is itself a sub-magma — the fiber at the F_9-idempotent coset, isomorphic to F_7(4,3). The other 8 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent. The database contains 3 inequivalent (non-isomorphic) Family B twists with this same F_9(3,7) × F_7(4,3) skeleton: e8303565, aa98186d, and a24a85fe — they share the same fiber-bundle structure but differ by non-trivial cocycle twists across fibers.","submitted_at":"2026-04-23 21:20:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/a24a85feef58ddab4c391c9a1de4c871b079971f7b4143c6d1225a457f6447d5.txt"},{"canonical_hash":"607a07969134cfa88efe22510846af60e37ae7aefc80b511768d1286f0e9b101","size":63,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,3,1,4,7,5,15,35,51,16,31,48,18,36,50,19,30,52,20,37,47,21,33,53,22,40,54,23,41,55,24,45,57,25,43,56,26,42,61,28,38,58,49,14,62,17,34,8,6,2,9,44,60,12,27,39,10,32,46,11,59,29,13","comment":"F_7(4, 1) sub-magma S={8,9,10,11,12,13,62} + 21 R_0 cycles of 3 (14 non-S + 7 anchored). Contains an F_7 sub-magma; the remaining elements partition into R_0-cycles of length 3 (right-multiplication by 0 acts as a permutation of order 3 there).","submitted_at":"2026-04-23 21:20:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/63/607a07969134cfa88efe22510846af60e37ae7aefc80b511768d1286f0e9b101.txt"},{"canonical_hash":"5e80e1c2dc82944cee69cb7089d21c45f5ab65bc382c5d130a060fbb3f31d2ae","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"60,3,44,5,16,40,36,29,33,9,12,25,20,61,0,47,4,17,43,39,31,35,8,13,27,21,62,1,46,6,18,42,38,30,34,10,14,26,22,64,54,50,55,58,49,48,53,51,59,57,52,56,63,2,45,7,19,41,37,28,32,11,15,24,23","comment":"Direct product of two linear magmas: F_5 × F_13. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 9x₂ + 11y₂ (mod 13)).","submitted_at":"2026-04-23 21:20:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/5e80e1c2dc82944cee69cb7089d21c45f5ab65bc382c5d130a060fbb3f31d2ae.txt"},{"canonical_hash":"b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,8,9,10,11,60,12,18,22,26,30,34,39,43,47,51,55,59,62,14,19,23,27,31,35,36,40,44,49,53,57,61,15,17,21,25,29,33,38,42,46,50,54,58,63,13,16,20,24,28,32,37,41,45,48,52,56,64","comment":"F_5(2, 4) base × F_13 fiber: 5 fibers of 13 (each = F_13 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:20:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0.txt"},{"canonical_hash":"b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,8,9,10,11,62,12,13,14,15,16,17,18,19,20,21,22,23,63,48,49,50,51,52,53,54,55,56,57,58,59,64,36,37,38,39,40,41,42,43,44,45,46,47,60,24,25,26,27,28,29,30,31,32,33,34,35,61","comment":"F_5(2, 4) base × F_13 fiber: 5 fibers of 13 (each = F_13 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:20:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2.txt"},{"canonical_hash":"3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,6,64,5,11,4,10,3,9,2,8,1,7,12,25,63,23,35,21,33,19,31,17,29,15,27,37,49,61,47,59,45,57,43,55,41,53,39,51,36,48,60,46,58,44,56,42,54,40,52,38,50,13,24,62,22,34,20,32,18,30,16,28,14,26","comment":"F_5(2,4) base × F_13 fiber w/ within-fiber smoothing (c=6). Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:20:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d.txt"},{"canonical_hash":"f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,8,9,10,11,62,12,13,14,15,16,17,18,19,20,21,22,23,61,48,49,50,51,52,53,54,55,56,57,58,59,60,36,37,38,39,40,41,42,43,44,45,46,47,63,24,25,26,27,28,29,30,31,32,33,34,35,64","comment":"F_5(2, 4) base × F_13 fiber: 5 fibers of 13 (each = F_13 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:20:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9.txt"},{"canonical_hash":"22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,8,9,10,11,61,12,13,14,15,16,17,18,19,20,21,22,23,63,48,49,50,51,52,53,54,55,56,57,58,59,60,36,37,38,39,40,41,42,43,44,45,46,47,62,24,25,26,27,28,29,30,31,32,33,34,35,64","comment":"F_5(2, 4) base × F_13 fiber: 5 fibers of 13 (each = F_13 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:20:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf.txt"},{"canonical_hash":"17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"62,0,37,23,50,11,32,18,45,6,42,28,55,64,1,39,19,58,10,34,29,53,5,59,24,48,61,2,35,27,57,12,30,22,52,7,40,17,47,63,3,33,16,49,13,43,26,44,8,38,21,54,60,4,31,20,56,14,41,15,51,9,36,25,46","comment":"Non-idempotent fiber-bundle magma at size 65, with a \"pivot F_5 + 5 petals of 12\" structure.\n\nSize 65 = 5 * 13 = 5 + 60. Non-fully-idempotent (5 idempotents only), right-cancellative.\n\n**Pivot.** The 5 idempotents {60, 61, 62, 63, 64} form a size-5 sub-magma isomorphic to magma#e549b5f8 (the F_5 affine line). This is the ONLY size-5 (or smaller) sub-magma in M.\n\n**Petals.** The remaining 60 non-idempotent elements split into 5 disjoint \"petals\" of size 12 each, the orbits of left-multiplication by the idempotent 60 (i.e. the function y -> T(60, y) restricted to the non-idempotents). Each petal is a single 12-cycle under this L_60 action. No petal is itself a sub-magma, and no petal-plus-one-idempotent forms a size-13 sub-magma either - so the petal partition is not a congruence in the usual sense.\n\n|Aut(M)| = 60, with exactly 2 Aut-orbits:\n- 1 orbit of size 5 = the 5 idempotents (point-stabilizer 12)\n- 1 orbit of size 60 = all non-idempotents (point-stabilizer 1)\nSo Aut acts transitively on each of the two layers (pivot and petals), permuting petals and rotating within each petal.\n\nStructurally this is a \"twisted\" cousin of the F_5 x F_13 direct product (which would be fully idempotent with 65 idempotents). Here the global magma still has F_5 sub-structure (the idempotent pivot) and a \"5 x 12 = 60 non-idempotent\" layer that *resembles* the (F_13 \\ {0}) factor of an F_5 x F_13 product, but with twisting that breaks both:\n- idempotency on the petal layer (none of the 60 non-idempotents satisfy x*x = x)\n- the would-be 5 x 13 = 65 congruence partition (replaced by 5 x 12 + 5 pivot = 65)\n\nCompare with size 35 magma#c689a91b (5 fibers of 7, each fiber containing 1 idempotent, 5 idempotents total) - same \"split into 5 fibers, idempotents one-per-fiber\" pattern. The size-35 version has fiber size 7 and fully captures the fiber-congruence; this size-65 magma uses fiber size 12 (= 13 - 1) and removes the idempotent from each fiber to a separate pivot.\n\nOther size-65 non-idempotent magmas in the DB:\n- magma#5e80e1c2dc82: pure direct product F_5 * F_13 (would be fully idempotent if base were idempotent, but isn't here)\n- magma#b8dd5d8f5072, magma#b841b444f6b6, magma#f6a46900b44d, magma#22cb8afe1ff0, magma#3a1e3dea0200 (5 magmas): \"F_5(2,4) base x F_13 fiber\" bundles with 5 fibers of 13 (no separate pivot - the idempotent of each fiber sits inside the fiber)\n- magma#3e7f78778326: F_5 base x F_13 fiber with \"within-fiber smoothing\"\n\nThe structural distinction this magma represents: rather than 5 fibers of 13 each (with the idempotent inside the fiber), this magma \"extracts\" the 5 idempotents into a separate F_5 sub-magma and leaves 5 petals of 12 non-idempotents (one petal per idempotent).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1.txt"},{"canonical_hash":"a09c4223a53d9ee14658179f06e2710a6fedf12cd2694adc96da2384fad4d68c","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,45,24,13,37,60,42,14,31,44,57,55,40,28,49,15,43,22,16,25,2,50,11,58,41,4,27,5,6,38,30,20,19,8,3,33,56,29,10,53,36,52,54,63,35,39,48,46,7,59,32,26,62,12,34,9,47,51,61,21,18,23,64,17","comment":"Translation-only Steiner-line magma at size 65 (Type A slope pattern - 5 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design. Each block = the F_5 affine line magma#e549b5f8. |Aut(M)| = 65 (only Z_65 translation, no multiplicative stabilizer).\n\nIn the suggested reorder, Z_65 labeling makes translation x -> x+1 an automorphism. Operation: x*y = x + f(y - x) mod 65.\n\nSlope analysis on Z_65* (48 units): alpha takes 12 distinct values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63}, with the following class sizes (Type A pattern):\n  3 slopes on size-6 classes (sum 18)\n  6 slopes on size-4 classes (sum 24)\n  3 slopes on size-2 classes (sum 6)\nTotal: 18 + 24 + 6 = 48 = |Z_65*|.\n\nThree of the 12 slopes ({15, 35, 45}) are non-units mod 65 (multiples of 5); the other 9 are units and form 4 inverse pairs in Z_65* {3,22}, {21,31}, {32,63}, {34,44} plus the self-inverse 51 (= -14, 51^2 = 1 mod 65).\n\nThis 12-value slope set is exactly the one obtained by taking all Z_65* elements that \"could be Eq 677 multipliers\" plus the 3 multiples of 5. Compare with magma#eff27734 (Z_4-symmetric) which uses only the 4-element subset {3, 22, 35, 51} as slopes - that subset is the Z_4 = <34> stabilizer multiplied by representative slope values.\n\nThis (Type A) slope-class-size pattern is shared by 5 magmas at size 65: this one and magma#86e94818, magma#4d60c34f, magma#bcf3ee89, magma#84076266. They differ in how the 12 slope values are assigned to specific Z_65*-subsets. Other Type B/C patterns (also using the same 12-value slope set) are: Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0), Type C (1 magma: magma#62917c53).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/a09c4223a53d9ee14658179f06e2710a6fedf12cd2694adc96da2384fad4d68c.txt"},{"canonical_hash":"62917c535a9a39410b91578bf68539f1b7a3307d59313de07fe0c7f99fc95c11","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,52,3,23,19,9,55,13,27,7,38,63,22,25,40,33,47,18,20,31,60,48,21,53,35,43,61,15,12,4,64,39,5,37,32,29,51,24,62,58,49,10,34,16,2,57,11,42,50,56,46,44,28,45,41,54,17,59,14,30,6,36,26,8","comment":"Translation-only Steiner-line magma at size 65 (Type C slope pattern - unique variant).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design. |Aut(M)| = 65 (Z_65 translation only).\n\nIn the Z_65 translation labeling, slope analysis on Z_65* shows 12 distinct slope values (same value set {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63} as the other 7 non-Z_4-symmetric Steiner-line magmas at size 65), with the unique Type C class-size pattern:\n  3 slopes on size-9 classes (sum 27)\n  1 slope on a size-8 class\n  5 slopes on size-2 classes\n  3 slopes on size-1 classes\nTotal: 27 + 8 + 10 + 3 = 48 = |Z_65*|.\n\nThis magma is the unique Type C variant in the DB. The presence of 3 size-1 classes is distinctive - 3 specific units in Z_65* receive their own unique slope value, unmatched by any other unit.\n\nCompare:\n  magma#eff27734 (Z_4-symmetric, |Aut|=260, 4 slope values, all classes size 12)\n  Type A (5 magmas: magma#a09c4223, magma#86e94818, magma#4d60c34f, magma#bcf3ee89, magma#84076266 - 3 classes of size 6, 6 of size 4, 3 of size 2)\n  Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0 - 1 class of size 8, 6 of size 5, 5 of size 2)\n  this Type C (this magma alone - 3 classes of size 9, 1 of size 8, 5 of size 2, 3 of size 1)\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/62917c535a9a39410b91578bf68539f1b7a3307d59313de07fe0c7f99fc95c11.txt"},{"canonical_hash":"d8ba33b5c6c7428d429501ddecc764c36a6013c1f007f3eab053a820894a49e8","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,8,24,52,33,6,13,54,59,9,42,16,15,57,49,53,12,29,63,25,2,48,21,43,14,38,26,39,36,32,56,31,62,23,3,46,41,58,20,18,35,17,19,5,45,34,50,10,37,40,44,27,7,55,47,22,11,51,4,28,61,30,64,60","comment":"Translation-only Steiner-line magma at size 65 (Type B slope pattern - 2 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design (each = the F_5 affine line magma#e549b5f8). |Aut(M)| = 65 (Z_65 translation only).\n\nIn the Z_65 translation labeling, x*y = x + f(y - x) mod 65. Slope analysis on Z_65*: 12 distinct slope values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63} (same set as in Type A and Type C - 4 inverse pairs + 1 self-inverse + 3 non-units), but with class sizes following the Type B pattern:\n  1 slope on a size-8 class\n  6 slopes on size-5 classes\n  5 slopes on size-2 classes\nTotal: 8 + 30 + 10 = 48 = |Z_65*|.\n\nThis Type B pattern is shared by exactly 2 size-65 magmas in the DB: this one and magma#2db4eae0. They share the slope value set but differ in the assignment.\n\nCompare: \n  magma#eff27734 (Z_4-symmetric, |Aut|=260, 4 slope values, all classes size 12)\n  Type A (5 magmas: 3 classes of size 6, 6 of size 4, 3 of size 2)\n  this Type B (2 magmas: 1 class of size 8, 6 classes of size 5, 5 classes of size 2)\n  Type C (1 magma magma#62917c53: 3 classes of size 9, 1 of size 8, 5 of size 2, 3 of size 1)\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:56","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/d8ba33b5c6c7428d429501ddecc764c36a6013c1f007f3eab053a820894a49e8.txt"},{"canonical_hash":"86e9481802b128ea22a573462b1b43da3a564a9d5038f1bebb49883d004565e3","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,4,10,40,31,34,33,54,27,6,57,23,19,3,61,30,49,53,24,41,13,7,44,17,55,25,2,42,56,38,22,28,46,62,20,51,21,63,52,64,26,48,60,12,50,14,37,16,15,32,5,29,1,47,45,59,35,43,9,18,39,36,8,58,11","comment":"Translation-only Steiner-line magma at size 65 (Type A slope pattern - 5 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design. Each block = the F_5 affine line magma#e549b5f8. |Aut(M)| = 65 (only Z_65 translation, no multiplicative stabilizer).\n\nIn the suggested reorder, Z_65 labeling makes translation x -> x+1 an automorphism. Operation: x*y = x + f(y - x) mod 65.\n\nSlope analysis on Z_65* (48 units): alpha takes 12 distinct values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63}, with the following class sizes (Type A pattern):\n  3 slopes on size-6 classes (sum 18)\n  6 slopes on size-4 classes (sum 24)\n  3 slopes on size-2 classes (sum 6)\nTotal: 18 + 24 + 6 = 48 = |Z_65*|.\n\nThree of the 12 slopes ({15, 35, 45}) are non-units mod 65 (multiples of 5); the other 9 are units and form 4 inverse pairs in Z_65* {3,22}, {21,31}, {32,63}, {34,44} plus the self-inverse 51 (= -14, 51^2 = 1 mod 65).\n\nThis 12-value slope set is exactly the one obtained by taking all Z_65* elements that \"could be Eq 677 multipliers\" plus the 3 multiples of 5. Compare with magma#eff27734 (Z_4-symmetric) which uses only the 4-element subset {3, 22, 35, 51} as slopes - that subset is the Z_4 = <34> stabilizer multiplied by representative slope values.\n\nThis (Type A) slope-class-size pattern is shared by 5 magmas at size 65: this one and magma#a09c4223, magma#4d60c34f, magma#bcf3ee89, magma#84076266. They differ in how the 12 slope values are assigned to specific Z_65*-subsets. Other Type B/C patterns (also using the same 12-value slope set) are: Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0), Type C (1 magma: magma#62917c53).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:20:59","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/86e9481802b128ea22a573462b1b43da3a564a9d5038f1bebb49883d004565e3.txt"},{"canonical_hash":"eff277346f46dd798eb554bd894073aca4ed5bf25592c111c9735ddf792d4fd0","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,62,54,22,57,33,13,12,8,63,38,59,24,4,1,45,25,42,26,47,31,64,19,41,44,53,43,52,15,32,55,3,20,5,10,29,16,37,14,60,51,34,28,17,50,36,48,11,23,49,61,7,30,18,56,58,21,39,27,35,9,46,6,40","comment":"Z_4-symmetric Steiner-line magma at size 65 (the unique multi-stabilizer variant).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) Steiner system (each = the F_5 affine line magma#e549b5f8). Every pair of distinct elements lies in exactly one block.\n\n|Aut(M)| = 260 = 4 * 65. Aut is Z_65 : Z_4: the regular Z_65 = Z_5 x Z_13 translation, and the point-stabilizer Z_4 = {1, 34, 51, 44} = <34> is an order-4 cyclic subgroup of Z_65*. Note: 34^2 = 51, 34^3 = 44, 34^4 = 1 mod 65; 51 = -14 mod 65 is the unique involution in this Z_4. The stabilizer acts by multiplication.\n\nIn the suggested reorder, Z_65 labeling makes translation x -> x+1 an automorphism. The operation x*y = x + f(y - x) mod 65 with f a non-linear permutation of Z_65. The Z_4 multiplicative stabilizer forces f to be Z_4-equivariant: f(34y) = 34 * f(y), so the slope function alpha(y) = f(y)/y (where defined) is constant on Z_4-orbits in Z_65*.\n\nSlope analysis on Z_65* (the 48 units mod 65): alpha takes 4 distinct values, each on a size-12 Z_4-coset:\n  alpha=3:  on {17, 22, 28, 33, 38, 42, 47, 53, 57, 58, 62, 63} (coset of 17 mod Z_4)\n  alpha=22: on {1, 11, 19, 29, 34, 41, 44, 49, 51, 56, 59, 61} (coset of 1, includes Z_4 itself)\n  alpha=35: on {2, 3, 7, 8, 12, 18, 23, 27, 32, 37, 43, 48} (coset of 2)\n  alpha=51: on {4, 6, 9, 14, 16, 21, 24, 31, 36, 46, 54, 64} (coset of 4)\nThe 4 slope values {3, 22, 35, 51} are partly Z_65* elements (3, 22, 51) and partly not (35 is a multiple of 5, so non-unit mod 65 - a phenomenon unique to composite sizes).\n\nThis is the analog of magma#b7e8bf90 (size 41, Z_5-symmetric) and magma#0bcf3cca (size 61, Z_15-symmetric): the \"most symmetric\" Steiner-line magma at its size, with the largest available cyclic multiplicative stabilizer matching the (F_q*)^{|Phi-roots|}-structure. Note 65 has no F_q (since composite) and no Phi_10 roots in Z_65, so the analog uses a Z_4 multiplicative stabilizer instead of a multi-root-based Z_5 or Z_15.\n\nAmong the 9 fully idempotent size-65 Steiner-line magmas, this is the unique one with |Aut| > 65. The other 8 have only Z_65 translation symmetry (|Aut| = 65) and split by slope-class-size patterns into 3 sub-types (see size-65 page commentary).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:01","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/eff277346f46dd798eb554bd894073aca4ed5bf25592c111c9735ddf792d4fd0.txt"},{"canonical_hash":"4d60c34fc53b199d6315b06433dae65aee77d175a2b21ff70466c03be0e6c6cc","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,12,39,14,16,58,13,47,5,35,32,11,54,36,30,27,7,18,62,44,22,8,53,57,42,29,50,45,9,55,17,38,4,3,24,59,48,60,26,21,25,63,10,64,52,23,61,40,20,41,2,37,43,34,46,28,19,51,49,56,33,6,15,31","comment":"Translation-only Steiner-line magma at size 65 (Type A slope pattern - 5 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design. Each block = the F_5 affine line magma#e549b5f8. |Aut(M)| = 65 (only Z_65 translation, no multiplicative stabilizer).\n\nIn the suggested reorder, Z_65 labeling makes translation x -> x+1 an automorphism. Operation: x*y = x + f(y - x) mod 65.\n\nSlope analysis on Z_65* (48 units): alpha takes 12 distinct values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63}, with the following class sizes (Type A pattern):\n  3 slopes on size-6 classes (sum 18)\n  6 slopes on size-4 classes (sum 24)\n  3 slopes on size-2 classes (sum 6)\nTotal: 18 + 24 + 6 = 48 = |Z_65*|.\n\nThree of the 12 slopes ({15, 35, 45}) are non-units mod 65 (multiples of 5); the other 9 are units and form 4 inverse pairs in Z_65* {3,22}, {21,31}, {32,63}, {34,44} plus the self-inverse 51 (= -14, 51^2 = 1 mod 65).\n\nThis 12-value slope set is exactly the one obtained by taking all Z_65* elements that \"could be Eq 677 multipliers\" plus the 3 multiples of 5. Compare with magma#eff27734 (Z_4-symmetric) which uses only the 4-element subset {3, 22, 35, 51} as slopes - that subset is the Z_4 = <34> stabilizer multiplied by representative slope values.\n\nThis (Type A) slope-class-size pattern is shared by 5 magmas at size 65: this one and magma#a09c4223, magma#86e94818, magma#bcf3ee89, magma#84076266. They differ in how the 12 slope values are assigned to specific Z_65*-subsets. Other Type B/C patterns (also using the same 12-value slope set) are: Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0), Type C (1 magma: magma#62917c53).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:04","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/4d60c34fc53b199d6315b06433dae65aee77d175a2b21ff70466c03be0e6c6cc.txt"},{"canonical_hash":"bcf3ee8943b4307ac63cfc357874ada089cb18959878171c336a05930755307e","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,13,42,46,61,6,38,22,4,28,7,19,31,53,64,34,17,59,29,56,18,3,41,58,21,24,11,15,55,35,37,2,47,5,10,54,32,30,40,16,12,39,57,26,44,52,33,62,60,43,8,51,45,14,48,25,50,23,20,36,49,9,63,27","comment":"Translation-only Steiner-line magma at size 65 (Type A slope pattern - 5 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design. Each block = the F_5 affine line magma#e549b5f8. |Aut(M)| = 65 (only Z_65 translation, no multiplicative stabilizer).\n\nIn the suggested reorder, Z_65 labeling makes translation x -> x+1 an automorphism. Operation: x*y = x + f(y - x) mod 65.\n\nSlope analysis on Z_65* (48 units): alpha takes 12 distinct values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63}, with the following class sizes (Type A pattern):\n  3 slopes on size-6 classes (sum 18)\n  6 slopes on size-4 classes (sum 24)\n  3 slopes on size-2 classes (sum 6)\nTotal: 18 + 24 + 6 = 48 = |Z_65*|.\n\nThree of the 12 slopes ({15, 35, 45}) are non-units mod 65 (multiples of 5); the other 9 are units and form 4 inverse pairs in Z_65* {3,22}, {21,31}, {32,63}, {34,44} plus the self-inverse 51 (= -14, 51^2 = 1 mod 65).\n\nThis 12-value slope set is exactly the one obtained by taking all Z_65* elements that \"could be Eq 677 multipliers\" plus the 3 multiples of 5. Compare with magma#eff27734 (Z_4-symmetric) which uses only the 4-element subset {3, 22, 35, 51} as slopes - that subset is the Z_4 = <34> stabilizer multiplied by representative slope values.\n\nThis (Type A) slope-class-size pattern is shared by 5 magmas at size 65: this one and magma#a09c4223, magma#86e94818, magma#4d60c34f, magma#84076266. They differ in how the 12 slope values are assigned to specific Z_65*-subsets. Other Type B/C patterns (also using the same 12-value slope set) are: Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0), Type C (1 magma: magma#62917c53).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:07","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/bcf3ee8943b4307ac63cfc357874ada089cb18959878171c336a05930755307e.txt"},{"canonical_hash":"84076266185609a19509ecf8be95ddf42b611fc99ea7f893ba24df2eb333a704","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,17,14,60,8,38,33,20,31,48,27,43,39,40,42,59,21,26,16,46,2,30,22,18,58,5,23,15,44,37,56,63,9,62,64,11,34,35,47,25,4,49,57,54,7,36,45,28,41,53,24,13,6,55,61,10,12,32,50,19,29,52,3,51","comment":"Translation-only Steiner-line magma at size 65 (Type A slope pattern - 5 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design. Each block = the F_5 affine line magma#e549b5f8. |Aut(M)| = 65 (only Z_65 translation, no multiplicative stabilizer).\n\nIn the suggested reorder, Z_65 labeling makes translation x -> x+1 an automorphism. Operation: x*y = x + f(y - x) mod 65.\n\nSlope analysis on Z_65* (48 units): alpha takes 12 distinct values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63}, with the following class sizes (Type A pattern):\n  3 slopes on size-6 classes (sum 18)\n  6 slopes on size-4 classes (sum 24)\n  3 slopes on size-2 classes (sum 6)\nTotal: 18 + 24 + 6 = 48 = |Z_65*|.\n\nThree of the 12 slopes ({15, 35, 45}) are non-units mod 65 (multiples of 5); the other 9 are units and form 4 inverse pairs in Z_65* {3,22}, {21,31}, {32,63}, {34,44} plus the self-inverse 51 (= -14, 51^2 = 1 mod 65).\n\nThis 12-value slope set is exactly the one obtained by taking all Z_65* elements that \"could be Eq 677 multipliers\" plus the 3 multiples of 5. Compare with magma#eff27734 (Z_4-symmetric) which uses only the 4-element subset {3, 22, 35, 51} as slopes - that subset is the Z_4 = <34> stabilizer multiplied by representative slope values.\n\nThis (Type A) slope-class-size pattern is shared by 5 magmas at size 65: this one and magma#a09c4223, magma#86e94818, magma#4d60c34f, magma#bcf3ee89. They differ in how the 12 slope values are assigned to specific Z_65*-subsets. Other Type B/C patterns (also using the same 12-value slope set) are: Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0), Type C (1 magma: magma#62917c53).\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/84076266185609a19509ecf8be95ddf42b611fc99ea7f893ba24df2eb333a704.txt"},{"canonical_hash":"2db4eae0618ea13ab95220b99f79c5e38ffc82b9ba35f7d819ca4fb3e32e9eae","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,30,7,62,37,54,40,49,10,55,32,53,9,19,64,21,34,8,15,33,12,3,44,13,48,58,43,28,17,22,60,2,4,26,47,16,23,24,63,27,29,59,25,6,41,18,20,38,36,56,61,52,46,31,11,42,35,50,51,5,14,57,39,45","comment":"Translation-only Steiner-line magma at size 65 (Type B slope pattern - 2 magmas).\n\nSize 65 = 5 * 13, fully idempotent, RC. 208 size-5 sub-magmas on a cyclic S(2, 5, 65) design (each = the F_5 affine line magma#e549b5f8). |Aut(M)| = 65 (Z_65 translation only).\n\nIn the Z_65 translation labeling, x*y = x + f(y - x) mod 65. Slope analysis on Z_65*: 12 distinct slope values {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63} (same set as in Type A and Type C - 4 inverse pairs + 1 self-inverse + 3 non-units), but with class sizes following the Type B pattern:\n  1 slope on a size-8 class\n  6 slopes on size-5 classes\n  5 slopes on size-2 classes\nTotal: 8 + 30 + 10 = 48 = |Z_65*|.\n\nThis Type B pattern is shared by exactly 2 size-65 magmas in the DB: this one and magma#d8ba33b5. They share the slope value set but differ in the assignment.\n\nCompare: \n  magma#eff27734 (Z_4-symmetric, |Aut|=260, 4 slope values, all classes size 12)\n  Type A (5 magmas: 3 classes of size 6, 6 of size 4, 3 of size 2)\n  this Type B (2 magmas: 1 class of size 8, 6 classes of size 5, 5 classes of size 2)\n  Type C (1 magma magma#62917c53: 3 classes of size 9, 1 of size 8, 5 of size 2, 3 of size 1)\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:12","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/2db4eae0618ea13ab95220b99f79c5e38ffc82b9ba35f7d819ca4fb3e32e9eae.txt"},{"canonical_hash":"3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75","size":65,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,7,12,16,20,25,30,35,40,46,51,56,63,1,6,10,17,22,27,31,36,41,45,50,55,61,4,5,11,15,21,26,33,38,43,48,53,58,62,2,8,13,18,23,28,32,37,42,47,52,57,60,3,9,14,19,24,29,34,39,44,49,54,59,64","comment":"F_5(2, 4) base × F_13 fiber: 5 fibers of 13 (each = F_13 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:21:13","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/65/3a1e3dea02005faeb7a32ea89e0ebcd7060d0e295c5a20add7fb441719113d75.txt"},{"canonical_hash":"e7e27553218a5c0b41777cba7f061336f8685dc05471afcb125c86b58db2c3aa","size":67,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,0,60,28,8,25,38,43,29,4,35,42,48,54,53,7,39,30,56,37,45,10,52,31,2,65,13,24,63,16,64,46,49,9,51,18,15,33,47,32,5,44,20,27,62,21,41,14,57,36,61,59,23,22,34,17,11,55,26,1,12,58,6,50,3,40,19","comment":"Linear magma over Z/67Z (the prime field F_67): x ◇ y = 29x + 32y (mod 67).","submitted_at":"2026-04-23 21:21:13","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/67/e7e27553218a5c0b41777cba7f061336f8685dc05471afcb125c86b58db2c3aa.txt"},{"canonical_hash":"99e2765ff4be43b63e3db5537eb87d04e459f995aec948f7290e45366c9ee3fa","size":67,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,0,60,34,45,35,30,15,41,6,31,19,17,62,11,7,26,29,54,25,18,48,4,65,2,8,47,39,59,46,55,14,13,52,16,49,50,28,21,23,3,22,33,38,63,40,12,43,61,27,56,64,32,36,1,53,44,58,42,5,51,57,10,20,9,24,37","comment":"Linear magma over Z/67Z (the prime field F_67): x ◇ y = 29x + 64y (mod 67).","submitted_at":"2026-04-23 21:21:13","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/67/99e2765ff4be43b63e3db5537eb87d04e459f995aec948f7290e45366c9ee3fa.txt"},{"canonical_hash":"ae850597310ca1e4e432d9166a7108f5487ce49948bce500209d7acd9fde2b9f","size":69,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"60,61,62,63,64,65,66,67,0,47,1,6,45,16,5,17,4,2,3,46,7,10,41,13,9,18,14,15,11,12,40,8,19,42,20,21,29,24,22,23,27,25,26,28,30,36,44,43,35,39,37,38,33,31,32,34,48,56,49,50,58,53,51,52,59,54,55,57,68","comment":"Asymmetric \"mixed-pencil\" magma at size 69 = 3 * 23.\n\nSize 69, exactly 1 idempotent (element 68), right-cancellative. |Aut(M)| = 1 (only the identity automorphism); every element is a singleton Aut-orbit. So the magma is maximally rigid.\n\nSub-magma structure: there are exactly 6 proper non-singleton sub-magmas, all containing the unique idempotent 68 (= \"the origin\"):\n- 1 size-9 sub-magma: {60, 61, 62, 63, 64, 65, 66, 67, 68} — iso class magma#2925dc18 (a size-9 Eq 677 magma with exactly 1 idempotent; NOT the fully-idempotent F_9 linear magma).\n- 5 size-13 sub-magmas, ALL of the same iso class magma#babb8d44 (a size-13 Eq 677 magma with 1 idempotent):\n    {0, 1, 2, 3, 4, 5, 6, 16, 17, 45, 46, 47, 68}\n    {7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 40, 41, 68}\n    {19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 42, 68}\n    {30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 44, 68}\n    {48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 68}\n\nThe 6 sub-magmas all pass through 68 (the only shared element). Outside of 68, they partition the remaining 68 elements as: 8 (= size-9 minus 68) + 5*12 (= 5 * size-13 minus 68) = 68 ✓.\n\nThis is a \"pencil of 6 lines through a common point\" structure with TWO different line sizes (9 and 13) - asymmetric in a way that no AG(2, q) or PG(2, q) geometry produces. 69 = 3 * 23 is composite, and there is no Eq 677 magma at size 3 (see size-3 page commentary), so the construction isn't a Z_3 x Z_23 product either. This is genuinely sporadic.\n\nSuggested reorder lays out 7 consecutive blocks:\n  positions 0..7: size-9 sub-magma minus 68 (8 elements)\n  positions 8..19: size-13 line 1 minus 68 (12 elements)\n  positions 20..31: size-13 line 2 minus 68 (12 elements)\n  positions 32..43: size-13 line 3 minus 68 (12 elements)\n  positions 44..55: size-13 line 4 minus 68 (12 elements)\n  positions 56..67: size-13 line 5 minus 68 (12 elements)\n  position 68: the idempotent 68\n\nWithin each size-13 line, the 12 non-idempotent elements are reordered via the line's iso to the CANONICAL form of magma#babb8d44 (the size-13 sub-magma iso class). Consequence: all 5 diagonal 12x12 blocks of the Cayley table show the SAME within-block pattern (the canonical babb8d44 layout, with the global idempotent 68 represented in the last row/column). The off-diagonal blocks remain chaotic because |Aut| = 1 - there is no group symmetry to align cross-line operations.\n\nL_0 cycle 1 + 12 + 28*2 and R_0 cycle 1 + 4*3 + 14*4 reflect the global asymmetry. \n\nComparable structures:\n  magma#1b32837d (size 49): 8 size-7 lines through a common idempotent, in 2 iso classes (7+1) - a \"twisted AG(2, 7) pencil\".\n  This magma: 6 lines through a common idempotent, with MIXED line sizes (5 size-13 + 1 size-9) - distinct from any AG(2, q) or PG(2, q) interpretation.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/69/ae850597310ca1e4e432d9166a7108f5487ce49948bce500209d7acd9fde2b9f.txt"},{"canonical_hash":"24908b755d4475fb6e8f18895cb9143e6dfbb44ed3779fa842e5070393033ec8","size":71,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,38,15,6,19,63,20,65,57,24,34,50,25,32,3,62,47,59,4,7,49,30,41,10,8,58,18,52,69,45,9,33,16,54,22,44,46,5,66,13,43,40,23,11,26,39,68,61,14,35,60,21,29,56,27,55,42,51,2,37,36,67,53,48,64,70,28,12,17,31","comment":"Linear magma over Z/71Z (the prime field F_71): x ◇ y = 6x + 66y (mod 71).","submitted_at":"2026-04-23 21:21:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/71/24908b755d4475fb6e8f18895cb9143e6dfbb44ed3779fa842e5070393033ec8.txt"},{"canonical_hash":"4c5c6adda2d8e1761011a06a7b3befdb7b4aabd73cce11672a2d73665f46adfd","size":71,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,68,23,18,6,55,66,19,51,47,12,16,54,31,20,41,53,58,33,36,35,17,26,24,44,11,45,3,42,57,67,14,62,43,50,37,29,13,40,69,63,39,25,65,21,70,56,30,60,4,28,34,5,48,64,2,15,8,27,49,32,22,7,38,10,46,9,59,61,52","comment":"Linear magma over Z/71Z (the prime field F_71): x ◇ y = 26x + 46y (mod 71).","submitted_at":"2026-04-23 21:21:15","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/71/4c5c6adda2d8e1761011a06a7b3befdb7b4aabd73cce11672a2d73665f46adfd.txt"},{"canonical_hash":"7cafd296a7338f3c56850e5b0b08872e8a8ffc3b28b7955fba679f6acee9acfd","size":71,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,11,50,6,15,31,9,51,27,35,49,21,47,34,32,56,70,63,39,41,54,14,42,28,20,44,2,38,22,13,43,4,8,7,24,33,67,45,53,68,10,37,64,26,23,18,69,36,59,55,58,5,12,65,48,66,29,62,25,16,19,57,30,3,61,46,52,60,40,17","comment":"Linear magma over Z/71Z (the prime field F_71): x ◇ y = 55x + 17y (mod 71).","submitted_at":"2026-04-23 21:21:15","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/71/7cafd296a7338f3c56850e5b0b08872e8a8ffc3b28b7955fba679f6acee9acfd.txt"},{"canonical_hash":"21a87d495b64c12e4ea73b97544456f126c5f26d32c3bb7491aa5b403dac8342","size":71,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,60,27,38,67,55,2,62,40,57,64,59,61,70,14,12,17,10,28,15,49,8,20,26,39,13,48,47,31,6,68,18,32,24,52,37,56,11,7,46,23,45,3,29,69,4,42,66,63,16,19,30,51,22,41,50,33,35,34,54,58,9,25,5,36,44,65,21,53,43","comment":"Linear magma over Z/71Z (the prime field F_71): x ◇ y = 58x + 14y (mod 71).","submitted_at":"2026-04-23 21:21:16","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/71/21a87d495b64c12e4ea73b97544456f126c5f26d32c3bb7491aa5b403dac8342.txt"},{"canonical_hash":"cceef898c06671f8bddd9293722701938c8678bfc5476b2ee52fa83f939db045","size":73,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"72,0,63,21,55,26,57,38,47,59,62,18,49,14,30,20,39,50,51,11,54,32,10,69,41,25,6,53,66,36,56,60,31,12,42,37,43,9,3,8,46,23,68,64,2,58,19,40,33,7,61,44,24,1,45,17,16,5,28,22,48,15,52,70,67,13,4,65,34,71,29,27,35","comment":"Linear magma over Z/73Z (the prime field F_73): x ◇ y = 8x + 34y (mod 73).","submitted_at":"2026-04-23 21:21:16","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/73/cceef898c06671f8bddd9293722701938c8678bfc5476b2ee52fa83f939db045.txt"},{"canonical_hash":"06f91b15dd7f2a1d37f91a84401f74f280ef3a4b444baa5c49daafa91959dfcd","size":73,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"72,0,13,71,51,18,2,60,28,26,68,15,52,40,37,19,5,70,3,10,45,61,65,56,29,12,17,27,14,36,69,44,55,16,35,54,53,47,48,41,22,49,38,63,42,20,33,23,6,1,50,59,67,39,4,9,64,11,25,43,46,58,21,62,32,34,66,8,24,57,31,7,30","comment":"Linear magma over Z/73Z (the prime field F_73): x ◇ y = 8x + 47y (mod 73).","submitted_at":"2026-04-23 21:21:17","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/73/06f91b15dd7f2a1d37f91a84401f74f280ef3a4b444baa5c49daafa91959dfcd.txt"},{"canonical_hash":"882574997286180eb67ca1c7e27992d77d3597f78b7f59bc1c9a77bfc81a519f","size":73,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,21,32,43,29,7,17,58,57,59,28,44,71,10,51,49,50,35,25,11,69,14,3,18,20,16,13,34,53,12,66,47,46,9,65,23,4,33,67,62,42,61,24,63,38,8,52,48,72,56,60,26,64,37,6,2,68,54,41,15,22,5,39,27,70,55,40,30,45,19,31,36","comment":"Translation invariant model on F_q with q = 73 of the form (x,y) -> x + delta_i * (y - x) where delta_i is in (33, 49, 18, 34) depending on the class of (y-x) in F_q^* / (F_q^*)^4.","submitted_at":"2026-05-12 09:05:02","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/73/882574997286180eb67ca1c7e27992d77d3597f78b7f59bc1c9a77bfc81a519f.txt"},{"canonical_hash":"875876e7e31c7e05609680a9cec26f61bd10edc86d499722c7c21a6126088e27","size":76,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"62,3,4,11,14,17,20,27,30,33,36,43,46,49,52,59,2,7,10,13,16,23,26,29,32,39,42,45,48,55,58,60,61,63,64,65,66,67,68,69,70,71,72,73,74,75,0,6,9,12,19,22,25,28,35,38,41,44,51,54,57,1,5,8,15,18,21,24,31,34,37,40,47,50,53,56","comment":"Size-76 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The structure is a **'pencil' of 5 size-16 sub-magmas through a common pivot element**, with the 75 non-pivot elements glued together by a **transversal design TD(5, 15)** of size-5 sub-magmas.\n\nConcretely:\n  • There is one distinguished element (the 'pivot', canonical label 62) that lies in 5 sub-magmas of size 16 and 0 sub-magmas of size 5.\n  • The 5 size-16 sub-magmas (the 'petals') all contain the pivot and partition the other 75 elements into 5 groups of 15 each. Every petal is isomorphic to magma#6fa95655 (the size-16 idempotent linear magma over Z/16Z with x ◇ y = 9x + 8y mod 16) — verified by submitting each petal's 16×16 sub-Cayley table to the canonicalization API.\n  • There are 225 = 15² size-5 sub-magmas, each isomorphic to the unique size-5 Eq 677 magma over F_5 (the affine sharply-2-transitive one). Every such size-5 sub-magma is a **transversal of the 5 petal groups**: it has exactly one element in each petal-group (excluding the pivot). The 225 transversals form a TD(5, 15) (transversal design), equivalently 3 mutually orthogonal Latin squares of order 15.\n  • Every pair of distinct elements (x, y) generates:\n      - the full petal (size 16) if x, y are in the same petal (= same group plus possibly the pivot);\n      - a unique transversal (size 5) if x, y are non-pivot elements in different petal-groups;\n  • Each non-pivot element sits in exactly 1 petal and 15 transversals; the pivot sits in all 5 petals and no transversals.\n\nThis is a 'near-pencil' / Tao-style design construction: 5 copies of a size-16 building-block Eq 677 magma, glued at one shared point, with cross-petal multiplication coordinated by the TD(5, 15) so the whole structure satisfies Eq 677.\n\nDisplay reorder places the pivot at index 0 and then lays out the 5 petals in consecutive 15-blocks (indices 1-15, 16-30, 31-45, 46-60, 61-75). Under this reorder the Cayley table shows a clear 5×5 grid of 15×15 blocks plus a pivot row/column: the 5 diagonal blocks correspond to within-petal operations (each block is the action of one F_16-petal on itself), and the 20 off-diagonal blocks reflect the cross-petal TD(5, 15) structure.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:21:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/76/875876e7e31c7e05609680a9cec26f61bd10edc86d499722c7c21a6126088e27.txt"},{"canonical_hash":"6c0663526a98218824273cacd03aac8d37a819b5d14a330cc1cd23f8e7fff8ad","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,73,76,68,71,72,74,70,75,69,1,0,7,64,2,5,6,8,4,9,3,22,21,28,63,23,26,27,29,25,20,24,42,41,48,65,43,46,47,49,45,40,44,10,11,17,62,12,15,16,18,14,19,13,52,51,58,60,53,56,57,59,55,50,54,30,31,37,61,32,35,36,38,34,39,33","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 4x₂ + 8y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:24","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/6c0663526a98218824273cacd03aac8d37a819b5d14a330cc1cd23f8e7fff8ad.txt"},{"canonical_hash":"74c2b3c081debeba123eb77544690d7ded5a1824946fccb13e95b8196af8499d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,76,71,72,69,73,75,70,68,74,0,7,65,8,1,9,3,6,5,2,4,40,48,64,49,41,45,43,47,46,42,44,52,58,60,59,50,51,54,57,56,53,55,20,28,62,29,21,25,23,27,26,22,24,10,18,61,19,11,15,13,17,16,12,14,30,38,63,39,31,35,33,37,36,32,34","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 3y₁ (mod 7), 6x₂ + 6y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/74c2b3c081debeba123eb77544690d7ded5a1824946fccb13e95b8196af8499d.txt"},{"canonical_hash":"ca8e8dba8adc6702e3d8ee12eca6bf29113521fc49a0cbc215f184f3ae4bad35","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,69,75,73,68,70,74,71,72,76,7,6,1,5,3,8,0,4,2,9,65,48,47,41,46,44,49,40,45,42,43,64,58,57,51,56,54,59,52,55,53,50,60,28,27,21,26,24,29,20,25,22,23,62,18,17,11,16,14,19,10,15,12,13,61,38,37,31,36,34,39,30,35,32,33,63","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 3y₁ (mod 7), 10x₂ + 2y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/ca8e8dba8adc6702e3d8ee12eca6bf29113521fc49a0cbc215f184f3ae4bad35.txt"},{"canonical_hash":"750328f1a2990ffd7db07d783e80f02cf584ad72d1ba7ccb23b4ce19aeead26b","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,74,68,73,69,71,72,75,76,70,0,1,8,2,7,3,5,6,9,64,4,22,21,29,23,28,24,26,27,20,63,25,44,43,40,45,41,46,48,49,42,65,47,10,11,18,12,17,13,15,16,19,62,14,54,53,51,55,50,56,58,59,52,60,57,33,32,30,34,31,35,37,38,39,61,36","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 5x₂ + 7y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/750328f1a2990ffd7db07d783e80f02cf584ad72d1ba7ccb23b4ce19aeead26b.txt"},{"canonical_hash":"f79fc5331f458d02d4e78f64dca968a65056af7ebe34d7d0ef117631414f3151","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,76,71,72,69,73,75,70,68,74,1,0,64,5,6,3,7,9,4,2,8,22,21,63,26,27,24,28,20,25,23,29,45,44,65,49,41,47,40,43,48,46,42,10,11,62,15,16,13,17,19,14,12,18,55,54,60,59,51,57,52,50,58,56,53,34,33,61,38,31,36,30,39,37,35,32","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 6x₂ + 6y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:26","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/f79fc5331f458d02d4e78f64dca968a65056af7ebe34d7d0ef117631414f3151.txt"},{"canonical_hash":"4a1fb8605639da49106a26631019a15cd198a6c8d9ed882322a7a649a8f8265a","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,73,76,68,71,72,74,70,75,69,1,6,9,65,7,3,4,5,8,0,2,42,47,41,64,48,44,45,46,49,40,43,50,57,51,60,58,54,55,56,59,52,53,22,27,20,62,28,24,25,26,29,21,23,12,17,10,61,18,14,15,16,19,11,13,32,37,30,63,38,34,35,36,39,31,33","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 3y₁ (mod 7), 4x₂ + 8y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/4a1fb8605639da49106a26631019a15cd198a6c8d9ed882322a7a649a8f8265a.txt"},{"canonical_hash":"5da407abe4e69ea2e8e77e634a9a34d8ab5d7df6477bcbd8c80289a0abfd3c16","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,69,75,73,68,70,74,71,72,76,0,1,3,9,7,2,4,8,5,6,64,22,21,24,20,28,23,25,29,26,27,63,40,41,43,49,47,42,44,48,45,46,65,10,11,13,19,17,12,14,18,15,16,62,52,51,54,50,58,53,55,59,56,57,60,31,30,33,39,37,32,34,38,35,36,61","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 10x₂ + 2y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/5da407abe4e69ea2e8e77e634a9a34d8ab5d7df6477bcbd8c80289a0abfd3c16.txt"},{"canonical_hash":"889f5984d564a0102d69c2441a9759c96b931b04e9110bc017112fc402619ea4","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"66,67,74,68,73,69,71,72,75,76,70,3,6,8,4,2,1,0,5,9,65,7,44,47,49,45,43,42,40,46,41,64,48,54,57,59,55,53,50,52,56,51,60,58,24,27,29,25,23,22,21,26,20,62,28,14,17,19,15,13,12,11,16,10,61,18,34,37,39,35,33,32,31,36,30,63,38","comment":"Direct product of two linear magmas: F_7 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 3y₁ (mod 7), 5x₂ + 7y₂ (mod 11)).","submitted_at":"2026-04-23 21:21:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/889f5984d564a0102d69c2441a9759c96b931b04e9110bc017112fc402619ea4.txt"},{"canonical_hash":"432e4c006dcd7a87bd51f20718c8a2600c80c9e6f4728c9b2189310a93934f23","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,15,27,37,45,62,71,1,17,28,38,46,63,73,2,13,26,36,50,61,69,8,18,23,33,47,58,74,5,12,22,32,51,57,68,4,11,24,34,48,59,67,9,19,29,39,54,64,75,7,16,21,31,53,56,72,40,41,42,43,44,65,76,3,10,25,35,49,60,66,6,14,20,30,52,55,70","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:28","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/432e4c006dcd7a87bd51f20718c8a2600c80c9e6f4728c9b2189310a93934f23.txt"},{"canonical_hash":"b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,75,6,7,8,9,10,11,72,60,61,62,63,64,65,76,42,43,44,45,46,47,68,24,25,26,27,28,29,66,18,19,20,21,22,23,71,12,13,14,15,16,17,73,30,31,32,33,34,35,74,48,49,50,51,52,53,70,36,37,38,39,40,41,67,54,55,56,57,58,59,69","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa.txt"},{"canonical_hash":"fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,72,6,7,8,9,10,11,71,18,19,20,21,22,23,75,30,31,32,33,34,35,67,54,55,56,57,58,59,74,36,37,38,39,40,41,69,48,49,50,51,52,53,70,60,61,62,63,64,65,66,12,13,14,15,16,17,68,24,25,26,27,28,29,76,42,43,44,45,46,47,73","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711.txt"},{"canonical_hash":"5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,72,6,7,8,9,10,11,76,36,37,38,39,40,41,68,18,19,20,21,22,23,75,12,13,14,15,16,17,73,60,61,62,63,64,65,66,24,25,26,27,28,29,74,54,55,56,57,58,59,71,30,31,32,33,34,35,70,42,43,44,45,46,47,67,48,49,50,51,52,53,69","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239.txt"},{"canonical_hash":"8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,68,6,7,8,9,10,11,76,36,37,38,39,40,41,72,18,19,20,21,22,23,70,12,13,14,15,16,17,67,60,61,62,63,64,65,73,24,25,26,27,28,29,75,54,55,56,57,58,59,66,30,31,32,33,34,35,74,42,43,44,45,46,47,71,48,49,50,51,52,53,69","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d.txt"},{"canonical_hash":"4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,75,6,7,8,9,10,11,71,54,55,56,57,58,59,67,48,49,50,51,52,53,74,24,25,26,27,28,29,68,12,13,14,15,16,17,76,60,61,62,63,64,65,73,36,37,38,39,40,41,72,30,31,32,33,34,35,70,18,19,20,21,22,23,69,42,43,44,45,46,47,66","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1.txt"},{"canonical_hash":"e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,15,68,5,6,7,8,9,16,70,18,19,20,21,22,23,69,10,11,12,13,14,17,76,42,43,44,45,46,47,71,30,31,32,33,34,35,66,24,25,26,27,28,29,74,60,61,62,63,64,65,67,48,49,50,51,52,53,72,54,55,56,57,58,59,73,36,37,38,39,40,41,75","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444.txt"},{"canonical_hash":"7d1ca7f19a6476d5d19958a01b2b150bc7a0c60d280d02593b805c82a69bb42e","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,32,46,57,74,1,12,22,30,47,56,70,4,15,25,35,50,60,68,6,17,27,37,52,62,71,9,11,21,31,45,55,75,7,18,28,38,53,63,67,2,13,23,33,48,58,72,5,16,26,36,51,61,69,40,41,42,43,44,65,76,3,14,24,34,49,59,66,8,19,29,39,54,64,73","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:32","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/7d1ca7f19a6476d5d19958a01b2b150bc7a0c60d280d02593b805c82a69bb42e.txt"},{"canonical_hash":"81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,68,6,7,8,9,10,11,67,42,43,44,45,46,47,75,30,31,32,33,34,35,74,36,37,38,39,40,41,70,18,19,20,21,22,23,76,48,49,50,51,52,53,71,24,25,26,27,28,29,66,12,13,14,15,16,17,69,54,55,56,57,58,59,73,60,61,62,63,64,65,72","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:32","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e.txt"},{"canonical_hash":"09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,70,6,7,8,9,10,11,69,54,55,56,57,58,59,73,24,25,26,27,28,29,75,42,43,44,45,46,47,71,18,19,20,21,22,23,72,60,61,62,63,64,65,67,30,31,32,33,34,35,76,12,13,14,15,16,17,66,48,49,50,51,52,53,74,36,37,38,39,40,41,68","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:33","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1.txt"},{"canonical_hash":"dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,67,6,7,8,9,10,11,71,42,43,44,45,46,47,69,18,19,20,21,22,23,74,54,55,56,57,58,59,66,60,61,62,63,64,65,72,36,37,38,39,40,41,75,24,25,26,27,28,29,73,48,49,50,51,52,53,76,30,31,32,33,34,35,68,12,13,14,15,16,17,70","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:33","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47.txt"},{"canonical_hash":"52d4614aac36602fb386b87bb7ef7aa0910b87bb89053f8f7d172ae1bee280b9","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,13,26,36,45,61,69,1,17,28,38,47,63,73,5,12,20,30,51,55,68,8,18,23,33,50,58,74,4,11,24,34,49,59,67,3,10,25,35,46,60,66,6,14,22,32,53,57,70,40,41,42,43,44,65,76,9,19,29,39,54,64,75,7,16,21,31,48,56,72,2,15,27,37,52,62,71","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/52d4614aac36602fb386b87bb7ef7aa0910b87bb89053f8f7d172ae1bee280b9.txt"},{"canonical_hash":"0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,73,6,7,8,9,10,11,76,36,37,38,39,40,41,70,54,55,56,57,58,59,75,60,61,62,63,64,65,66,12,13,14,15,16,17,72,48,49,50,51,52,53,68,18,19,20,21,22,23,69,42,43,44,45,46,47,74,30,31,32,33,34,35,71,24,25,26,27,28,29,67","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b.txt"},{"canonical_hash":"dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,69,6,7,8,9,10,11,76,42,43,44,45,46,47,66,18,19,20,21,22,23,73,24,25,26,27,28,29,68,54,55,56,57,58,59,72,12,13,14,15,16,17,67,60,61,62,63,64,65,70,48,49,50,51,52,53,71,36,37,38,39,40,41,74,30,31,32,33,34,35,75","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f.txt"},{"canonical_hash":"890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,73,6,7,8,9,10,11,76,29,30,31,32,33,62,69,57,58,59,60,61,65,70,12,13,14,15,16,63,66,34,35,36,37,38,39,74,51,52,53,54,55,56,67,40,41,42,43,44,64,68,45,46,47,48,49,50,71,23,24,25,26,27,28,75,17,18,19,20,21,22,72","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c.txt"},{"canonical_hash":"056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,74,6,7,8,9,10,11,70,54,55,56,57,58,59,69,48,49,50,51,52,53,66,42,43,44,45,46,47,68,18,19,20,21,22,23,76,12,13,14,15,16,17,75,30,31,32,33,34,35,72,36,37,38,39,40,41,71,60,61,62,63,64,65,67,24,25,26,27,28,29,73","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0.txt"},{"canonical_hash":"c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,72,6,7,8,9,10,11,73,30,31,32,33,34,35,76,60,61,62,63,64,65,68,48,49,50,51,52,53,70,24,25,26,27,28,29,75,18,19,20,21,22,23,66,54,55,56,57,58,59,71,12,13,14,15,16,17,69,42,43,44,45,46,47,67,36,37,38,39,40,41,74","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a.txt"},{"canonical_hash":"9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,73,6,7,8,9,10,11,76,30,31,32,33,34,35,69,18,19,20,21,22,23,72,24,25,26,27,28,29,68,48,49,50,51,52,53,75,12,13,14,15,16,17,70,54,55,56,57,58,59,67,36,37,38,39,40,41,74,42,43,44,45,46,47,71,60,61,62,63,64,65,66","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f.txt"},{"canonical_hash":"a5ceaca916191ef68f2e3b6b2367dcc497ee860690a383f5692cc65c6f41ad3d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,11,20,32,46,57,74,1,12,22,30,47,55,68,7,18,28,38,53,63,73,6,17,27,37,52,62,69,8,19,29,39,54,64,71,2,13,23,33,48,58,72,5,16,26,36,51,61,66,40,41,42,43,44,65,76,4,15,25,35,50,60,70,9,10,21,31,45,56,75,3,14,24,34,49,59,67","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:37","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/a5ceaca916191ef68f2e3b6b2367dcc497ee860690a383f5692cc65c6f41ad3d.txt"},{"canonical_hash":"50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,66,6,7,8,9,10,11,68,30,31,32,33,34,35,67,18,19,20,21,22,23,71,12,13,14,15,16,17,70,54,55,56,57,58,59,75,42,43,44,45,46,47,69,60,61,62,63,64,65,73,48,49,50,51,52,53,76,36,37,38,39,40,41,72,24,25,26,27,28,29,74","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:37","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65.txt"},{"canonical_hash":"51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,67,6,7,8,9,10,11,75,54,55,56,57,58,59,70,36,37,38,39,40,41,69,60,61,62,63,64,65,68,48,49,50,51,52,53,73,42,43,44,45,46,47,76,18,19,20,21,22,23,66,24,25,26,27,28,29,74,12,13,14,15,16,17,72,30,31,32,33,34,35,71","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b.txt"},{"canonical_hash":"7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,72,6,7,8,9,10,11,71,42,43,44,45,46,47,68,12,13,14,15,16,17,73,54,55,56,57,58,59,66,24,25,26,27,28,29,76,18,19,20,21,22,23,69,48,49,50,51,52,53,75,60,61,62,63,64,65,67,30,31,32,33,34,35,74,36,37,38,39,40,41,70","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218.txt"},{"canonical_hash":"494ba0deb454b14b2cb7bbc62844432905ec783aba817e90b87a28e07ff9818c","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,15,27,37,50,62,71,1,17,28,38,49,63,73,5,12,22,32,47,57,68,4,11,24,34,48,59,67,7,16,20,30,51,55,72,9,19,29,39,54,64,75,8,18,23,33,46,58,74,40,41,42,43,44,65,76,2,13,26,36,53,61,69,6,14,21,31,45,56,70,3,10,25,35,52,60,66","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/494ba0deb454b14b2cb7bbc62844432905ec783aba817e90b87a28e07ff9818c.txt"},{"canonical_hash":"6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,75,6,7,8,9,10,11,76,36,37,38,39,40,41,68,30,31,32,33,34,35,70,54,55,56,57,58,59,73,24,25,26,27,28,29,66,12,13,14,15,16,17,67,42,43,44,45,46,47,69,48,49,50,51,52,53,74,18,19,20,21,22,23,71,60,61,62,63,64,65,72","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719.txt"},{"canonical_hash":"45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,66,6,7,8,9,10,11,76,30,31,32,33,34,35,75,24,25,26,27,28,29,68,42,43,44,45,46,47,67,12,13,14,15,16,17,70,54,55,56,57,58,59,71,36,37,38,39,40,41,69,48,49,50,51,52,53,73,18,19,20,21,22,23,74,60,61,62,63,64,65,72","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60.txt"},{"canonical_hash":"9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,11,68,5,6,7,8,9,10,74,48,49,50,51,52,53,75,18,19,20,21,22,23,71,30,31,32,33,34,35,73,42,43,44,45,46,47,67,54,55,56,57,58,59,69,36,37,38,39,40,41,70,60,61,62,63,64,65,66,24,25,26,27,28,29,72,12,13,14,15,16,17,76","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019.txt"},{"canonical_hash":"a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,76,6,7,8,9,10,11,69,36,37,38,39,40,41,70,18,19,20,21,22,23,75,30,31,32,33,34,35,73,60,61,62,63,64,65,72,12,13,14,15,16,17,68,54,55,56,57,58,59,71,24,25,26,27,28,29,67,42,43,44,45,46,47,66,48,49,50,51,52,53,74","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f.txt"},{"canonical_hash":"a5dba37ae82f5d1e2c854105d6ba510f1387eb5ee3dcc59dd48a683e84cf35f4","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,30,45,55,71,1,11,21,31,46,56,75,4,14,24,34,49,59,66,3,13,23,33,48,58,72,8,19,29,39,54,64,70,2,12,22,32,47,57,67,7,18,28,38,53,63,69,9,16,26,36,51,61,68,40,41,42,43,44,65,76,5,15,25,35,50,60,73,6,17,27,37,52,62,74","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/a5dba37ae82f5d1e2c854105d6ba510f1387eb5ee3dcc59dd48a683e84cf35f4.txt"},{"canonical_hash":"83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,70,6,7,8,9,10,11,75,54,55,56,57,58,59,69,12,13,14,15,16,17,66,60,61,62,63,64,65,67,30,31,32,33,34,35,74,18,19,20,21,22,23,76,36,37,38,39,40,41,72,48,49,50,51,52,53,73,42,43,44,45,46,47,71,24,25,26,27,28,29,68","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5.txt"},{"canonical_hash":"3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,76,6,7,8,9,10,11,70,36,37,38,39,40,41,68,48,49,50,51,52,53,69,60,61,62,63,64,65,66,18,19,20,21,22,23,71,24,25,26,27,28,29,75,54,55,56,57,58,59,73,42,43,44,45,46,47,72,30,31,32,33,34,35,74,12,13,14,15,16,17,67","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6.txt"},{"canonical_hash":"b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,66,6,7,8,9,10,11,68,42,43,44,45,46,47,76,18,19,20,21,22,23,74,36,37,38,39,40,41,72,60,61,62,63,64,65,70,12,13,14,15,16,17,75,54,55,56,57,58,59,73,30,31,32,33,34,35,71,24,25,26,27,28,29,69,48,49,50,51,52,53,67","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5.txt"},{"canonical_hash":"d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,75,6,7,8,9,10,11,72,56,57,58,61,63,65,66,24,25,26,27,28,29,70,36,37,38,39,40,41,74,48,49,50,51,52,53,69,18,19,20,21,22,23,76,54,55,59,60,62,64,71,42,43,44,45,46,47,73,30,31,32,33,34,35,68,12,13,14,15,16,17,67","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4.txt"},{"canonical_hash":"ccc40d3a7572bc817f1e0e643b0b882fca97901472beda34cd022d7e757b2855","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,15,27,37,49,62,71,1,13,26,36,50,61,69,8,18,23,33,46,58,74,4,11,24,34,45,59,67,6,14,20,30,48,55,70,3,10,25,35,52,60,66,5,12,21,31,51,56,68,40,41,42,43,44,65,76,2,17,28,38,53,63,73,7,16,22,32,47,57,72,9,19,29,39,54,64,75","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/ccc40d3a7572bc817f1e0e643b0b882fca97901472beda34cd022d7e757b2855.txt"},{"canonical_hash":"e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,72,6,7,8,9,10,11,73,48,49,50,51,52,53,69,24,25,26,27,28,29,74,54,55,56,57,58,59,68,12,13,14,15,16,17,70,42,43,44,45,46,47,75,30,31,32,33,34,35,71,36,37,38,39,40,41,67,60,61,62,63,64,65,66,18,19,20,21,22,23,76","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76.txt"},{"canonical_hash":"a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,74,6,7,8,9,10,11,67,48,49,50,51,52,53,70,54,55,56,57,58,59,69,42,43,44,45,46,47,66,18,19,20,21,22,23,73,36,37,38,39,40,41,75,60,61,62,63,64,65,71,30,31,32,33,34,35,76,24,25,26,27,28,29,72,12,13,14,15,16,17,68","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f.txt"},{"canonical_hash":"75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,27,28,29,53,69,2,3,30,31,32,33,66,6,7,38,39,40,41,72,10,11,46,47,48,49,67,22,23,58,59,60,61,73,20,21,54,55,56,57,70,24,25,26,62,63,64,75,12,13,14,15,16,50,74,17,18,19,51,52,65,76,4,5,34,35,36,37,68,8,9,42,43,44,45,71","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0.txt"},{"canonical_hash":"564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,76,6,7,8,9,10,11,69,54,55,56,57,58,59,75,18,19,20,21,22,23,70,24,25,26,27,28,29,74,36,37,38,39,40,41,67,48,49,50,51,52,53,66,12,13,14,15,16,17,72,30,31,32,33,34,35,71,60,61,62,63,64,65,73,42,43,44,45,46,47,68","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83.txt"},{"canonical_hash":"edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,75,6,7,8,9,10,11,76,24,25,26,27,28,29,66,30,31,32,33,34,35,72,54,55,56,57,58,59,67,36,37,38,39,40,41,71,60,61,62,63,64,65,69,18,19,20,21,22,23,70,48,49,50,51,52,53,73,12,13,14,15,16,17,68,42,43,44,45,46,47,74","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a.txt"},{"canonical_hash":"bcdaeba3e5c42bac8c75df4a4ea039608cfd6919340934a2200e9da4b34d4d34","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,31,45,56,74,1,11,21,30,46,57,75,6,17,27,37,52,62,71,2,13,23,33,48,58,67,3,14,24,34,49,59,68,7,18,28,38,53,63,72,4,15,25,35,50,60,69,5,16,26,36,51,61,70,40,41,42,43,44,65,76,9,12,22,32,47,55,66,8,19,29,39,54,64,73","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/bcdaeba3e5c42bac8c75df4a4ea039608cfd6919340934a2200e9da4b34d4d34.txt"},{"canonical_hash":"4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,76,6,7,8,9,10,11,71,30,31,32,33,34,35,73,24,25,26,27,28,29,75,36,37,38,39,40,41,69,48,49,50,51,52,53,74,60,61,62,63,64,65,72,54,55,56,57,58,59,70,42,43,44,45,46,47,67,18,19,20,21,22,23,66,12,13,14,15,16,17,68","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010.txt"},{"canonical_hash":"10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,66,6,7,8,9,10,11,69,12,13,14,15,16,17,74,48,49,50,51,52,53,71,18,19,20,21,22,23,68,30,31,32,33,34,35,75,54,55,56,57,58,59,70,42,43,44,45,46,47,73,24,25,26,27,28,29,72,60,61,62,63,64,65,67,36,37,38,39,40,41,76","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6.txt"},{"canonical_hash":"4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,37,38,55,74,3,4,5,39,40,56,66,30,33,35,53,54,65,75,6,7,8,41,42,57,69,16,17,18,46,47,60,67,12,13,14,15,45,59,72,19,20,21,22,48,61,68,23,24,25,49,50,62,71,9,10,11,43,44,58,70,29,31,32,34,36,64,76,26,27,28,51,52,63,73","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d.txt"},{"canonical_hash":"e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,70,6,7,8,9,10,11,75,60,61,62,63,64,65,68,18,19,20,21,22,23,76,24,25,26,27,28,29,66,42,43,44,45,46,47,73,48,49,50,51,52,53,72,30,31,32,33,34,35,67,54,55,56,57,58,59,71,12,13,14,15,16,17,69,36,37,38,39,40,41,74","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:49","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378.txt"},{"canonical_hash":"d2a61d29742d49dd19922ccc12aa75e870a46faf3bc859fdd0d579ff1b31399f","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,12,20,35,46,56,68,1,11,21,36,47,57,71,7,17,27,32,42,52,70,60,61,62,63,64,65,76,9,19,29,39,44,54,75,4,10,24,34,45,55,67,8,18,28,33,43,53,73,5,15,25,31,41,51,66,6,16,26,30,40,50,69,3,14,23,38,49,59,74,2,13,22,37,48,58,72","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:49","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/d2a61d29742d49dd19922ccc12aa75e870a46faf3bc859fdd0d579ff1b31399f.txt"},{"canonical_hash":"80df7fad9fa66fe51195cb8d2555ac1097b0db320b0a8ffa63e3cf8c589c8a0d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,12,20,37,48,58,72,1,11,21,36,47,57,71,6,16,26,32,42,52,69,8,18,28,33,43,53,73,2,13,22,35,46,56,68,3,14,23,38,49,59,74,4,10,24,34,45,55,67,5,15,25,30,40,50,66,7,17,27,31,41,51,70,60,61,62,63,64,65,76,9,19,29,39,44,54,75","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/80df7fad9fa66fe51195cb8d2555ac1097b0db320b0a8ffa63e3cf8c589c8a0d.txt"},{"canonical_hash":"d08bad00a7853889faa2a48338611ef91bafb3bf67fae9d85c6f3c5fac5bd4d3","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,11,20,34,45,55,67,1,10,21,35,46,56,68,3,13,23,37,48,58,72,6,16,26,30,40,50,69,7,17,27,32,42,52,70,60,61,62,63,64,65,76,9,19,29,39,44,54,75,4,14,24,38,49,59,74,5,15,25,31,41,51,66,8,18,28,33,43,53,73,2,12,22,36,47,57,71","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/d08bad00a7853889faa2a48338611ef91bafb3bf67fae9d85c6f3c5fac5bd4d3.txt"},{"canonical_hash":"0f7c66027161d31f043d2259f1b801f34900a7f6d1954571489032d4812f5629","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,12,20,35,46,56,68,1,11,21,36,47,57,71,2,13,22,37,48,58,72,3,14,23,38,49,59,74,7,17,27,33,43,53,70,9,19,29,39,44,54,75,6,16,26,32,42,52,69,5,15,25,30,40,50,66,4,10,24,34,45,55,67,8,18,28,31,41,51,73,60,61,62,63,64,65,76","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/0f7c66027161d31f043d2259f1b801f34900a7f6d1954571489032d4812f5629.txt"},{"canonical_hash":"c1ed850353bdcc1eb7475edf09be0052f6ed9804a50fcfe49c6fc3e50f297091","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,30,40,50,71,1,11,21,39,41,51,72,6,16,26,35,46,56,69,4,14,24,33,44,54,73,8,18,28,37,48,58,75,7,17,27,36,47,57,70,3,13,23,32,43,53,68,5,15,25,34,45,55,74,2,12,22,31,42,52,66,9,19,29,38,49,59,67,60,61,62,63,64,65,76","comment":"F_11(6, 6) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/c1ed850353bdcc1eb7475edf09be0052f6ed9804a50fcfe49c6fc3e50f297091.txt"},{"canonical_hash":"a2d5cf5003dd84c3a903146e7a6e34fbb5c6b0b2b4ddc575a055f83bab0bfd65","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,30,40,50,70,1,11,21,31,41,51,72,5,15,25,34,45,55,73,9,19,29,38,49,59,67,60,61,62,63,64,65,76,7,17,27,36,47,57,71,3,13,23,39,43,53,68,6,16,26,35,46,56,66,8,18,28,37,48,58,75,4,14,24,33,44,54,69,2,12,22,32,42,52,74","comment":"F_11(5, 7) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/a2d5cf5003dd84c3a903146e7a6e34fbb5c6b0b2b4ddc575a055f83bab0bfd65.txt"},{"canonical_hash":"a8bf484a26d6d970fa38b68ff8761a583a974592ed3d92ce3524bc40b356dd63","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,11,20,30,41,51,66,1,10,21,31,40,50,68,60,61,62,63,64,65,76,6,16,26,35,46,56,73,5,15,25,34,45,55,72,8,18,28,37,48,58,75,4,14,24,33,44,54,71,2,12,22,32,42,52,69,7,17,27,36,47,57,74,9,19,29,38,49,59,67,3,13,23,39,43,53,70","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/a8bf484a26d6d970fa38b68ff8761a583a974592ed3d92ce3524bc40b356dd63.txt"},{"canonical_hash":"1c5b0e2a4c81e28721405b66c6a75a5d826a870554de2ffc705981d353b98d0b","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,30,40,50,68,1,11,21,31,41,51,74,5,15,25,34,45,55,69,7,17,27,36,47,57,73,6,16,26,35,46,56,71,2,12,22,32,42,52,70,4,14,24,39,44,54,66,60,61,62,63,64,65,76,3,13,23,33,43,53,72,8,18,28,37,48,58,75,9,19,29,38,49,59,67","comment":"F_11(4, 8) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/1c5b0e2a4c81e28721405b66c6a75a5d826a870554de2ffc705981d353b98d0b.txt"},{"canonical_hash":"fbe9ed86dadd1d2d3ad6392c3ea8f135eb4c63ec1eafb4df5c2be2f85a75ce9e","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"2,13,23,33,43,53,66,1,11,21,31,40,50,67,0,10,20,30,41,51,73,60,61,62,63,64,65,76,5,16,26,36,46,56,68,4,15,25,35,45,55,71,7,18,28,37,48,58,72,3,14,24,34,44,54,74,9,12,22,32,42,52,70,6,17,27,39,47,57,75,8,19,29,38,49,59,69","comment":"F_11(4, 8) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/fbe9ed86dadd1d2d3ad6392c3ea8f135eb4c63ec1eafb4df5c2be2f85a75ce9e.txt"},{"canonical_hash":"0effecc631b9063b611e8121df7e3bf991837e519c86db48be6642e79e27c755","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"6,17,27,36,47,57,66,9,11,21,31,41,51,67,5,16,26,35,46,56,74,3,14,24,33,44,54,68,8,19,29,38,49,59,73,0,10,20,30,40,50,69,4,15,25,34,45,55,71,1,12,22,32,42,52,72,2,13,23,39,43,53,75,60,61,62,63,64,65,76,7,18,28,37,48,58,70","comment":"F_11(5, 7) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/0effecc631b9063b611e8121df7e3bf991837e519c86db48be6642e79e27c755.txt"},{"canonical_hash":"ccdb12afb22da8ed9220f5a50b1f559a5f1d11488934a41ba79194e674f7c3c3","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,19,29,38,49,59,66,1,11,21,31,41,51,67,60,61,62,63,64,65,76,9,15,25,34,45,55,71,4,14,24,33,44,54,72,6,17,27,36,47,57,69,3,13,23,32,43,53,73,0,10,20,39,40,50,75,5,16,26,35,46,56,70,7,18,28,37,48,58,68,2,12,22,30,42,52,74","comment":"F_11(6, 6) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:54","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/ccdb12afb22da8ed9220f5a50b1f559a5f1d11488934a41ba79194e674f7c3c3.txt"},{"canonical_hash":"d62af2ad60397a700452f49c0d965613c81ad9ae14661d4bf638a9ab33745a99","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,19,29,33,43,53,66,1,11,21,34,44,54,67,6,17,27,30,40,51,69,0,10,20,39,45,55,75,2,13,23,36,47,57,73,7,18,28,32,42,52,68,5,16,26,31,41,50,70,9,12,22,35,46,56,74,4,15,25,38,49,59,71,3,14,24,37,48,58,72,60,61,62,63,64,65,76","comment":"F_11(10, 2) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:54","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/d62af2ad60397a700452f49c0d965613c81ad9ae14661d4bf638a9ab33745a99.txt"},{"canonical_hash":"609c8488c1221ec7cc1b224882281cdf16c044d84dccec5c4b9550762e96f98c","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"6,17,27,37,48,58,66,0,11,21,30,42,52,67,1,10,22,32,43,53,69,3,13,24,39,40,50,75,8,19,29,31,41,51,73,4,14,25,34,45,55,68,7,18,28,38,49,59,70,9,16,20,36,47,57,74,5,15,26,35,46,56,71,2,12,23,33,44,54,72,60,61,62,63,64,65,76","comment":"F_11(10, 2) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/609c8488c1221ec7cc1b224882281cdf16c044d84dccec5c4b9550762e96f98c.txt"},{"canonical_hash":"b69d7fba7733d8ec194d1fe470c23299a6bbf7f834fcda60a95bfadcfba0958c","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,19,29,31,41,50,66,0,11,21,30,40,51,67,2,12,23,32,43,53,74,7,18,28,38,49,59,68,3,13,24,33,44,54,73,6,17,27,37,48,58,69,5,15,26,35,46,56,71,4,14,25,34,45,55,72,1,10,22,39,42,52,75,60,61,62,63,64,65,76,9,16,20,36,47,57,70","comment":"F_11(5, 7) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/b69d7fba7733d8ec194d1fe470c23299a6bbf7f834fcda60a95bfadcfba0958c.txt"},{"canonical_hash":"5e6aa1badf9e56cb7fdedb488e3ef1dcf34cbc2a2c9af577c3e3b36d4606ad9f","size":77,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"66,67,69,75,73,68,70,74,71,72,76,0,1,7,26,29,32,37,40,43,46,49,3,9,25,28,31,34,36,39,42,45,48,5,12,15,18,21,24,50,53,56,59,62,2,8,27,30,33,35,38,41,44,47,65,6,10,13,16,19,22,51,54,57,60,63,4,11,14,17,20,23,52,55,58,61,64","comment":"F_7(4, 1) base × F_11(10, 2) fiber: 7 blocks of 11 (sub-magma at F_7 nat 0). Size-77 twisted F_7 × F_11 fiber bundle: the F_11 sub-magma occupies one of the F_7 cosets of the base, the other 6 cosets are F_11 fibers.","submitted_at":"2026-04-23 21:21:56","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/5e6aa1badf9e56cb7fdedb488e3ef1dcf34cbc2a2c9af577c3e3b36d4606ad9f.txt"},{"canonical_hash":"ee4583ce949a0e270f9516e470f60a7aca92780fb01c370ddec5857db8ff994f","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,22,38,49,59,66,1,12,20,35,46,56,67,60,61,62,63,64,65,76,4,15,25,30,40,50,71,7,18,28,33,44,54,72,8,19,29,34,45,55,69,2,13,23,36,47,57,73,6,17,27,39,43,53,75,3,14,24,37,48,58,70,5,16,26,32,42,52,68,9,11,21,31,41,51,74","comment":"F_11(6, 6) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:56","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/ee4583ce949a0e270f9516e470f60a7aca92780fb01c370ddec5857db8ff994f.txt"},{"canonical_hash":"1d02f36e6e79c4e0d5c5938f4a162287d3bad833584e12b2db918f3e2fd08f81","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"3,13,23,35,46,56,66,1,11,21,32,43,53,67,8,19,29,30,42,52,69,7,17,27,39,40,50,75,0,10,20,33,44,54,73,6,16,26,38,49,59,68,2,12,22,34,45,55,70,4,14,24,36,47,57,74,5,15,25,37,48,58,71,9,18,28,31,41,51,72,60,61,62,63,64,65,76","comment":"F_11(10, 2) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:57","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/1d02f36e6e79c4e0d5c5938f4a162287d3bad833584e12b2db918f3e2fd08f81.txt"},{"canonical_hash":"2570115b07c414cfeeb7a2c6e109688ea10588036adc8542cf84a052a83df0ff","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"6,17,27,32,43,53,66,9,11,21,35,46,56,67,60,61,62,63,64,65,76,4,15,25,37,48,58,71,1,12,22,30,40,51,72,0,10,20,31,41,50,69,8,19,29,34,45,55,73,2,13,23,39,42,52,75,7,18,28,33,44,54,70,3,14,24,36,47,57,68,5,16,26,38,49,59,74","comment":"F_11(6, 6) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:57","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/2570115b07c414cfeeb7a2c6e109688ea10588036adc8542cf84a052a83df0ff.txt"},{"canonical_hash":"629ab6341cd973980cbbd61496a9220b9a2ad2f6cbea16f417813914f777cc43","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,19,29,30,42,52,66,0,11,21,31,41,51,67,3,13,24,35,46,56,73,60,61,62,63,64,65,76,7,18,28,33,44,54,68,5,15,26,37,48,58,71,4,14,25,36,47,57,72,2,12,23,34,45,55,74,9,16,20,38,49,59,70,1,10,22,39,40,50,75,6,17,27,32,43,53,69","comment":"F_11(4, 8) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:58","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/629ab6341cd973980cbbd61496a9220b9a2ad2f6cbea16f417813914f777cc43.txt"},{"canonical_hash":"18fc683ad71bf835c93d962472c5b8d41f476fc340d80895a072fbcb35a73c32","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"9,11,21,33,43,53,66,3,14,24,36,46,56,67,8,19,29,35,45,55,73,60,61,62,63,64,65,76,1,12,20,31,41,51,68,2,13,23,30,40,50,71,5,16,26,38,48,58,72,0,10,22,32,42,52,74,7,18,28,34,44,54,70,6,17,27,39,49,59,75,4,15,25,37,47,57,69","comment":"F_11(4, 8) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:21:58","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/18fc683ad71bf835c93d962472c5b8d41f476fc340d80895a072fbcb35a73c32.txt"},{"canonical_hash":"ba2659e3d875edec9a58973d1e5a59a409e503dd8379d7758e48aa8aa91fe243","size":77,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"66,67,73,76,68,71,72,74,70,75,69,0,20,23,26,29,32,50,53,56,59,62,1,22,25,28,31,34,52,55,58,61,64,5,7,9,12,15,18,36,39,42,45,48,2,21,24,27,30,33,51,54,57,60,63,3,6,10,13,16,19,37,40,43,46,49,4,8,11,14,17,35,38,41,44,47,65","comment":"F_7(4, 1) base × F_11(4, 8) fiber: 7 blocks of 11 (sub-magma at F_7 nat 0). Size-77 twisted F_7 × F_11 fiber bundle: the F_11 sub-magma occupies one of the F_7 cosets of the base, the other 6 cosets are F_11 fibers.","submitted_at":"2026-04-23 21:21:58","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/ba2659e3d875edec9a58973d1e5a59a409e503dd8379d7758e48aa8aa91fe243.txt"},{"canonical_hash":"142468854d405b83c00226884d8f598ec4006f0ae2920d7a6c0d23cc63337a08","size":77,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"66,67,76,71,72,69,73,75,70,68,74,0,7,26,29,32,35,38,41,44,47,65,1,3,25,28,31,34,37,40,43,46,49,5,9,12,15,18,21,51,54,57,60,63,2,8,24,27,30,33,36,39,42,45,48,6,10,13,16,19,22,52,55,58,61,64,4,11,14,17,20,23,50,53,56,59,62","comment":"F_7(4,1) base × F_11(6,6) fiber: 7 blocks of 11 (sub-magma at F_7 left-id). Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:21:59","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/142468854d405b83c00226884d8f598ec4006f0ae2920d7a6c0d23cc63337a08.txt"},{"canonical_hash":"f59982e06fd8e46ca8a925a818bbbfbe68d94087e0cfa4cbef7756bcf9a9fdcb","size":77,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"66,67,74,68,73,69,71,72,75,76,70,0,8,11,14,17,20,52,55,58,61,64,3,7,10,13,16,19,51,54,57,60,63,5,24,27,30,33,35,38,41,44,47,65,2,9,12,15,18,21,50,53,56,59,62,6,22,25,28,31,34,36,39,42,45,48,1,4,23,26,29,32,37,40,43,46,49","comment":"F_7(4, 1) base × F_11(5, 7) fiber: 7 blocks of 11 (sub-magma at F_7 nat 0). Size-77 twisted F_7 × F_11 fiber bundle: the F_11 sub-magma occupies one of the F_7 cosets of the base, the other 6 cosets are F_11 fibers.","submitted_at":"2026-04-23 21:22:00","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/f59982e06fd8e46ca8a925a818bbbfbe68d94087e0cfa4cbef7756bcf9a9fdcb.txt"},{"canonical_hash":"096971eaef83bffb395a381c19275e6a285568ab61ce7a4c541144386a9bcf7a","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"2,13,23,36,47,57,66,9,11,21,33,44,54,67,3,14,24,37,48,58,74,5,16,26,31,41,52,68,0,10,20,34,45,55,73,8,19,29,32,43,53,69,4,15,25,38,49,59,71,7,18,28,30,42,51,72,6,17,27,39,40,50,75,60,61,62,63,64,65,76,1,12,22,35,46,56,70","comment":"F_11(5, 7) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:00","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/096971eaef83bffb395a381c19275e6a285568ab61ce7a4c541144386a9bcf7a.txt"},{"canonical_hash":"3e111b62f9a34338b05a1eef31634eeac98395a3f63ae47135fffb9f3d1d128d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"5,16,26,36,46,56,66,0,10,20,30,40,52,67,60,61,62,63,64,65,76,2,12,22,32,42,53,71,8,19,29,39,49,59,72,4,14,24,34,44,55,69,7,18,28,38,48,58,73,1,11,21,31,41,51,75,3,13,23,33,43,54,70,9,15,25,35,45,50,68,6,17,27,37,47,57,74","comment":"F_11(6, 6) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:01","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/3e111b62f9a34338b05a1eef31634eeac98395a3f63ae47135fffb9f3d1d128d.txt"},{"canonical_hash":"7e98ac517f8529e10edd64a2dbdcf0716b1e1ea6d4bcabf776f7c383cda5136d","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,14,24,34,44,55,66,8,19,29,39,49,59,67,2,12,22,32,42,53,73,60,61,62,63,64,65,76,0,10,20,30,40,52,68,5,16,26,36,46,56,71,6,17,27,37,47,57,72,9,15,25,35,45,50,74,3,13,23,33,43,54,70,1,11,21,31,41,51,75,7,18,28,38,48,58,69","comment":"F_11(4, 8) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:01","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/7e98ac517f8529e10edd64a2dbdcf0716b1e1ea6d4bcabf776f7c383cda5136d.txt"},{"canonical_hash":"f58a04628c4b32a3a47f1e9514cd8eddf616a7738b914b3b5e3d18424442b87b","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"3,14,24,34,44,54,66,9,11,21,30,40,50,67,8,19,29,39,49,59,74,6,17,27,37,47,57,68,5,16,26,36,46,56,73,1,12,20,31,41,51,69,7,18,28,38,48,58,71,2,13,23,33,43,53,72,0,10,22,32,42,52,75,60,61,62,63,64,65,76,4,15,25,35,45,55,70","comment":"F_11(5, 7) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:02","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/f58a04628c4b32a3a47f1e9514cd8eddf616a7738b914b3b5e3d18424442b87b.txt"},{"canonical_hash":"fdfa89915be5d31f2386e8b8ea269a0304e33f3ecc732e692a9cd354624a419e","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,15,25,35,45,55,66,5,16,26,36,46,56,67,8,19,29,39,49,59,69,1,11,20,30,41,51,75,2,13,23,33,43,53,73,9,12,22,32,42,50,68,0,10,21,31,40,52,70,7,18,28,38,48,58,74,6,17,27,37,47,57,71,3,14,24,34,44,54,72,60,61,62,63,64,65,76","comment":"F_11(10, 2) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:02","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/fdfa89915be5d31f2386e8b8ea269a0304e33f3ecc732e692a9cd354624a419e.txt"},{"canonical_hash":"890afe7d18fc5829c22763230887bcc55424b15f1aafa8ec136cb8772e59bad6","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"1,11,21,31,41,51,66,5,16,26,36,46,56,67,8,19,29,39,49,59,73,60,61,62,63,64,65,76,7,18,28,38,48,58,68,6,17,27,37,47,57,71,0,10,20,30,40,50,72,4,15,25,35,45,55,74,2,12,22,32,42,53,70,9,13,23,33,43,52,75,3,14,24,34,44,54,69","comment":"F_11(4, 8) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:02","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/890afe7d18fc5829c22763230887bcc55424b15f1aafa8ec136cb8772e59bad6.txt"},{"canonical_hash":"c6087800d19344ec7a4e6a4d71758b884911e8f7e7474c34d898093b3bb64a91","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,19,29,39,49,59,66,5,16,26,36,46,56,67,3,14,24,34,44,54,74,9,13,23,33,43,52,68,2,12,22,32,42,53,73,4,15,25,35,45,55,69,6,17,27,37,47,57,71,7,18,28,38,48,58,72,1,11,21,31,41,51,75,60,61,62,63,64,65,76,0,10,20,30,40,50,70","comment":"F_11(5, 7) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:03","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/c6087800d19344ec7a4e6a4d71758b884911e8f7e7474c34d898093b3bb64a91.txt"},{"canonical_hash":"c539940867c986a0a1073206aa606fb301b27139c3e9357da4da5988ddbec2ae","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"2,12,22,32,42,53,66,1,11,21,31,41,51,67,5,16,26,36,46,56,69,9,13,23,33,43,52,75,3,14,24,34,44,54,73,8,19,29,39,49,59,68,7,18,28,38,48,58,70,0,10,20,30,40,50,74,4,15,25,35,45,55,71,6,17,27,37,47,57,72,60,61,62,63,64,65,76","comment":"F_11(10, 2) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:03","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/c539940867c986a0a1073206aa606fb301b27139c3e9357da4da5988ddbec2ae.txt"},{"canonical_hash":"8b38eb0e4ba28ac2ddc3e949bb31ba8d1b7d25f5047510fd5f5ea112d69bd788","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"5,16,26,36,46,56,66,8,19,29,39,49,59,67,2,12,22,32,42,53,73,60,61,62,63,64,65,76,0,10,20,30,40,50,68,4,15,25,35,45,55,71,1,11,21,31,41,51,72,6,17,27,37,47,57,74,7,18,28,38,48,58,70,9,14,24,34,44,52,75,3,13,23,33,43,54,69","comment":"F_11(4, 8) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:04","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/8b38eb0e4ba28ac2ddc3e949bb31ba8d1b7d25f5047510fd5f5ea112d69bd788.txt"},{"canonical_hash":"e28c792184790f687caadc40055bb14fcba72e2bd9ede02943d40b210ab03e94","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"2,13,23,33,43,53,66,1,11,20,30,41,51,67,60,61,62,63,64,65,76,4,15,25,35,45,55,71,8,19,29,39,49,59,72,3,14,24,34,44,54,69,0,10,21,31,40,52,73,9,12,22,32,42,50,75,7,18,28,38,48,58,70,6,17,27,37,47,57,68,5,16,26,36,46,56,74","comment":"F_11(6, 6) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:05","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/e28c792184790f687caadc40055bb14fcba72e2bd9ede02943d40b210ab03e94.txt"},{"canonical_hash":"68a9b50691fe703ac73d06598244743c1485cfa9a6e73798a1481e5e49783ad7","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,15,25,35,45,55,66,1,11,21,31,41,51,67,9,12,22,32,42,52,69,2,13,23,33,43,53,75,5,16,26,36,46,56,73,6,17,27,37,47,57,68,8,19,29,39,49,59,70,7,18,28,38,48,58,74,3,14,24,34,44,54,71,0,10,20,30,40,50,72,60,61,62,63,64,65,76","comment":"F_11(10, 2) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:05","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/68a9b50691fe703ac73d06598244743c1485cfa9a6e73798a1481e5e49783ad7.txt"},{"canonical_hash":"884b08d51449ed77e1a667f669d83886c6bad5f585ed6ff76e2bf63ff2c61f44","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"9,10,20,30,41,51,66,0,11,21,31,40,52,67,6,17,27,37,47,57,74,5,16,26,36,46,56,68,2,13,23,33,43,53,73,4,15,25,35,45,55,69,3,14,24,34,44,54,71,7,18,28,38,48,58,72,1,12,22,32,42,50,75,60,61,62,63,64,65,76,8,19,29,39,49,59,70","comment":"F_11(5, 7) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:06","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/884b08d51449ed77e1a667f669d83886c6bad5f585ed6ff76e2bf63ff2c61f44.txt"},{"canonical_hash":"1371a8eb1a0d3fdea23dd40f0b4e492a4d113abf96c87d6a9392efa8a6f14aef","size":77,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"3,13,23,33,43,54,66,7,18,28,38,48,58,67,60,61,62,63,64,65,76,9,14,24,34,44,50,71,6,17,27,37,47,57,72,5,16,26,36,46,56,69,2,12,22,32,42,53,73,4,15,25,35,45,55,75,8,19,29,39,49,59,70,1,10,20,30,41,51,68,0,11,21,31,40,52,74","comment":"F_11(6, 6) base × 7-fiber (twisted): 11 fibers of 7. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:22:06","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/1371a8eb1a0d3fdea23dd40f0b4e492a4d113abf96c87d6a9392efa8a6f14aef.txt"},{"canonical_hash":"95709784173c62166e0281107140dd53c0e7c31d22d3a5dbc25d4f33f2e58a2e","size":77,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,7,12,17,22,28,66,1,6,13,18,23,27,67,32,37,42,46,51,56,74,30,36,40,48,53,58,75,33,38,43,47,52,57,71,3,9,11,16,20,25,70,34,39,44,45,50,55,72,60,61,62,63,64,65,76,2,8,14,19,24,29,68,31,35,41,49,54,59,73,4,5,10,15,21,26,69","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:22:07","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/95709784173c62166e0281107140dd53c0e7c31d22d3a5dbc25d4f33f2e58a2e.txt"},{"canonical_hash":"d4908b869d5ae67b274ea23e98d3a2b2496095883ef30e4d122d513034ccac45","size":77,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,6,12,19,24,28,67,1,7,13,16,20,25,69,2,8,14,17,22,27,68,32,37,42,47,52,57,72,31,36,41,45,50,55,71,34,39,44,46,51,56,74,4,5,11,18,23,29,66,30,35,40,48,53,58,73,60,61,62,63,64,65,76,3,9,10,15,21,26,70,33,38,43,49,54,59,75","comment":"F_11(10, 2) base × 7-fiber: 11 fibers of 7. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:22:07","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/77/d4908b869d5ae67b274ea23e98d3a2b2496095883ef30e4d122d513034ccac45.txt"},{"canonical_hash":"48fa6b96a24eaf1f44a8f747b2758350b130fbc6dc60815158901616de4728f7","size":79,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,2,24,51,77,38,48,32,69,4,9,36,23,28,33,12,34,68,13,47,75,66,7,63,57,46,61,53,70,41,8,39,11,71,15,26,3,5,52,30,55,78,29,56,76,18,17,6,10,45,21,65,14,67,44,27,35,72,31,37,19,40,49,73,22,42,60,16,59,54,1,62,20,25,43,58,74,64,50","comment":"Translation invariant model on F_q with q = 79 of the form (x,y) -> x + delta_i * (y - x) where delta_i is in [5,53,6] depending on the class of (y-x) in F_q^* / (F_q^*)^3.","submitted_at":"2026-05-12 09:24:45","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/79/48fa6b96a24eaf1f44a8f747b2758350b130fbc6dc60815158901616de4728f7.txt"},{"canonical_hash":"ebeb9249e630de2d476c2deabac28702cd4bd8a2e9f390037679125f2f8e9a45","size":80,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,3,2,79,21,66,36,51,16,77,62,32,47,12,65,50,20,35,15,73,58,28,43,8,49,34,64,19,14,61,46,76,31,11,41,26,56,71,6,69,54,24,39,4,25,70,40,55,5,45,30,60,75,10,53,38,68,23,18,57,42,72,27,7,29,74,44,59,9,37,22,52,67,17,33,78,48,63,13","comment":"Linear magma over the extension field F_16: x ◇ y = (9, 8) × F_5(2,4) direct product (coefficients in F_16).","submitted_at":"2026-04-23 21:22:07","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/80/ebeb9249e630de2d476c2deabac28702cd4bd8a2e9f390037679125f2f8e9a45.txt"},{"canonical_hash":"9ec34e5d7233e8953a2fa801c206b195473c59d0c7836b1f0f582edb83284699","size":80,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"75,76,77,79,78,3,1,0,62,2,45,46,44,71,47,57,56,58,61,59,28,30,29,60,31,53,52,54,73,55,40,42,41,70,43,20,22,21,67,23,12,14,13,65,15,16,18,17,66,19,36,38,37,69,39,8,10,9,64,11,24,26,25,68,27,32,34,33,74,35,4,6,5,63,7,49,50,48,72,51","comment":"Direct product of two linear magmas: F_16 × F_5. The operation is (x₁, x₂) ◇ (y₁, y₂) = (6x₁ + 11y₁ (mod 16), 2x₂ + 4y₂ (mod 5)).","submitted_at":"2026-04-23 21:22:08","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/80/9ec34e5d7233e8953a2fa801c206b195473c59d0c7836b1f0f582edb83284699.txt"},{"canonical_hash":"afeae577d2282082c9a37ff1c658983483099e1335de87d821c98b8bb04da69f","size":80,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,20,56,40,32,48,60,52,64,28,24,76,72,68,44,36,1,21,53,41,73,45,77,61,65,29,57,25,49,37,33,69,3,19,55,31,75,59,63,23,27,47,51,67,39,71,43,35,2,22,74,58,66,34,50,30,38,54,70,62,26,78,42,46,4,5,10,18,7,9,17,13,79,16,12,15,8,14,11,6","comment":"Size-80 (= 5 × 16) right-cancellative magma, with EVERY element idempotent. Decomposes as a TWISTED fiber bundle: F_5(2,4) base × F_16(9,8) fiber. The 80 elements partition into 5 fibers of 16 (an F_5-quotient congruence), and every fiber is itself a closed sub-magma isomorphic to F_16(9,8) (a linear magma over the extension field F_16 = F_2⁴). However, the cross-fiber multiplication has a non-trivial cocycle, so the magma is NOT isomorphic to the direct product F_5 × F_16. The all-idempotence comes from both factors being all-idempotent: F_5(2,4) has 2+4=6≡1 (mod 5) and F_16(9,8) has 9+8=1 (in F_16, where addition is XOR), so x ◇ x = (a+b)·x = x in each. Quasigroup (LC + RC). Compare with the size-80 twist 0998765e, which uses F_16(6,11) instead of F_16(9,8) as fiber: F_16(6,11) is NOT all-idempotent (6 XOR 11 = 13 in F_16), so 0998765e has only 5 idempotents (one per fiber), not all 80.","submitted_at":"2026-04-23 21:22:08","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/80/afeae577d2282082c9a37ff1c658983483099e1335de87d821c98b8bb04da69f.txt"},{"canonical_hash":"0998765ec1482be10f1d3ba0fd5c4e73adbfa919f225aca7155f0867dcd51bc9","size":80,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"76,0,44,56,28,52,40,20,12,16,36,8,24,32,4,48,78,1,45,57,29,53,41,21,13,17,37,9,25,33,5,49,77,3,47,59,31,55,43,23,15,19,39,11,27,35,7,51,75,2,46,58,30,54,42,22,14,18,38,10,26,34,6,50,79,60,65,68,61,67,64,72,70,71,63,69,73,62,74,66","comment":"Size-80 (= 5 × 16) right-cancellative magma decomposing as a TWISTED fiber bundle: F_5(2,4) base × F_16 fiber. The 80 elements partition into 5 fibers of 16 (an F_5-quotient congruence), and EVERY fiber is itself a closed sub-magma isomorphic to F_16(6, 11) (a linear magma over the field F_16 = F_2⁴). However, unlike the direct product F_5 × F_16, the cross-fiber multiplication has a non-trivial cocycle, so the magma is NOT isomorphic to the direct product. Each fiber contains its own F_16-idempotent, and the 5 idempotents together form a 5-element sub-magma. Quasigroup (LC + RC). Analogous in structure to the 4 fiber-closed cocycle-twisted size-45 magmas (F_5 × F_9) in the database.","submitted_at":"2026-04-23 21:22:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/80/0998765ec1482be10f1d3ba0fd5c4e73adbfa919f225aca7155f0867dcd51bc9.txt"},{"canonical_hash":"761fd630bdac1efe0388c407a30f871ae136390d81e5d2d13299109d4b5156c2","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"80,0,5,4,6,3,8,7,2,1,42,38,12,52,19,63,79,27,69,34,46,59,31,78,16,23,56,68,55,30,45,22,58,33,15,77,70,9,60,73,47,49,24,32,35,67,76,21,29,14,44,54,40,57,66,26,51,37,72,11,41,62,18,65,17,74,50,61,36,25,48,10,71,64,13,20,39,28,75,53,43","comment":"Direct product of two linear magmas: F_9 × F_9.","submitted_at":"2026-04-23 21:22:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/761fd630bdac1efe0388c407a30f871ae136390d81e5d2d13299109d4b5156c2.txt"},{"canonical_hash":"b9170dc7b819205b58e39f842d5087f493a59482d7b76b80aa3b80f86428ddc9","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,76,29,42,25,8,35,45,12,80,32,30,64,58,78,44,10,56,21,20,65,15,28,5,62,9,16,19,49,18,41,79,70,77,54,26,53,75,71,52,63,68,13,4,31,47,3,14,60,46,7,22,17,23,67,11,37,2,27,66,40,34,55,73,6,24,33,48,43,72,51,69,39,36,74,57,50,59,61,38","comment":"Linear magma over the extension field F_81 = F_3[α]/⟨α⁴ + α + 2⟩.\n\nOperation: x ◇ y = a·x + b·y in F_81 with (a, b) = (2α², 1 + α²). Since α + β = 2α² + 1 + α² = 1 + 3α² = 1 in F_81 (char 3), this is the \"Type 1\" translation-invariant fully-idempotent linear 677 magma, equivalent to x ◇ y = x + β·(y - x) with β = 1 + α² a primitive 10th root of unity in F_81* (which has order 80, divisible by 10).\n\nF_81 is the proper degree-4 extension of F_3; do NOT confuse with the ring Z/81Z (which has zero divisors and is NOT a field).\n\nSize 81, fully idempotent, right-cancellative.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:10","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/b9170dc7b819205b58e39f842d5087f493a59482d7b76b80aa3b80f86428ddc9.txt"},{"canonical_hash":"67110840a79d94d64583763d62d2d2f65ec1f4dc075016fc3fafed86c2e9823f","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":null,"comment":"Size-81 non-idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The unique idempotent is at index 80; it lies in the unique 9-element sub-magma of M, namely {72, 73, …, 80}, which is isomorphic to the unique size-9 Eq 677 magma magma#2925dc18 (the 'x ◇ y = x + 3y mod 9' magma over Z/9Z).\n\nThis magma has no non-trivial congruence (no homomorphism onto a smaller magma), so unlike magma#0dd86070 it is NOT a fiber bundle — there is no 'projection' M → F_9 compatible with the operation. The only sub-magma of size 9 is the one above; pairs {x, y} with x or y outside {72…80} generate the entire magma.\n\nAutomorphism group: Aut(M) is isomorphic to AGL(1, F_9) = F_9 ⋊ F_9* of order 72 — the full automorphism group of the size-9 sub-magma, lifted to all of M. Max element order is 8 (so Aut is not cyclic). Aut acts on M with three orbits:\n  • {80} — the unique idempotent (size 1)\n  • {72, …, 79} — the size-9 sub-magma minus the idempotent (size 8)\n  • {0, …, 71} — everything outside the sub-magma (size 72)\n\nCompare magma#761fd630 (F_9 × F_9 direct product, with 10 size-9 sub-magmas = the 10 projective lines through origin in F_9²) and magma#0dd86070 (size-9 fiber bundle over a size-9 base). All three are non-idempotent RC size-81 extensions of the size-9 Eq 677 magma, distinguished by the kind of extension.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:10","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/67110840a79d94d64583763d62d2d2f65ec1f4dc075016fc3fafed86c2e9823f.txt"},{"canonical_hash":"0dd86070b42eb55a1a255aa4e6a7ee17e6a356f4c97ab7c8fc1c48e3adb556bb","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":null,"comment":"Size-81 non-idempotent right-cancellative magma satisfying Eq 677 and Eq 255. A clean fiber bundle structure:\n\n  • The canonical labeling 0, 1, …, 80 partitions into 9 consecutive blocks B_k = {9k, 9k+1, …, 9k+8} for k = 0, …, 8.\n  • The block partition is a magma congruence: the block of x ◇ y depends only on the blocks of x and y.\n  • The 9-element quotient magma is the unique size-9 Eq 677 magma magma#2925dc18 ('x ◇ y = x + 3y mod 9' over Z/9Z), non-idempotent with a single idempotent.\n  • The unique idempotent of M is at index 80, sitting in block B_8 (the 'idempotent block' of the quotient).\n  • The 9-element sub-magma {72, …, 80} is exactly block B_8 — the canonical section of the bundle.\n\nAutomorphism group: Aut(M) is small — only 9 automorphisms total, corresponding to the additive translation group of F_9 inside the fiber (orbit-stabilizer: 1 fixed point at 80, plus 8 orbits of size 9 + 1 orbit of size 8 = 81). Compare magma#67110840 (also Eq 677 extension of size-9 magma but NOT a fiber bundle, with |Aut| = 72 = full AGL(1, F_9)) and magma#761fd630 (F_9 × F_9 direct product).\n\nThe canonical Cayley table already exposes the fiber-bundle structure — the rendered image shows a clean 9×9 grid of 9×9 blocks. No display reorder is needed.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:11","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/0dd86070b42eb55a1a255aa4e6a7ee17e6a356f4c97ab7c8fc1c48e3adb556bb.txt"},{"canonical_hash":"8c8fe34b2bf069fdf8c12ee7df6a1fa5fccabb7318f8ca239853ec405e58bd83","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,69,73,1,13,41,9,31,32,12,58,23,40,29,39,59,27,3,45,55,21,77,79,50,43,78,46,22,44,8,19,33,51,15,36,61,60,11,64,80,6,35,66,7,52,57,16,24,68,25,10,48,34,62,20,70,67,5,18,28,26,76,74,37,30,14,49,71,54,38,72,56,75,17,53,63,47,42,65,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:18","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/8c8fe34b2bf069fdf8c12ee7df6a1fa5fccabb7318f8ca239853ec405e58bd83.txt"},{"canonical_hash":"c953a56ce5e7ec144e851649e78cefe68bc0f2a7777701c2b8a47e8d6beac300","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,43,7,10,57,73,44,27,18,61,20,29,71,26,25,56,12,24,48,39,70,4,1,31,63,28,9,40,17,68,21,47,38,49,59,41,78,36,74,67,35,8,2,46,42,45,55,30,37,15,62,75,69,19,6,22,72,77,60,51,64,33,13,79,76,16,65,80,34,23,66,32,5,54,52,11,50,53,14,3,58","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:23","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/c953a56ce5e7ec144e851649e78cefe68bc0f2a7777701c2b8a47e8d6beac300.txt"},{"canonical_hash":"2dfb65a748eaf3fab37b6c2f84340eee0c670742f2d5c5a703e75cd65e224b53","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,8,66,54,77,9,45,19,43,71,63,70,29,6,20,73,22,74,3,62,79,40,58,37,32,16,14,35,46,7,36,2,28,61,65,34,53,11,18,33,39,30,78,55,49,51,25,26,47,60,50,5,24,52,41,31,57,44,38,59,15,42,76,12,1,69,68,56,67,48,23,80,75,27,10,13,21,72,17,64,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/2dfb65a748eaf3fab37b6c2f84340eee0c670742f2d5c5a703e75cd65e224b53.txt"},{"canonical_hash":"fb3d42593f8d08ab5b0665bf055a9d91d6bc487eaf0631cdbb9f164718e54339","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,65,3,12,7,74,68,13,36,31,80,19,42,69,79,22,72,77,39,33,41,23,24,11,6,15,26,53,70,27,75,51,76,46,44,20,49,28,17,67,52,66,48,1,25,61,10,9,34,64,35,37,2,40,29,16,50,56,32,5,38,45,43,54,55,73,63,30,18,59,21,60,14,58,8,71,57,62,47,78,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/fb3d42593f8d08ab5b0665bf055a9d91d6bc487eaf0631cdbb9f164718e54339.txt"},{"canonical_hash":"80f35e67e63a8d8ec8d4b221c3134778e7c249320106f5e2e0b5fec99147d80c","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,34,52,80,13,39,27,71,23,16,40,10,55,12,43,51,61,19,5,69,64,45,67,7,58,20,42,21,49,8,57,73,70,3,2,18,24,25,59,41,6,29,4,1,31,33,26,38,76,47,53,15,74,54,14,79,56,9,75,77,35,62,37,17,65,32,72,36,63,22,46,78,60,48,30,28,44,68,11,66,50","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/80f35e67e63a8d8ec8d4b221c3134778e7c249320106f5e2e0b5fec99147d80c.txt"},{"canonical_hash":"4e1ee4652e8de9a7f60b3b8864e5133bcedcba3abc3c82b1ad9cdef564f0023b","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,27,70,36,38,22,26,12,18,23,78,17,3,76,21,8,48,72,75,15,35,9,51,54,55,46,61,32,60,65,29,67,59,45,5,10,49,34,31,57,39,63,6,68,64,40,37,41,33,56,71,44,24,2,74,47,28,62,19,11,80,50,79,66,7,30,53,13,20,4,1,69,58,16,73,77,42,14,25,43,52","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/4e1ee4652e8de9a7f60b3b8864e5133bcedcba3abc3c82b1ad9cdef564f0023b.txt"},{"canonical_hash":"74547d11c47386323a0fce9d3f9fd1835772c23019dfb94baf9bb105954fb98d","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,16,67,11,24,32,30,26,33,72,8,45,42,39,74,68,50,44,63,47,77,6,70,73,12,37,64,21,23,38,55,52,76,18,75,49,79,60,19,3,57,56,28,14,41,22,9,17,54,40,51,36,61,7,29,20,48,27,80,34,62,53,10,65,15,78,13,5,59,43,71,58,66,2,69,25,35,46,4,1,31","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:22:55","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/74547d11c47386323a0fce9d3f9fd1835772c23019dfb94baf9bb105954fb98d.txt"},{"canonical_hash":"4dbcf783500dfbfcacb784433af0293ca504f0852fe418e7eb6476d424b6a28b","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,67,47,7,32,34,58,3,56,8,35,40,66,22,51,55,52,11,13,75,31,80,18,60,37,20,28,16,25,78,33,44,53,79,74,50,63,30,17,9,59,54,24,21,71,2,29,19,1,5,57,77,68,73,14,61,70,39,41,49,42,15,48,72,38,62,26,10,46,27,45,23,6,43,69,12,65,64,36,76,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:02","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/4dbcf783500dfbfcacb784433af0293ca504f0852fe418e7eb6476d424b6a28b.txt"},{"canonical_hash":"1e8e6553248ad68a61e3026d14f46adf2429803b6ec20b655e6de64e4523127d","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,77,36,27,21,74,66,76,58,52,73,9,47,30,70,78,49,19,13,41,35,12,2,64,55,14,60,59,8,38,24,37,26,57,31,48,67,29,18,46,39,80,25,68,33,17,10,1,32,51,45,44,71,69,53,3,75,28,62,54,42,16,22,79,34,23,43,56,5,20,6,63,65,72,40,50,61,11,15,7,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:11","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/1e8e6553248ad68a61e3026d14f46adf2429803b6ec20b655e6de64e4523127d.txt"},{"canonical_hash":"37090f2f3fe52333ac622e77760750b500073b580fad93f820514949574a6d43","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,19,26,13,31,34,52,5,53,24,32,65,64,63,51,48,17,22,45,62,12,67,10,57,80,38,71,50,7,47,28,42,27,58,36,29,59,39,61,21,11,54,69,46,72,55,41,20,18,30,74,2,77,79,43,73,25,9,3,70,35,8,76,68,66,78,15,49,14,75,6,23,4,1,60,16,56,37,40,44,33","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:18","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/37090f2f3fe52333ac622e77760750b500073b580fad93f820514949574a6d43.txt"},{"canonical_hash":"8990f3f2d7f5b51b4cb38299b60b11090a78f3b9580e56a56063fa5a77e7a4b2","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,63,32,34,61,72,69,35,36,2,67,30,15,44,53,56,24,25,75,31,51,80,76,45,38,48,78,9,60,43,5,41,33,12,19,26,20,16,74,50,79,37,7,68,1,73,27,29,39,46,49,77,70,28,17,47,13,40,23,3,59,18,54,42,71,6,8,22,57,62,58,14,66,65,11,52,10,64,55,21,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:25","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/8990f3f2d7f5b51b4cb38299b60b11090a78f3b9580e56a56063fa5a77e7a4b2.txt"},{"canonical_hash":"6eb542448d0d9e5cfcb49f5bf419a5111613d6e32739e1dc6a42801f80d8cfde","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,24,32,17,67,79,34,37,44,72,12,16,31,47,48,73,62,61,64,68,21,18,59,57,41,46,2,53,45,43,38,26,54,27,1,78,15,77,63,10,25,40,28,71,80,23,49,55,76,7,56,30,66,50,14,29,11,51,19,9,42,5,65,52,6,70,22,3,74,75,39,69,20,60,35,8,33,13,36,58,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/6eb542448d0d9e5cfcb49f5bf419a5111613d6e32739e1dc6a42801f80d8cfde.txt"},{"canonical_hash":"23f005a86b95d80a2c72527182973b5e7e921ea831418f2ac76cd993e788f38b","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,32,74,48,72,39,19,62,16,77,43,51,25,45,59,55,49,41,22,11,40,71,50,28,52,69,13,29,37,36,78,1,33,27,7,67,63,56,58,66,10,68,44,31,60,76,38,20,26,61,46,73,79,70,3,80,35,30,24,17,23,47,8,12,57,9,21,65,15,64,5,75,2,34,14,18,42,6,53,54,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/23f005a86b95d80a2c72527182973b5e7e921ea831418f2ac76cd993e788f38b.txt"},{"canonical_hash":"c5da328406e07eaee32726fad2de6a2df97630181c6b6b053af530682792eaee","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,11,74,27,80,78,58,16,31,53,26,77,65,54,73,64,57,44,47,62,38,50,22,33,45,5,14,20,13,49,40,23,51,39,36,75,63,56,15,1,37,35,8,30,60,18,32,61,55,70,34,7,41,67,42,24,76,10,3,12,19,72,28,59,43,68,21,52,66,46,48,25,79,6,9,4,2,17,71,69,29","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:23:53","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/c5da328406e07eaee32726fad2de6a2df97630181c6b6b053af530682792eaee.txt"},{"canonical_hash":"b1d541b5a8d5bfdf9fa533caa6ff8fa030deae0e0ff452ed328de9272047af1e","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,6,13,45,68,24,73,74,60,55,61,30,14,47,19,29,17,64,7,11,57,59,27,66,31,10,12,46,32,63,3,2,33,72,20,16,70,78,69,23,28,34,79,75,54,51,21,58,52,76,49,62,37,5,22,65,15,80,44,8,77,26,42,18,36,50,4,1,48,41,25,56,38,53,35,39,67,40,9,71,43","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#0d529c59, magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:00","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/b1d541b5a8d5bfdf9fa533caa6ff8fa030deae0e0ff452ed328de9272047af1e.txt"},{"canonical_hash":"0d529c590c9e935e1a6f0f2683c7438aaed4bd36df91c728892f65114c62dca6","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,16,46,29,45,13,40,51,31,65,52,9,22,5,75,34,48,18,20,50,21,60,63,58,7,15,49,37,26,12,55,44,3,1,54,68,62,24,78,66,27,11,14,59,71,67,72,80,35,8,76,38,53,17,69,19,42,77,2,43,57,73,33,23,39,56,41,28,25,36,61,30,74,32,64,70,10,47,79,6,4","comment":"Size-81 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_81, NOT the additive group of F_81 = (Z/3)⁴ — this places it in a different family from the (Z/3)⁴-based size-81 magmas (which have an order-10 directional permutation δ).\n\nStructure: x ◇ y = x + f(y − x) in Z_81, where f : Z_81 → Z_81 is a fixed-point-free involution with f(0) = 0 (cycle structure (1, 2⁴⁰): 40 transpositions on Z_81 \\ {0}, plus f(0)=0).\n\nSub-magma design: every pair {x, y} of distinct points generates exactly a 5-element sub-magma, isomorphic to the unique Eq 677 magma over F_5 (the affine sharply 2-transitive one with Aut = AGL(1, 5)). There are 324 = C(81, 2)/C(5, 2) such sub-magmas, every pair on exactly one — a Steiner system S(2, 5, 81). Each point lies on 20 lines. Locally on each line, f acts as F_5 negation (= L_0 of the size-5 magma).\n\nAutomorphism group: Aut(M) = Z_81 (the additive translation group acting regularly; no non-trivial stabilizer of any element). This is the smallest possible Aut for a translation-invariant magma of this size.\n\nThis magma is one of 16 size-81 entries in the DB sharing this Z_81-cyclic + involution + S(2, 5, 81) template. The others (15): magma#1e8e6553, magma#23f005a8, magma#2dfb65a7, magma#37090f2f, magma#4dbcf783, magma#4e1ee465, magma#6eb54244, magma#74547d11, magma#80f35e67, magma#8990f3f2, magma#8c8fe34b, magma#b1d541b5, magma#c5da3284, magma#c953a56c, magma#fb3d4259.\n\nDisplay reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-81 magma automorphism τ (the hidden additive translation by 1 in Z_81). Under this reorder the table is fully translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:07","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/0d529c590c9e935e1a6f0f2683c7438aaed4bd36df91c728892f65114c62dca6.txt"},{"canonical_hash":"cdf12d2049fa8cf9423165df4bccff8988cfe909f16c71cdd3c920ee1bb15bef","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,72,2,27,37,74,58,41,3,31,51,53,15,28,57,38,79,45,6,43,75,67,56,50,64,10,4,40,13,12,80,32,33,60,24,68,34,62,69,16,19,29,46,25,5,66,9,39,36,49,42,14,48,61,78,54,17,7,22,52,21,20,30,44,70,76,47,55,63,26,65,59,18,77,8,35,73,71,11,23","comment":"Size-81 (= 3^4) translation-invariant idempotent right-cancellative magma — same structural template as a1ef80ed26012f89. Carrier is F_81 viewed additively as (Z/3)^4; the operation has the form x ◇ y = x + δ(y - x) for a permutation δ : F_81 → F_81 with δ(0) = 0, where:\n\n  • δ has order exactly 10\n  • δ^5 = -id (additive negation)\n  • δ has cycle structure (10^8, 1) on F_81 — 8 orbits of length 10 on F_81*, fixed at 0\n  • δ acts as multiplication by an element of the order-10 subgroup H ⊂ F_81* on each of the 8 cosets of H; the 8 directional scalars δ_i are roots of x^4 - x^3 + x² - x + 1 mod 3 (i.e., primitive 10th roots of unity in F_81)\n  • NOT F_3-linear → magma is non-medial\n\nAut(magma) has order 81 × 40 = 3240; Sylow-3 = (Z/3)^4 = translation group, stabilizer of 0 is cyclic of order 40 acting F_3-linearly (= the index-2 subgroup of F_81* by multiplication).\n\nDisplay reorder places point with (Z/3)^4 coords (c_0, c_1, c_2, c_3) at index c_0 + 3c_1 + 9c_2 + 27c_3 with respect to a basis recovered from the Sylow-3 of Aut. Under this reorder T[a+x][a+y] = a + T[x][y] for every a in (Z/3)^4 — the nested 3×3×3×3 circulant structure is directly visible.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:08","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/81/cdf12d2049fa8cf9423165df4bccff8988cfe909f16c71cdd3c920ee1bb15bef.txt"},{"canonical_hash":"632999fe988720d6e4b1122c58d44ae4b38c3c642c3b4fe2a9fb06707fadcca2","size":81,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,5,27,29,42,73,66,63,6,45,49,28,35,13,40,3,77,53,50,15,59,10,64,20,57,60,76,56,19,46,71,54,52,55,68,31,23,7,39,58,72,69,44,18,4,22,47,51,48,65,62,78,37,25,33,17,34,2,38,11,41,75,26,74,80,79,32,1,61,67,24,9,30,12,8,21,70,36,16,43,14","comment":"Translation invariant model on F_q with q = 81 of the form (x,y) -> x + delta_i * (y - x) depending on the class of (y-x) in F_q^* / (F_q^*)^5.","submitted_at":"2026-05-12 13:28:07","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/81/632999fe988720d6e4b1122c58d44ae4b38c3c642c3b4fe2a9fb06707fadcca2.txt"},{"canonical_hash":"b89c1afe51cc2a8075432cc11c327084a0045663ac446126480311c22e7196de","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"78,79,23,37,57,50,38,76,36,3,68,41,69,49,46,74,9,12,75,17,45,5,20,55,30,24,53,80,1,56,64,34,40,42,6,35,60,7,18,25,16,77,29,31,70,59,8,0,67,71,10,26,43,72,44,13,28,2,66,51,58,54,48,14,62,33,63,39,11,15,47,4,22,61,27,52,32,21,73,65,19","comment":"Translation invariant model on F_q with q = 81 of the form (x,y) -> x + delta_i * (y - x) depending on the class of (y-x) in F_q^* / (F_q^*)^8.","submitted_at":"2026-05-12 15:10:48","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/81/b89c1afe51cc2a8075432cc11c327084a0045663ac446126480311c22e7196de.txt"},{"canonical_hash":"a1ef80ed26012f89e473c672644e98f29cda7977cd067c0b8dee7b83eb1ca6af","size":81,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,63,2,27,37,69,61,50,3,31,40,46,15,28,58,38,44,62,6,56,72,48,55,77,79,10,4,47,13,12,80,32,33,67,24,51,34,73,54,16,19,29,65,25,5,45,9,39,36,74,53,14,71,70,41,49,17,7,22,43,21,20,30,59,57,75,68,52,76,26,42,64,18,78,8,35,66,60,11,23","comment":"Size-81 (= 3^4) translation-invariant idempotent right-cancellative magma. Carrier is F_81 viewed additively as (Z/3)^4; the operation has the form x ◇ y = x + δ(y - x) for a fixed permutation δ : F_81 → F_81 with δ(0) = 0.\n\nProperties of δ:\n  • permutation of order exactly 10\n  • cycle structure (10^8, 1) — eight orbits of length 10 on F_81*, fixed point at 0\n  • δ^5 = -id (negation), so δ has order exactly 10 with δ^5 the additive negation\n  • commutes with F_3-scalar action: δ(-a) = -δ(a) (δ preserves 1-D subspaces)\n  • NOT F_3-linear, hence the magma is non-medial\n\nStructural interpretation: the 8 δ-orbits coincide with the 8 cosets of the unique order-10 subgroup H ⊂ F_81*. On each coset, δ acts as multiplication by some specific element δ_i ∈ H of order dividing 10. So the magma fits the b-reinke template \"(x,y) ↦ x + δ_i · (y - x)\" with 8 directional scalars (one per coset of H). The automorphism group has order |Aut| = 81 × 40 = 3240; the order-81 Sylow-3 subgroup is the regular translation group (Z/3)^4, and the order-40 stabilizer of 0 is cyclic and acts as F_3-linear maps on (Z/3)^4 = F_81 (specifically, the index-2 subgroup of F_81* of order 40).\n\nDisplay reorder coordinates each point by its base-3 digits (c_0, c_1, c_2, c_3) with respect to a chosen (Z/3)^4 basis, placing it at index c_0 + 3c_1 + 9c_2 + 27c_3. Under this reorder the table is fully (Z/3)^4-translation-invariant: T[a+x][a+y] = a + T[x][y] for every a in the additive group, which is visually evident as a nested 3 × 3 × 3 × 3 circulant-like structure.\n\n[text written by Claude]","submitted_at":"2026-05-12 17:52:42","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/81/a1ef80ed26012f89e473c672644e98f29cda7977cd067c0b8dee7b83eb1ca6af.txt"},{"canonical_hash":"0b5942e586fb32c27f22fa162ea5918ad21b2a1c0e77f6b218411c030d16b62b","size":83,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,82,25,70,28,49,20,62,52,43,7,12,2,63,27,8,31,73,9,22,55,21,66,34,71,32,36,48,41,42,53,40,23,37,24,72,57,17,65,10,47,60,19,16,50,74,3,51,78,14,77,69,4,58,45,26,35,11,79,76,54,68,44,64,29,59,15,6,75,56,61,38,30,81,46,5,80,13,67,18,33,39","comment":"Size-83 sporadic magma. Prime size, but no F_83-linear magma satisfies equation 677 — the diophantine system \"ab(b²+1) ≡ 1 (mod 83) and a + a²b² + b³ ≡ 0 (mod 83)\" has no solution. So this is a non-linear 677 magma at prime size, like the size-29 magma 9f34fd7d. It is a quasigroup (LC + RC), all 83 elements are idempotent, and it has NO non-trivial sub-magmas (every pair of distinct elements generates the whole magma). Both L_x and R_x are permutations with uniform cycle types across all x: L_x = (82 + 1) — one 82-cycle and the fixed point at x — and R_x = (41 + 41 + 1) — two 41-cycles plus the fixed point at x. The L vs R asymmetry distinguishes this from the size-29 sporadic magma, which has matching L_x and R_x types (14 + 14 + 1). This is the only size-83 magma in the database.","submitted_at":"2026-04-23 21:24:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/83/0b5942e586fb32c27f22fa162ea5918ad21b2a1c0e77f6b218411c030d16b62b.txt"},{"canonical_hash":"10e5c920f5780a0b5d924c2ee6bee15adaa8e2f28718719e2b11ae181bf422e1","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,64,39,65,26,37,80,11,66,9,53,33,46,20,84,63,78,49,2,45,10,77,41,32,72,47,48,76,22,60,16,14,23,62,57,24,67,56,17,55,30,38,8,3,82,73,58,44,15,79,34,25,42,51,83,70,71,21,61,27,31,75,40,28,5,13,4,36,19,74,69,6,29,59,68,81,35,7,18,50,52,54,12,43","comment":"Size-85 = 5·17 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Z_85 cyclic + involution + Steiner system S(2, 5, 85) template.\n\nStructure: x ◇ y = x + f(y − x) on the cyclic group Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²); R_0 typically has cycle structure (1, 4²¹). The magma is fully Z_85-translation-invariant — verified by exhibiting an order-85 fix-free magma automorphism.\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. The 357 such sub-magmas (= C(85, 2) / C(5, 2)) form a Steiner system S(2, 5, 85), with each element lying on exactly 21 sub-magmas (= (85−1)/(5−1)). (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nSibling magmas at size 85 with the same Z_85-cyclic + involution + S(2, 5, 85) template: magma#10e5c920, magma#31ae2815, magma#5d5c0411, magma#6282dd11, magma#d02731a8. They differ in which specific involution f is used. (Two other size-85 entries — magma#84944e78 and magma#4b5e27f5 — share the Steiner-system + L_0-involution properties but are NOT Z_85-cyclically translation-invariant, so use a different additive structure or non-translation-invariant construction.)\n\nSame family as the 16 size-81 magmas of 'family 4' (e.g. magma#c5da3284), which use the Z_81 + involution + S(2, 5, 81) template. The construction generalizes to any n ≡ 1 or 5 mod 20.\n\nDisplay reorder lays elements out as 0, τ(0), τ²(0), … along the orbit of an order-85 fix-free magma automorphism τ (= the hidden additive translation by 1 in Z_85). Under this reorder the Cayley table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:20","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/10e5c920f5780a0b5d924c2ee6bee15adaa8e2f28718719e2b11ae181bf422e1.txt"},{"canonical_hash":"5d5c0411a4608630e697d03f7469f0ebc90481a241797b743f394c0b287f1a4b","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,51,26,9,53,7,25,66,6,71,75,67,31,77,59,8,54,33,63,38,17,41,35,49,43,79,20,74,4,62,56,18,14,81,10,55,60,22,19,24,39,70,61,11,84,52,16,29,50,65,23,80,21,76,78,45,3,82,5,83,42,72,44,13,69,34,27,28,47,32,46,64,15,12,40,2,57,36,73,58,68,48,37,30","comment":"Size-85 = 5·17 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Z_85 cyclic + involution + Steiner system S(2, 5, 85) template.\n\nStructure: x ◇ y = x + f(y − x) on the cyclic group Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²); R_0 typically has cycle structure (1, 4²¹). The magma is fully Z_85-translation-invariant — verified by exhibiting an order-85 fix-free magma automorphism.\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. The 357 such sub-magmas (= C(85, 2) / C(5, 2)) form a Steiner system S(2, 5, 85), with each element lying on exactly 21 sub-magmas (= (85−1)/(5−1)). (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nSibling magmas at size 85 with the same Z_85-cyclic + involution + S(2, 5, 85) template: magma#10e5c920, magma#31ae2815, magma#5d5c0411, magma#6282dd11, magma#d02731a8. They differ in which specific involution f is used. (Two other size-85 entries — magma#84944e78 and magma#4b5e27f5 — share the Steiner-system + L_0-involution properties but are NOT Z_85-cyclically translation-invariant, so use a different additive structure or non-translation-invariant construction.)\n\nSame family as the 16 size-81 magmas of 'family 4' (e.g. magma#c5da3284), which use the Z_81 + involution + S(2, 5, 81) template. The construction generalizes to any n ≡ 1 or 5 mod 20.\n\nDisplay reorder lays elements out as 0, τ(0), τ²(0), … along the orbit of an order-85 fix-free magma automorphism τ (= the hidden additive translation by 1 in Z_85). Under this reorder the Cayley table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:27","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/5d5c0411a4608630e697d03f7469f0ebc90481a241797b743f394c0b287f1a4b.txt"},{"canonical_hash":"84944e78cd5f315ea543e8e0fc4d34c8b7143055b4859050921bd4aad0873cb4","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,19,39,80,1,78,22,69,72,47,43,33,14,28,51,55,38,24,16,71,25,46,35,10,6,63,59,52,3,32,26,79,56,83,57,18,23,42,66,27,60,62,36,34,65,61,67,49,41,73,48,4,17,12,31,40,11,58,76,9,50,68,5,45,75,74,82,70,15,84,29,44,21,13,30,54,77,53,8,81,37,64,20,7","comment":"Size-85 = 5·17 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Z_85 cyclic + involution + Steiner system S(2, 5, 85) template.\n\nStructure: x ◇ y = x + f(y − x) on the cyclic group Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²); R_0 typically (1, 4²¹). The magma is fully Z_85-translation-invariant under an order-85 fix-free magma automorphism.\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. The 357 such sub-magmas (= C(85, 2) / C(5, 2)) form a Steiner system S(2, 5, 85), with each element lying in exactly 21 sub-magmas. (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nSibling magmas at size 85 with the same template: magma#10e5c920, magma#31ae2815, magma#4b5e27f5, magma#5d5c0411, magma#6282dd11, magma#84944e78, magma#d02731a8. They differ in which specific involution f is used.\n\nSame family as the 16 size-81 Family-4 magmas (Z_81 + involution + S(2, 5, 81), e.g. magma#c5da3284). The construction generalizes to any n ≡ 1 or 5 mod 20; explicit DB entries at small n with the same template include sizes 21, 25, 41, 61, 65, 81, 85, 125.\n\nDisplay reorder lays elements out as 0, τ(0), τ²(0), … along the orbit of an order-85 fix-free magma automorphism τ (= the hidden additive translation by 1 in Z_85). Under this reorder the table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/84944e78cd5f315ea543e8e0fc4d34c8b7143055b4859050921bd4aad0873cb4.txt"},{"canonical_hash":"d02731a874c056435b9c2ddaa26e783a813a4cb2c987e4542f688ad324f08aa3","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,22,84,55,20,52,77,70,68,10,71,7,33,80,44,73,14,58,43,25,15,31,62,5,45,8,56,60,61,18,63,50,66,4,28,78,26,41,57,65,81,36,51,19,9,72,76,17,59,13,40,32,74,24,83,64,39,11,82,3,12,23,53,46,29,38,34,69,75,49,27,30,6,79,67,35,16,37,47,2,42,21,54,48","comment":"Size-85 = 5·17 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Z_85 cyclic + involution + Steiner system S(2, 5, 85) template.\n\nStructure: x ◇ y = x + f(y − x) on the cyclic group Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²); R_0 typically has cycle structure (1, 4²¹). The magma is fully Z_85-translation-invariant — verified by exhibiting an order-85 fix-free magma automorphism.\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. The 357 such sub-magmas (= C(85, 2) / C(5, 2)) form a Steiner system S(2, 5, 85), with each element lying on exactly 21 sub-magmas (= (85−1)/(5−1)). (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nSibling magmas at size 85 with the same Z_85-cyclic + involution + S(2, 5, 85) template: magma#10e5c920, magma#31ae2815, magma#5d5c0411, magma#6282dd11, magma#d02731a8. They differ in which specific involution f is used. (Two other size-85 entries — magma#84944e78 and magma#4b5e27f5 — share the Steiner-system + L_0-involution properties but are NOT Z_85-cyclically translation-invariant, so use a different additive structure or non-translation-invariant construction.)\n\nSame family as the 16 size-81 magmas of 'family 4' (e.g. magma#c5da3284), which use the Z_81 + involution + S(2, 5, 81) template. The construction generalizes to any n ≡ 1 or 5 mod 20.\n\nDisplay reorder lays elements out as 0, τ(0), τ²(0), … along the orbit of an order-85 fix-free magma automorphism τ (= the hidden additive translation by 1 in Z_85). Under this reorder the Cayley table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/d02731a874c056435b9c2ddaa26e783a813a4cb2c987e4542f688ad324f08aa3.txt"},{"canonical_hash":"6282dd1189846e380487d045754c7db5c27bf15655467821335bc07ed48a1cff","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,28,60,40,45,63,33,42,38,39,68,50,16,57,79,75,69,53,64,11,67,82,59,34,71,66,48,62,70,76,5,15,58,56,81,24,46,83,17,23,32,2,61,52,74,9,72,30,65,47,36,73,44,41,7,14,25,35,51,80,21,78,27,4,13,3,20,18,29,19,26,49,54,6,84,12,8,77,22,55,43,10,31,37","comment":"Size-85 = 5·17 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Z_85 cyclic + involution + Steiner system S(2, 5, 85) template.\n\nStructure: x ◇ y = x + f(y − x) on the cyclic group Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²); R_0 typically has cycle structure (1, 4²¹). The magma is fully Z_85-translation-invariant — verified by exhibiting an order-85 fix-free magma automorphism.\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. The 357 such sub-magmas (= C(85, 2) / C(5, 2)) form a Steiner system S(2, 5, 85), with each element lying on exactly 21 sub-magmas (= (85−1)/(5−1)). (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nSibling magmas at size 85 with the same Z_85-cyclic + involution + S(2, 5, 85) template: magma#10e5c920, magma#31ae2815, magma#5d5c0411, magma#6282dd11, magma#d02731a8. They differ in which specific involution f is used. (Two other size-85 entries — magma#84944e78 and magma#4b5e27f5 — share the Steiner-system + L_0-involution properties but are NOT Z_85-cyclically translation-invariant, so use a different additive structure or non-translation-invariant construction.)\n\nSame family as the 16 size-81 magmas of 'family 4' (e.g. magma#c5da3284), which use the Z_81 + involution + S(2, 5, 81) template. The construction generalizes to any n ≡ 1 or 5 mod 20.\n\nDisplay reorder lays elements out as 0, τ(0), τ²(0), … along the orbit of an order-85 fix-free magma automorphism τ (= the hidden additive translation by 1 in Z_85). Under this reorder the Cayley table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:24:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/6282dd1189846e380487d045754c7db5c27bf15655467821335bc07ed48a1cff.txt"},{"canonical_hash":"4b5e27f5375d866e192afb998de23ab559a1f0d4c0f4e57a0f793cec1b602e83","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,10,68,79,78,52,61,53,82,63,14,75,54,73,1,65,35,4,84,18,58,30,77,34,74,57,70,64,43,32,29,56,6,19,27,8,5,16,38,80,55,37,24,3,46,60,72,76,12,40,39,33,9,59,66,81,71,28,13,23,21,7,17,83,47,42,69,44,48,11,51,62,26,41,20,49,45,36,22,15,67,50,25,31","comment":"Size-85 = 5·17 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Z_85 cyclic + involution + Steiner system S(2, 5, 85) template.\n\nStructure: x ◇ y = x + f(y − x) on the cyclic group Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²); R_0 typically (1, 4²¹). The magma is fully Z_85-translation-invariant under an order-85 fix-free magma automorphism.\n\nSub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. The 357 such sub-magmas (= C(85, 2) / C(5, 2)) form a Steiner system S(2, 5, 85), with each element lying in exactly 21 sub-magmas. (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nSibling magmas at size 85 with the same template: magma#10e5c920, magma#31ae2815, magma#4b5e27f5, magma#5d5c0411, magma#6282dd11, magma#84944e78, magma#d02731a8. They differ in which specific involution f is used.\n\nSame family as the 16 size-81 Family-4 magmas (Z_81 + involution + S(2, 5, 81), e.g. magma#c5da3284). The construction generalizes to any n ≡ 1 or 5 mod 20; explicit DB entries at small n with the same template include sizes 21, 25, 41, 61, 65, 81, 85, 125.\n\nDisplay reorder lays elements out as 0, τ(0), τ²(0), … along the orbit of an order-85 fix-free magma automorphism τ (= the hidden additive translation by 1 in Z_85). Under this reorder the table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:25:00","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/4b5e27f5375d866e192afb998de23ab559a1f0d4c0f4e57a0f793cec1b602e83.txt"},{"canonical_hash":"31ae28154314946e3a9ef48b4c69dca8a95b80aad15724c44244f42d1d2e7c6b","size":85,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,72,5,3,52,18,11,24,28,44,4,54,7,61,79,64,41,30,82,75,34,35,76,38,84,59,42,39,57,9,2,67,50,23,48,71,78,29,43,63,22,26,46,55,66,33,51,47,36,56,68,32,6,20,37,58,31,60,27,15,73,19,62,65,77,10,40,13,70,14,16,74,21,69,49,25,8,17,81,83,53,12,80,45","comment":"Size-85 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_85 (= Z_5 × Z_17 by CRT, since 85 = 5·17), and the magma is fully Z_85-translation-invariant — verified by exhibiting an order-85 fix-free magma automorphism.\n\nStructure: x ◇ y = x + f(y − x) in Z_85, where f: Z_85 → Z_85 is a fixed-point-free INVOLUTION (f² = id, f(0) = 0, 42 transpositions on Z_85 \\ {0}). L_0 has cycle structure (1, 2⁴²) and R_0 has cycle structure (1, 4²¹).\n\nSub-magma design: EVERY pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. There are exactly C(85, 2) / C(5, 2) = 3570 / 10 = 357 distinct size-5 sub-magmas, and every element lies in exactly (85 − 1)/(5 − 1) = 21 of them — this is a **Steiner system S(2, 5, 85)**. (S(2, 5, v) exists for v ≡ 1 or 5 mod 20; here 85 ≡ 5 mod 20 ✓.)\n\nThis is the direct size-85 analog of the 16 size-81 Family-4 magmas (magma#c5da3284, magma#8c8fe34b, etc.), which use the same Z_n + involution + S(2, 5, n) template at size 81 (where 81 ≡ 1 mod 20). The construction generalizes to any n ≡ 1 or 5 mod 20 with an appropriate involution f satisfying Eq 677; explicit DB entries currently exist at n = 81 (16 magmas, S(2, 5, 81)) and n = 85 (this one, S(2, 5, 85)).\n\nLocally on each 5-element line, f acts as F_5 negation (= the L_0 of the unique size-5 Eq 677 magma). Globally f is an involution that, restricted to each of the 357 size-5 lines through 0 (— wait, 0 is the fixed point of f and is in 21 lines, not 357 —) restricts coherently.\n\nDisplay reorder presents elements as 0, τ(0), τ²(0), …, τ⁸⁴(0) along the orbit of an order-85 fix-free magma automorphism τ (the hidden additive translation by 1 in Z_85). Under this reorder the Cayley table is fully Z_85-translation-invariant: every row is a horizontal shift of row 0 = f, and the rendered image shows clean diagonal banding revealing the cyclic translation symmetry.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:25:08","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/85/31ae28154314946e3a9ef48b4c69dca8a95b80aad15724c44244f42d1d2e7c6b.txt"},{"canonical_hash":"1c1045d74cc5a6cd35415a2d56a5971c4505b0d3fed33db6316f8fcb706a4e5f","size":89,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,25,10,75,20,5,30,15,1,26,11,76,21,6,31,16,2,27,12,77,22,7,32,17,3,28,13,78,23,8,33,18,4,29,14,79,24,9,34,19,35,60,45,71,55,40,66,50,36,61,46,72,56,41,65,51,37,63,48,73,58,43,68,53,38,64,49,74,59,44,69,54,39,62,47,70,57,42,67,52,80,86,83,82,85,87,81,84,88","comment":"Size-89 magma: 88 = 11 × 8 elements form 11 fibers of 8 (with an F_11 base op), plus one adjoined right-identity element e. Left-multiplication by e is a finite-order permutation acting on the fibers.","submitted_at":"2026-04-23 21:25:08","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/89/1c1045d74cc5a6cd35415a2d56a5971c4505b0d3fed33db6316f8fcb706a4e5f.txt"},{"canonical_hash":"a95da9e5d489d9ff57fdf7f9cd532bcf7c91783f3daeb2e957fec76585d3279f","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,72,81,73,79,80,82,76,74,83,78,75,77,84,4,29,14,68,7,57,21,43,36,50,61,28,89,40,5,71,48,55,33,59,19,12,26,41,66,85,13,56,35,27,34,6,42,60,0,67,20,49,87,16,53,38,24,31,9,45,63,2,70,17,52,86,37,8,3,51,58,30,62,22,15,23,44,69,88,1,32,11,65,10,54,18,46,39,47,64,25","comment":"Direct product of two linear magmas: F_7 × F_13. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 3y₁ (mod 7), 9x₂ + 11y₂ (mod 13)).","submitted_at":"2026-04-23 21:25:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/a95da9e5d489d9ff57fdf7f9cd532bcf7c91783f3daeb2e957fec76585d3279f.txt"},{"canonical_hash":"0bce8f93656aff8f81b94bb2bd96c22f99ddf7a7811d3d6adb6df9136d4d8f42","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,72,76,74,79,75,77,81,82,73,78,83,80,84,36,1,69,34,33,37,70,39,40,38,35,0,85,52,57,68,60,59,53,64,55,56,54,51,58,89,18,12,71,16,15,19,14,10,11,9,17,13,86,49,44,67,47,46,50,63,42,43,41,48,45,87,8,3,66,32,31,7,61,5,4,6,20,2,88,24,29,65,22,21,25,62,27,28,26,23,30","comment":"Direct product of two linear magmas: F_7 × F_13. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 9x₂ + 11y₂ (mod 13)).","submitted_at":"2026-04-23 21:25:09","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/0bce8f93656aff8f81b94bb2bd96c22f99ddf7a7811d3d6adb6df9136d4d8f42.txt"},{"canonical_hash":"45fe20d3a83c5c01ed3fc5c0c37e2c9d661a2fec5a70dd287e214379722f440d","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,66,76,67,71,75,77,74,72,68,70,73,69,11,26,58,84,21,80,47,32,36,16,49,0,61,7,28,59,87,23,83,44,34,39,12,48,2,63,6,27,55,86,22,81,42,33,38,17,53,1,62,9,25,56,89,19,78,46,35,37,14,51,5,64,10,24,57,85,20,79,43,31,41,15,52,4,60,8,29,54,88,18,82,45,30,40,13,50,3,65","comment":"Size-91 (= 7 × 13) right-cancellative fiber bundle: F_7(4, 1) base × F_13(9,11) fiber, in the \"twisted\" Family B variant. The 91 elements partition into 7 fibers of 13 (a non-trivial congruence with F_7 quotient), but only ONE fiber is itself a sub-magma — the fiber at F_7-natural index 0 (the F_7 idempotent coset), which is isomorphic to F_13(9,11). The other 6 fibers are congruence classes that are NOT closed under ◇. The full magma is a quasigroup (LC + RC) with a unique idempotent, and the F_13 sub-magma acts regularly on each non-closed fiber via left-multiplication. Analogous in structure to the size-77 F_7 × F_11 family-B magmas in the database.","submitted_at":"2026-04-23 21:25:10","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/45fe20d3a83c5c01ed3fc5c0c37e2c9d661a2fec5a70dd287e214379722f440d.txt"},{"canonical_hash":"47a58a09c990e4f69a29ac8e41264996e777b5754cc28007899d0a6d3045992f","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,42,52,43,47,51,53,50,48,44,46,49,45,0,9,16,18,29,33,36,55,63,71,77,81,85,3,7,15,23,25,34,39,58,60,68,73,83,86,4,11,12,21,27,31,41,56,64,67,75,79,89,1,10,13,20,26,30,40,57,65,66,74,78,88,5,6,14,22,24,35,38,59,61,69,72,82,87,2,8,17,19,28,32,37,54,62,70,76,80,84","comment":"Size-91 (= 7 × 13) right-cancellative fiber bundle: F_7(4, 3) base × F_13(9,11) fiber, in the \"twisted\" Family B variant. The 91 elements partition into 7 fibers of 13 (a non-trivial congruence with F_7 quotient), but only ONE fiber is itself a sub-magma — the fiber at F_7-natural index 0 (the F_7 idempotent coset), which is isomorphic to F_13(9,11). The other 6 fibers are congruence classes that are NOT closed under ◇. The full magma is a quasigroup (LC + RC) with a unique idempotent, and the F_13 sub-magma acts regularly on each non-closed fiber via left-multiplication. Analogous in structure to the size-77 F_7 × F_11 family-B magmas in the database.","submitted_at":"2026-04-23 21:25:11","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/47a58a09c990e4f69a29ac8e41264996e777b5754cc28007899d0a6d3045992f.txt"},{"canonical_hash":"64aca2c8c653d0b65be3460afc2cc56b92482e67ad1041e7d75083b171bb4edf","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,84,85,89,86,87,88,0,12,34,45,57,65,74,7,21,27,47,51,60,76,4,18,30,37,48,69,73,11,16,32,43,55,71,78,3,17,31,42,49,70,75,2,13,24,46,58,66,77,5,19,29,36,50,68,82,9,23,26,39,54,62,83,8,22,35,41,52,63,72,10,14,25,40,53,67,80,1,15,33,44,56,64,81,6,20,28,38,59,61,79","comment":"Size-91 (= 13 × 7) right-cancellative fiber bundle: F_13(9,11) base × F_7(4, 1) fiber, in the \"twisted\" Family B variant. The 91 elements partition into 13 fibers of 7 (a non-trivial congruence with F_13 quotient), but only ONE fiber is itself a sub-magma — a 7-element F_7(4, 1) sub-magma; the other 12 fibers are non-closed congruence classes. The magma has no global idempotent (the F_7 sub-magma's internal idempotent is not idempotent in the full magma). Quasigroup (LC + RC). Same Family B shape as the other size-91 F_13 × F_7 magmas (5e5f5ada, 60a96978, ba24c51f, ff44e916).","submitted_at":"2026-04-23 21:25:12","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/64aca2c8c653d0b65be3460afc2cc56b92482e67ad1041e7d75083b171bb4edf.txt"},{"canonical_hash":"60a96978a85e484e3eadbe6f4c0955a6d578aaf49a65284b6a25932f63ca97a1","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,84,89,85,87,86,88,0,13,33,36,49,63,83,8,14,29,44,50,66,78,11,12,25,45,48,61,81,10,19,28,47,56,65,76,2,17,32,38,54,69,80,5,20,26,41,57,62,79,3,18,34,39,55,70,72,9,15,30,46,52,67,74,1,21,24,37,51,60,82,7,16,35,43,53,71,75,6,22,27,42,58,64,73,4,23,31,40,59,68,77","comment":"Size-91 (= 13 × 7) right-cancellative fiber bundle: F_13(9,11) base × F_7(4, 3) fiber, in a \"twisted\" Family B variant. The 91 elements partition into 13 fibers of 7 (a non-trivial congruence with F_13 quotient); 1 of the 13 fibers are themselves sub-magmas ≅ F_7(4, 3), and the rest are non-closed congruence classes. The full magma is a quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 21:25:12","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/60a96978a85e484e3eadbe6f4c0955a6d578aaf49a65284b6a25932f63ca97a1.txt"},{"canonical_hash":"f2b2cfb55941b5b6b37d4ac15f66796ab18b5ba0c0ebcc13740e36c389f4c475","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,78,82,80,85,81,83,87,88,79,84,89,86,0,71,42,27,13,54,60,51,16,30,39,74,4,3,73,38,29,15,50,59,53,18,26,41,76,6,8,23,34,66,64,69,31,20,11,58,43,46,55,2,5,75,40,25,17,52,61,49,14,28,37,72,1,12,21,32,70,62,67,35,24,9,56,47,44,7,77,45,48,57,10,19,36,68,63,65,33,22","comment":"Size-91 (= 7 × 13) right-cancellative fiber bundle: F_7(4,1) base × F_13(9,11) fiber, in the \"twisted\" Family B variant. The 91 elements partition into 7 fibers of 13 (this is a non-trivial congruence with F_7 quotient), but only ONE fiber is itself a sub-magma — the fiber over the F_7-idempotent coset, which is isomorphic to F_13(9,11). The other 6 fibers are congruence classes that are NOT closed under ◇ (so they are fibers in the sense of a fiber bundle, but not sub-magmas). The full magma is a quasigroup (LC + RC) with a unique idempotent, and the F_13 sub-magma acts regularly on each non-closed fiber via left-multiplication. Analogous in structure to the size-77 F_7 × F_11 family-B magmas in the database.","submitted_at":"2026-04-23 21:25:13","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/f2b2cfb55941b5b6b37d4ac15f66796ab18b5ba0c0ebcc13740e36c389f4c475.txt"},{"canonical_hash":"ff44e91630e5b7ced806f023ec7b48f62cf72b44e7d18f3c53ff3168cae8c08f","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,84,89,87,85,88,86,0,4,27,30,50,53,79,1,7,10,33,36,56,82,2,5,25,28,51,54,80,13,16,39,42,59,62,74,9,12,32,35,55,58,81,8,11,31,34,57,71,83,21,24,44,47,67,70,76,19,22,45,48,65,68,77,3,6,26,29,49,52,78,15,18,38,41,61,64,72,20,23,43,46,66,69,75,14,17,37,40,60,63,73","comment":"Size-91 (= 13 × 7) right-cancellative fiber bundle: F_13(9,11) base × F_7(4, 1) fiber, in a \"twisted\" Family B variant. The 91 elements partition into 13 fibers of 7 (a non-trivial congruence with F_13 quotient); 1 of the 13 fibers are themselves sub-magmas ≅ F_7(4, 1), and the rest are non-closed congruence classes. The full magma is a quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 21:25:13","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/ff44e91630e5b7ced806f023ec7b48f62cf72b44e7d18f3c53ff3168cae8c08f.txt"},{"canonical_hash":"ba24c51fbf527f14db1b1832913d1e96ae2bd8653361ec33255c8ec105458862","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,84,89,85,87,86,88,0,11,22,33,43,54,80,8,18,29,40,50,61,75,6,14,26,37,47,58,78,4,12,24,35,45,56,72,5,13,25,36,46,57,77,65,66,67,68,69,71,76,7,15,27,38,48,59,82,2,20,31,42,52,63,83,9,19,30,41,51,62,79,1,10,21,32,53,64,73,3,23,34,44,55,70,81,16,17,28,39,49,60,74","comment":"Size-91 (= 13 × 7) right-cancellative fiber bundle: F_13(9,11) base × F_7(4, 3) fiber, in a \"twisted\" Family B variant. The 91 elements partition into 13 fibers of 7 (a non-trivial congruence with F_13 quotient); 1 of the 13 fibers are themselves sub-magmas ≅ F_7(4, 3), and the rest are non-closed congruence classes. The full magma is a quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 21:25:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/ba24c51fbf527f14db1b1832913d1e96ae2bd8653361ec33255c8ec105458862.txt"},{"canonical_hash":"5e5f5adab8c5bbbec47cfec336dde941c6b0255890fff412505b2cca3c90cbec","size":91,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,84,89,85,87,86,88,0,16,30,38,56,61,79,9,22,29,43,51,70,75,6,15,33,37,59,63,80,1,14,35,41,54,60,74,11,21,24,47,53,65,77,3,18,26,44,49,67,76,7,19,27,45,48,68,83,4,20,25,46,52,64,81,10,13,34,40,55,71,78,5,12,32,36,58,62,72,2,23,28,42,50,66,82,8,17,31,39,57,69,73","comment":"Size-91 (= 13 × 7) right-cancellative fiber bundle: F_13(9,11) base × F_7(4, 3) fiber, in a \"twisted\" Family B variant. The 91 elements partition into 13 fibers of 7 (a non-trivial congruence with F_13 quotient); 1 of the 13 fibers are themselves sub-magmas ≅ F_7(4, 3), and the rest are non-closed congruence classes. The full magma is a quasigroup (LC + RC) with a unique idempotent.","submitted_at":"2026-04-23 21:25:14","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/91/5e5f5adab8c5bbbec47cfec336dde941c6b0255890fff412505b2cca3c90cbec.txt"},{"canonical_hash":"d671328c75f3b078a09e4140b6628b66d40868f3ccd2888d7557d3ce31efa2b6","size":95,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,2,38,62,6,35,31,14,42,19,70,27,66,46,50,58,10,23,54,91,0,36,61,4,32,30,13,40,17,68,25,64,44,49,56,8,20,52,92,3,39,63,7,33,29,15,43,16,71,24,67,47,51,59,11,21,55,94,74,83,80,75,73,89,77,84,78,82,72,81,85,86,88,76,79,87,93,1,37,60,5,34,28,12,41,18,69,26,65,45,48,57,9,22,53","comment":"Direct product of two linear magmas: F_5 × F_19. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 7x₂ + 4y₂ (mod 19)).","submitted_at":"2026-04-23 21:25:15","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/95/d671328c75f3b078a09e4140b6628b66d40868f3ccd2888d7557d3ce31efa2b6.txt"},{"canonical_hash":"b85efa920646d0c276d8942df07c8298194b9490a9505a7d5db9c633641fdfb4","size":95,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"90,3,43,67,19,23,7,15,59,31,63,27,47,39,55,51,35,11,71,91,0,41,65,16,20,4,12,56,28,60,24,44,37,52,48,32,8,69,92,1,40,64,17,21,5,13,57,29,61,25,45,36,53,49,33,9,68,94,83,77,74,86,87,89,85,72,81,73,88,78,76,80,79,82,84,75,93,2,42,66,18,22,6,14,58,30,62,26,46,38,54,50,34,10,70","comment":"Direct product of two linear magmas: F_5 × F_19. The operation is (x₁, x₂) ◇ (y₁, y₂) = (2x₁ + 4y₁ (mod 5), 7x₂ + 3y₂ (mod 19)).","submitted_at":"2026-04-23 21:25:15","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/95/b85efa920646d0c276d8942df07c8298194b9490a9505a7d5db9c633641fdfb4.txt"},{"canonical_hash":"9501b2ad1cd933de0311646b97b9547bb47e836a3f73124d56b88bcddad6361e","size":95,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,6,12,16,21,26,31,35,42,47,52,57,62,67,72,77,82,87,90,1,7,13,17,22,27,32,37,40,45,50,55,60,65,70,75,80,85,92,3,9,14,19,24,29,34,39,44,49,54,59,64,69,74,79,84,89,94,2,8,10,18,23,28,33,38,43,46,51,56,61,66,71,76,81,86,93,4,5,11,15,20,25,30,36,41,48,53,58,63,68,73,78,83,88,91","comment":"F_5(2, 4) base × F_19 fiber: 5 fibers of 19 (each = F_19 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:25:15","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/95/9501b2ad1cd933de0311646b97b9547bb47e836a3f73124d56b88bcddad6361e.txt"},{"canonical_hash":"4f88670da65119527ddb5ba349a16b4a09a12aedfa3667de845e6802909281d5","size":95,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,5,10,15,20,25,30,35,40,46,51,56,61,66,72,76,81,86,92,1,7,12,17,22,27,32,37,42,47,52,57,62,67,73,77,82,87,91,4,6,11,16,21,26,31,36,41,45,50,55,60,65,71,75,80,85,90,2,8,13,18,23,28,33,38,43,48,53,58,63,68,70,78,83,88,93,3,9,14,19,24,29,34,39,44,49,54,59,64,69,74,79,84,89,94","comment":"F_5(2, 4) base × F_19 fiber: 5 fibers of 19 (each = F_19 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:25:16","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/95/4f88670da65119527ddb5ba349a16b4a09a12aedfa3667de845e6802909281d5.txt"},{"canonical_hash":"6de1167dbd54b990b9182027ad9139ee18a819061005ac1907196f7271ef776d","size":95,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,8,12,16,20,24,30,34,37,41,45,49,53,57,61,65,69,92,1,5,9,13,17,21,25,29,33,36,40,44,48,52,56,60,64,68,91,3,7,11,15,19,23,27,28,32,39,43,47,51,55,59,63,67,71,90,2,6,10,14,18,22,26,31,35,38,42,46,50,54,58,62,66,70,93,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,94","comment":"F_5(2, 4) base × F_19 fiber: 5 fibers of 19 (each = F_19 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:25:16","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/95/6de1167dbd54b990b9182027ad9139ee18a819061005ac1907196f7271ef776d.txt"},{"canonical_hash":"67934624b7e6297f1ed34cfee06fe7ed9249c169159cd974d367eb577f433812","size":95,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,4,10,14,18,22,26,30,34,37,41,45,49,53,57,61,65,69,91,1,6,8,13,17,21,24,28,33,38,42,46,50,54,58,62,66,70,92,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,94,2,7,11,15,19,23,27,31,35,36,40,44,48,52,56,60,64,68,93,3,5,9,12,16,20,25,29,32,39,43,47,51,55,59,63,67,71,90","comment":"F_5(2, 4) base × F_19 fiber: 5 fibers of 19 (each = F_19 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-23 21:25:17","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/95/67934624b7e6297f1ed34cfee06fe7ed9249c169159cd974d367eb577f433812.txt"},{"canonical_hash":"689663a993182a1a2551c7d316b8f58a2bb5e804bcd7a89ea25934cf2263ee09","size":96,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,6,11,14,18,26,29,32,37,40,45,48,61,68,75,78,1,5,12,16,22,25,31,34,36,44,51,55,59,67,71,77,2,7,10,13,17,20,28,35,38,43,53,57,60,65,74,79,3,4,9,21,24,39,42,47,50,54,58,63,66,70,73,76,8,15,19,23,27,30,33,41,46,49,52,56,62,64,69,72,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95","comment":"Size-96 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. A '6-petal disjoint partition' construction — a close cousin of the size-76 pencil magma#875876e7, but **without a common pivot**.\n\nStructure:\n  • The 96 elements partition into 6 DISJOINT size-16 sub-magmas (the 'petals'). All 6 petals are isomorphic to magma#6fa95655 (the size-16 idempotent linear magma with x ◇ y = 9x + 8y mod 16) — verified by submitting each petal's 16×16 sub-Cayley table to the canonicalization API.\n  • Every pair (x, y) with x, y in the SAME petal generates the full 16-element petal.\n  • Every pair (x, y) with x, y in DIFFERENT petals generates a 5-element sub-magma (isomorphic to the unique size-5 Eq 677 magma over F_5).\n  • There are 384 such size-5 sub-magmas. Each is a transversal spanning 5 of the 6 petals (one element per petal, leaving 1 petal untouched), and each pair of distinct petals has exactly 256 such transversals connecting their elements.\n  • Each element sits in exactly 1 petal and 20 size-5 sub-magmas.\n\nCompare with the size-76 pencil magma#875876e7: same petal building block (magma#6fa95655) and same transversal type (the size-5 Eq 677 magma). The difference: 76 has 5 petals all sharing a common pivot element, while 96 has 6 disjoint petals with no pivot. The transversal designs are also different — TD(5, 15) at size 76 vs the 'one-petal-skipped' transversal pattern at size 96.\n\nDisplay reorder lays out the 6 petals as consecutive 16-blocks (indices 0–15, 16–31, …, 80–95). Under this reorder the Cayley table shows a clean 6×6 grid of 16×16 blocks: the 6 diagonal blocks are the within-petal operations (each block IS a copy of the size-16 magma's Cayley table), and the 30 off-diagonal blocks reflect the cross-petal 5-transversal gluing.\n\n[text written by Claude]","submitted_at":"2026-04-23 21:26:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/96/689663a993182a1a2551c7d316b8f58a2bb5e804bcd7a89ea25934cf2263ee09.txt"},{"canonical_hash":"86ae12c67f818b4c09b65b014a1f47ca32eb960076713cb306fcd47ce1331021","size":97,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"96,28,53,57,78,7,82,5,34,86,93,64,38,60,91,65,59,83,42,29,49,63,52,71,2,76,85,46,47,19,21,4,84,24,39,74,6,62,54,89,13,56,51,55,16,25,27,48,88,72,32,43,41,61,10,35,11,58,73,9,17,0,90,23,40,68,20,37,3,31,30,69,92,18,87,36,79,33,45,26,67,14,81,75,15,22,80,77,70,50,1,66,95,94,12,8,44","comment":"Linear magma over Z/97Z (the prime field F_97): x ◇ y = 61x + 8y (mod 97).","submitted_at":"2026-04-23 21:26:29","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/97/86ae12c67f818b4c09b65b014a1f47ca32eb960076713cb306fcd47ce1331021.txt"},{"canonical_hash":"8b1b27dc79b8afbd077fa2e0d3742efb11d4c67fc761fcdc5e55545e1342d505","size":97,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"96,0,1,80,90,43,55,83,65,67,18,49,30,66,58,75,40,81,42,27,85,23,24,47,5,38,41,7,33,77,50,57,15,36,56,78,17,71,2,6,60,54,45,28,46,62,22,59,72,26,13,68,16,92,74,91,8,14,52,48,25,63,32,10,82,61,11,4,31,79,53,87,84,51,93,70,95,39,73,88,35,86,29,12,20,76,3,64,21,19,37,9,89,44,34,69,94","comment":"Linear magma over Z/97Z (the prime field F_97): x ◇ y = 61x + 53y (mod 97).","submitted_at":"2026-04-23 21:26:30","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/97/8b1b27dc79b8afbd077fa2e0d3742efb11d4c67fc761fcdc5e55545e1342d505.txt"},{"canonical_hash":"96bc975c871a0bf4fe3bf702f8b0d559272841062bc26b367ffc80ea1d368715","size":97,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,28,86,89,30,9,55,75,82,14,12,81,32,40,49,25,5,85,79,21,4,22,87,45,84,26,74,36,93,39,70,52,69,31,37,53,73,94,88,80,33,60,62,34,27,7,57,78,41,38,76,47,48,23,15,51,66,83,64,77,11,43,54,2,65,20,42,13,8,67,92,10,95,72,96,24,46,58,44,19,56,61,90,68,17,50,6,91,59,29,16,35,18,3,63,71","comment":"Translation invariant model on F_q with q = 97 of the form (x,y) -> x + delta_i * (y - x) where delta_i is in [23,76,26] depending on the class of (y-x) in F_q^* / (F_q^*)^3.","submitted_at":"2026-05-12 09:26:55","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/97/96bc975c871a0bf4fe3bf702f8b0d559272841062bc26b367ffc80ea1d368715.txt"},{"canonical_hash":"3fc5b6b046482f4d44f26fe0ba7dc6a42f91960891533360d5ec9ec1660e05b6","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"88,89,92,97,95,96,93,91,98,90,94,4,2,6,7,3,5,1,9,81,8,0,44,42,46,47,43,45,40,49,84,48,41,34,32,36,37,33,35,30,39,83,38,31,55,53,57,58,54,56,52,51,85,59,50,24,22,26,27,23,25,20,29,87,28,21,75,73,77,78,74,76,71,72,80,79,70,65,63,67,68,64,66,60,61,86,69,62,14,12,16,17,13,15,11,19,82,18,10","comment":"Direct product of two linear magmas: F_9 × F_11(6,6).","submitted_at":"2026-04-23 21:26:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/3fc5b6b046482f4d44f26fe0ba7dc6a42f91960891533360d5ec9ec1660e05b6.txt"},{"canonical_hash":"8ecc53c103c09d5066e37482364244ff239f0a5bda000c6cef20a3cf480bea4e","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"88,89,98,92,94,97,91,95,93,96,90,3,7,81,0,5,4,1,2,9,8,6,43,47,84,41,45,44,40,42,49,48,46,33,37,83,31,35,34,30,32,39,38,36,54,58,85,51,56,55,52,53,50,59,57,23,27,87,21,25,24,20,22,29,28,26,74,78,80,70,76,75,72,73,71,79,77,64,68,86,61,66,65,62,63,60,69,67,13,17,82,10,15,14,11,12,19,18,16","comment":"Direct product of two linear magmas: F_9 × F_11(5,7).","submitted_at":"2026-04-23 21:26:31","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/8ecc53c103c09d5066e37482364244ff239f0a5bda000c6cef20a3cf480bea4e.txt"},{"canonical_hash":"4a96f301c450255bdcad454804b8fd984646ebe41deb085f2b49e335998ba22d","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"88,89,91,94,97,90,92,96,93,95,98,4,3,6,2,0,5,7,1,8,9,81,44,43,46,42,40,45,47,41,48,49,84,34,33,36,32,30,35,37,31,38,39,83,55,54,57,53,52,56,58,51,59,50,85,24,23,26,22,21,25,27,20,28,29,87,75,74,77,73,72,76,78,70,79,71,80,65,64,67,63,62,66,68,61,69,60,86,14,13,16,12,10,15,17,11,18,19,82","comment":"Direct product of two linear magmas: F_9 × F_11(10,2).","submitted_at":"2026-04-23 21:26:32","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/4a96f301c450255bdcad454804b8fd984646ebe41deb085f2b49e335998ba22d.txt"},{"canonical_hash":"caa79eaa31d9024dd332fe8a59cc18f6143a257f1414b954b06eda001fed9cb8","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"88,89,94,95,98,93,91,92,97,90,96,7,6,1,9,81,0,8,3,4,2,5,47,46,41,49,84,40,48,43,44,42,45,37,36,31,39,83,30,38,33,34,32,35,58,57,51,50,85,52,59,54,55,53,56,27,26,21,29,87,20,28,23,24,22,25,78,77,70,71,80,72,79,74,75,73,76,68,67,61,60,86,62,69,64,65,63,66,17,16,10,19,82,11,18,13,14,12,15","comment":"Direct product of two linear magmas: F_9 × F_11(4,8).","submitted_at":"2026-04-23 21:26:32","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/caa79eaa31d9024dd332fe8a59cc18f6143a257f1414b954b06eda001fed9cb8.txt"},{"canonical_hash":"082272476d971ecf2630093c454ae25ba43569a35e46d3310cdfd03bc31fdb2f","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,11,20,32,42,52,69,79,90,1,12,22,30,40,50,67,77,92,3,14,24,34,44,54,71,81,93,9,10,21,31,41,51,68,78,91,4,15,25,35,45,55,72,82,94,8,19,29,39,49,59,76,86,89,6,17,27,37,47,57,74,84,96,5,16,26,36,46,56,73,83,95,2,13,23,33,43,53,70,80,88,60,61,62,63,64,65,66,87,98,7,18,28,38,48,58,75,85,97","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:33","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/082272476d971ecf2630093c454ae25ba43569a35e46d3310cdfd03bc31fdb2f.txt"},{"canonical_hash":"b0042b702fff05b6d29cf9f83d2d0e257968e333e7746a804075fa5165120ab6","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,89,8,9,10,11,12,13,14,15,98,48,49,50,51,52,53,54,55,93,40,41,42,43,44,45,46,47,94,80,81,82,83,84,85,86,87,91,56,57,58,59,60,61,62,63,95,64,65,66,67,68,69,70,71,88,32,33,34,35,36,37,38,39,90,24,25,26,27,28,29,30,31,92,16,17,18,19,20,21,22,23,97,72,73,74,75,76,77,78,79,96","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:33","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/b0042b702fff05b6d29cf9f83d2d0e257968e333e7746a804075fa5165120ab6.txt"},{"canonical_hash":"e20ac13119361adeeb1be1405797a86db23f6cce0594211fe67a207fedf63ef6","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,96,8,9,10,11,12,13,14,15,94,48,49,50,51,52,53,54,55,89,40,41,42,43,44,45,46,47,90,16,17,18,19,20,21,22,23,93,24,25,26,27,28,29,30,31,88,80,81,82,83,84,85,86,87,91,72,73,74,75,76,77,78,79,95,56,57,58,59,60,61,62,63,97,32,33,34,35,36,37,38,39,92,64,65,66,67,68,69,70,71,98","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/e20ac13119361adeeb1be1405797a86db23f6cce0594211fe67a207fedf63ef6.txt"},{"canonical_hash":"dd27fbdf1b8d86cd375e0f7606e0be2aa365144d46de93b667d9535c07d75fef","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,91,8,9,10,11,12,13,14,15,90,16,17,18,19,20,21,22,23,98,72,73,74,75,76,77,78,79,94,64,65,66,67,68,69,70,71,92,48,49,50,51,52,53,54,55,96,24,25,26,27,28,29,30,31,93,56,57,58,59,60,61,62,63,89,80,81,82,83,84,85,86,87,88,32,33,34,35,36,37,38,39,97,40,41,42,43,44,45,46,47,95","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:34","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/dd27fbdf1b8d86cd375e0f7606e0be2aa365144d46de93b667d9535c07d75fef.txt"},{"canonical_hash":"d33b28af8b2c80bcfb6032e17246674d0998c479dfde09f313d4b936a6213197","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,88,8,9,10,11,12,13,14,15,97,64,65,66,67,68,69,70,71,90,32,33,34,35,36,37,38,39,89,16,17,18,19,20,21,22,23,95,40,41,42,43,44,45,46,47,93,56,57,58,59,60,61,62,63,91,48,49,50,51,52,53,54,55,94,72,73,74,75,76,77,78,79,98,24,25,26,27,28,29,30,31,96,80,81,82,83,84,85,86,87,92","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/d33b28af8b2c80bcfb6032e17246674d0998c479dfde09f313d4b936a6213197.txt"},{"canonical_hash":"1e0592d76c2c46e78459be9b9b81c9bd1518c2efc995f53594618284a552d8cf","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,95,8,9,10,11,12,13,14,15,92,48,49,50,51,52,53,54,55,96,80,81,82,83,84,85,86,87,97,64,65,66,67,68,69,70,71,88,24,25,26,27,28,29,30,31,90,72,73,74,75,76,77,78,79,89,16,17,18,19,20,21,22,23,93,40,41,42,43,44,45,46,47,94,56,57,58,59,60,61,62,63,91,32,33,34,35,36,37,38,39,98","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/1e0592d76c2c46e78459be9b9b81c9bd1518c2efc995f53594618284a552d8cf.txt"},{"canonical_hash":"c4bf13d620dc3b52b204afe625a1be5f7b3faea06367e3a9c4fa6fe270803595","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,3,5,7,9,65,67,69,90,1,2,4,6,8,64,66,68,91,29,33,37,41,45,49,79,83,88,30,34,38,42,46,50,80,84,94,11,13,15,17,18,20,73,75,96,52,54,56,58,60,62,70,86,98,22,23,24,25,26,27,76,77,92,53,55,57,59,61,63,71,87,97,10,12,14,16,19,21,72,74,95,31,35,39,43,47,51,81,85,93,28,32,36,40,44,48,78,82,89","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:35","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/c4bf13d620dc3b52b204afe625a1be5f7b3faea06367e3a9c4fa6fe270803595.txt"},{"canonical_hash":"8138b174c865a80a47e3d3d31863fc30f96c305048a4bc05ec20cfc818cf0863","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,95,8,9,10,11,12,13,14,15,98,80,81,82,83,84,85,86,87,93,32,33,34,35,36,37,38,39,97,72,73,74,75,76,77,78,79,90,48,49,50,51,52,53,54,55,94,56,57,58,59,60,61,62,63,92,24,25,26,27,28,29,30,31,88,16,17,18,19,20,21,22,23,89,40,41,42,43,44,45,46,47,96,64,65,66,67,68,69,70,71,91","comment":"F_11(4, 8) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/8138b174c865a80a47e3d3d31863fc30f96c305048a4bc05ec20cfc818cf0863.txt"},{"canonical_hash":"a720a6047a86f782eef38b4c25134b5fb922779d437572dbbd8f12750b494518","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,11,20,32,42,52,69,79,90,1,12,22,30,40,50,67,77,92,2,13,23,33,43,53,70,80,93,5,16,26,36,46,56,73,83,96,60,61,62,63,64,65,66,87,98,9,10,21,31,41,51,68,78,91,7,18,28,38,48,58,75,85,89,6,17,27,37,47,57,74,84,97,4,15,25,35,45,55,72,82,95,8,19,29,39,49,59,76,86,88,3,14,24,34,44,54,71,81,94","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:36","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/a720a6047a86f782eef38b4c25134b5fb922779d437572dbbd8f12750b494518.txt"},{"canonical_hash":"b8d7cd6c92b3fbb6d8d944b01cd2b42eb6384c5544b1a46c734230dcb4d82195","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,98,8,9,10,11,12,13,14,15,91,80,81,82,83,84,85,86,87,94,24,25,26,27,28,29,30,31,92,32,33,34,35,36,37,38,39,90,16,17,18,19,20,21,22,23,96,56,57,58,59,60,61,62,63,95,72,73,74,75,76,77,78,79,93,64,65,66,67,68,69,70,71,88,40,41,42,43,44,45,46,47,97,48,49,50,51,52,53,54,55,89","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:37","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/b8d7cd6c92b3fbb6d8d944b01cd2b42eb6384c5544b1a46c734230dcb4d82195.txt"},{"canonical_hash":"3e05354bf5b34246b4440d3b81ae121e88521049e1164fe50fdeb5fc54675280","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,98,8,9,10,11,12,13,14,15,88,80,81,82,83,84,85,86,87,95,24,25,26,27,28,29,30,31,93,32,33,34,35,36,37,38,39,96,16,17,18,19,20,21,22,23,92,56,57,58,59,60,61,62,63,97,72,73,74,75,76,77,78,79,94,64,65,66,67,68,69,70,71,91,40,41,42,43,44,45,46,47,90,48,49,50,51,52,53,54,55,89","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:37","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/3e05354bf5b34246b4440d3b81ae121e88521049e1164fe50fdeb5fc54675280.txt"},{"canonical_hash":"2edad5019683831bb7084e6a06b560042ec35bdd9c7c841639e117e771dbaf0b","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,88,8,9,10,11,12,13,14,15,92,16,17,18,19,20,21,22,23,91,40,41,42,43,44,45,46,47,94,72,73,74,75,76,77,78,79,96,64,65,66,67,68,69,70,71,95,56,57,58,59,60,61,62,63,90,24,25,26,27,28,29,30,31,93,80,81,82,83,84,85,86,87,89,48,49,50,51,52,53,54,55,98,32,33,34,35,36,37,38,39,97","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/2edad5019683831bb7084e6a06b560042ec35bdd9c7c841639e117e771dbaf0b.txt"},{"canonical_hash":"0dd6708ae95946f3b252717956bc263645bc77a522120f742b679a559d27139f","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,90,8,9,10,11,12,13,14,15,98,24,25,26,27,28,29,30,31,92,80,81,82,83,84,85,86,87,91,40,41,42,43,44,45,46,47,93,48,49,50,51,52,53,54,55,95,32,33,34,35,36,37,38,39,96,56,57,58,59,60,61,62,63,94,72,73,74,75,76,77,78,79,89,64,65,66,67,68,69,70,71,97,16,17,18,19,20,21,22,23,88","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:38","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/0dd6708ae95946f3b252717956bc263645bc77a522120f742b679a559d27139f.txt"},{"canonical_hash":"0bd3781f53f60cf77ada496acc1549856821da3c3e2246203a0caeb769c0e258","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,98,8,9,10,11,12,13,14,15,93,48,49,50,51,52,53,54,55,95,24,25,26,27,28,29,30,31,91,32,33,34,35,36,37,38,39,90,16,17,18,19,20,21,22,23,92,64,65,66,67,68,69,70,71,97,80,81,82,83,84,85,86,87,96,72,73,74,75,76,77,78,79,88,40,41,42,43,44,45,46,47,94,56,57,58,59,60,61,62,63,89","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/0bd3781f53f60cf77ada496acc1549856821da3c3e2246203a0caeb769c0e258.txt"},{"canonical_hash":"2d927e61ea584e807d2727587842fdeb46bb5483b27833bc2ba4258aa21e4135","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,94,8,9,10,11,12,13,14,15,88,56,57,58,59,60,61,62,63,90,24,25,26,27,28,29,30,31,91,32,33,34,35,36,37,38,39,95,16,17,18,19,20,21,22,23,93,72,73,74,75,76,77,78,79,92,48,49,50,51,52,53,54,55,89,80,81,82,83,84,85,86,87,98,40,41,42,43,44,45,46,47,97,64,65,66,67,68,69,70,71,96","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/2d927e61ea584e807d2727587842fdeb46bb5483b27833bc2ba4258aa21e4135.txt"},{"canonical_hash":"ea84e7d4ccc97889b947c88dcf9efd7f29b780b6742acd5f467c43203f1551b1","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,89,8,9,10,11,12,13,14,15,95,72,73,74,75,76,77,78,79,90,24,25,26,27,28,29,30,31,97,40,41,42,43,44,45,46,47,93,32,33,34,35,36,37,38,39,96,16,17,18,19,20,21,22,23,91,56,57,58,59,60,61,62,63,92,64,65,66,67,68,69,70,71,98,80,81,82,83,84,85,86,87,88,48,49,50,51,52,53,54,55,94","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:39","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/ea84e7d4ccc97889b947c88dcf9efd7f29b780b6742acd5f467c43203f1551b1.txt"},{"canonical_hash":"673cd12a07d625052f15aed00e2296010c7ea90e920b0213758a85385bca60a5","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,90,8,9,10,11,12,13,14,15,96,16,17,18,19,20,21,22,23,89,80,81,82,83,84,85,86,87,91,56,57,58,59,60,61,62,63,88,24,25,26,27,28,29,30,31,93,72,73,74,75,76,77,78,79,94,40,41,42,43,44,45,46,47,92,48,49,50,51,52,53,54,55,98,32,33,34,35,36,37,38,39,95,64,65,66,67,68,69,70,71,97","comment":"F_11(5, 7) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:40","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/673cd12a07d625052f15aed00e2296010c7ea90e920b0213758a85385bca60a5.txt"},{"canonical_hash":"a5b354014616e2029c1add09cc8a4c961df0fea291962f717b96a1f34e011b3b","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,21,31,40,50,69,77,97,1,11,20,32,41,51,68,78,96,7,18,28,38,48,58,75,85,90,2,12,22,33,43,53,70,80,93,4,14,24,35,45,55,72,82,89,8,19,29,39,49,59,76,86,91,6,17,27,37,47,57,74,84,92,3,13,23,34,44,54,71,81,88,5,16,26,36,46,56,73,83,94,9,15,25,30,42,52,67,79,95,60,61,62,63,64,65,66,87,98","comment":"F_11(6, 6) base × F_9 fiber: 11 fibers of 9 in natural F_11 order. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/a5b354014616e2029c1add09cc8a4c961df0fea291962f717b96a1f34e011b3b.txt"},{"canonical_hash":"0c7a497df7880ba0c71b0e5b249cee39d6c367842e2488238438036d308f050b","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,95,8,9,10,11,12,13,14,15,94,24,25,26,27,28,29,30,31,98,56,57,58,59,60,61,62,63,93,48,49,50,51,52,53,54,55,89,72,73,74,75,76,77,78,79,90,40,41,42,43,44,45,46,47,97,16,17,18,19,20,21,22,23,96,64,65,66,67,68,69,70,71,92,32,33,34,35,36,37,38,39,91,80,81,82,83,84,85,86,87,88","comment":"F_11(6, 6) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/0c7a497df7880ba0c71b0e5b249cee39d6c367842e2488238438036d308f050b.txt"},{"canonical_hash":"15d364d818087e0d41517a5bab071200273c808184f1b0f6f7cf537a5a141edd","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,13,14,88,6,7,8,9,10,11,12,15,93,80,81,82,83,84,85,86,87,91,40,41,42,43,44,45,46,47,97,72,73,74,75,76,77,78,79,89,24,25,26,27,28,29,30,31,98,32,33,34,35,36,37,38,39,94,48,49,50,51,52,53,54,55,96,64,65,66,67,68,69,70,71,95,56,57,58,59,60,61,62,63,92,16,17,18,19,20,21,22,23,90","comment":"F_11(6, 6) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:41","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/15d364d818087e0d41517a5bab071200273c808184f1b0f6f7cf537a5a141edd.txt"},{"canonical_hash":"edfef000f0d9b42a351ff4a79ab3df422872ad349d3cdf8740c63f226cf82024","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,89,8,9,10,11,12,13,14,15,95,48,49,50,51,52,53,54,55,96,72,73,74,75,76,77,78,79,92,64,65,66,67,68,69,70,71,90,32,33,34,35,36,37,38,39,94,56,57,58,59,60,61,62,63,97,16,17,18,19,20,21,22,23,91,80,81,82,83,84,85,86,87,88,24,25,26,27,28,29,30,31,93,40,41,42,43,44,45,46,47,98","comment":"F_11(6, 6) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/edfef000f0d9b42a351ff4a79ab3df422872ad349d3cdf8740c63f226cf82024.txt"},{"canonical_hash":"eb9e069c77601feb253bef92cb867da23a297c1037a33d7335be31dcbfb9a8a1","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,98,8,9,10,11,12,13,14,15,91,40,41,42,43,44,45,46,47,96,48,49,50,51,52,53,54,55,90,32,33,34,35,36,37,38,39,89,80,81,82,83,84,85,86,87,95,16,17,18,19,20,21,22,23,92,56,57,58,59,60,61,62,63,93,24,25,26,27,28,29,30,31,97,64,65,66,67,68,69,70,71,94,72,73,74,75,76,77,78,79,88","comment":"F_11(6, 6) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:42","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/eb9e069c77601feb253bef92cb867da23a297c1037a33d7335be31dcbfb9a8a1.txt"},{"canonical_hash":"12feaef7003a6e5f39d1c0f4f81e54dbd815c37fdf4337190b3ebe302577ac03","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,10,20,32,41,51,68,77,90,1,11,21,31,40,50,69,78,89,9,13,23,30,42,52,67,79,88,8,19,29,39,49,59,76,86,97,6,17,27,37,47,57,74,84,95,2,12,22,33,43,53,70,80,91,3,14,24,34,44,54,71,81,92,7,18,28,38,48,58,75,85,96,4,15,25,35,45,55,72,82,93,5,16,26,36,46,56,73,83,94,60,61,62,63,64,65,66,87,98","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/12feaef7003a6e5f39d1c0f4f81e54dbd815c37fdf4337190b3ebe302577ac03.txt"},{"canonical_hash":"13495103007e3ddf14966395e06d07b7cbab0d018e02346bfae56491d2fd32db","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,88,8,9,10,11,12,13,14,15,90,32,33,34,35,36,37,38,39,96,48,49,50,51,52,53,54,55,93,56,57,58,59,60,61,62,63,98,40,41,42,43,44,45,46,47,91,64,65,66,67,68,69,70,71,89,72,73,74,75,76,77,78,79,94,80,81,82,83,84,85,86,87,92,24,25,26,27,28,29,30,31,97,16,17,18,19,20,21,22,23,95","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:43","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/13495103007e3ddf14966395e06d07b7cbab0d018e02346bfae56491d2fd32db.txt"},{"canonical_hash":"ca1b645c12adbefd028608f12baf209cc387b8252d3ecc7f301bf9ef2626ecba","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,95,8,9,10,11,12,13,14,15,98,72,73,74,75,76,77,78,79,89,64,65,66,67,68,69,70,71,88,32,33,34,35,36,37,38,39,97,16,17,18,19,20,21,22,23,91,48,49,50,51,52,53,54,55,93,80,81,82,83,84,85,86,87,90,24,25,26,27,28,29,30,31,94,40,41,42,43,44,45,46,47,92,56,57,58,59,60,61,62,63,96","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/ca1b645c12adbefd028608f12baf209cc387b8252d3ecc7f301bf9ef2626ecba.txt"},{"canonical_hash":"a62f6850c1ac26b136926e9a4aa4a77c8dd7d9b800dff2e77636500b59cb1ecf","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,88,8,9,10,11,12,13,14,15,95,40,41,42,43,44,45,46,47,90,64,65,66,67,68,69,70,71,92,24,25,26,27,28,29,30,31,98,56,57,58,59,60,61,62,63,91,72,73,74,75,76,77,78,79,94,48,49,50,51,52,53,54,55,93,16,17,18,19,20,21,22,23,89,80,81,82,83,84,85,86,87,96,32,33,34,35,36,37,38,39,97","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:44","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/a62f6850c1ac26b136926e9a4aa4a77c8dd7d9b800dff2e77636500b59cb1ecf.txt"},{"canonical_hash":"ce04eb38af2829527844e9c822784857d979281c6a60399e00502aaae30f4509","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,93,8,9,10,11,12,13,14,15,97,64,65,66,67,68,69,70,71,94,24,25,26,27,28,29,30,31,89,48,49,50,51,52,53,54,55,98,72,73,74,75,76,77,78,79,96,56,57,58,59,60,61,62,63,91,16,17,18,19,20,21,22,23,88,80,81,82,83,84,85,86,87,92,40,41,42,43,44,45,46,47,95,32,33,34,35,36,37,38,39,90","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/ce04eb38af2829527844e9c822784857d979281c6a60399e00502aaae30f4509.txt"},{"canonical_hash":"57476de4a74eff7f966a11955c81f854adf3fc0995e06c090526caa78658ea80","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,1,2,3,4,5,6,7,88,8,11,13,15,17,19,21,23,89,25,27,29,31,33,35,37,39,95,40,42,44,46,48,50,52,54,98,57,59,61,63,65,67,69,71,91,73,75,77,79,81,83,85,87,93,72,74,76,78,80,82,84,86,94,56,58,60,62,64,66,68,70,92,41,43,45,47,49,51,53,55,97,24,26,28,30,32,34,36,38,96,9,10,12,14,16,18,20,22,90","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:45","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/57476de4a74eff7f966a11955c81f854adf3fc0995e06c090526caa78658ea80.txt"},{"canonical_hash":"beb3f622e9533b36539e7e964d42291fa9e40077ea871f5f90c6a9760108bdfb","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,3,5,7,9,11,13,15,90,1,2,4,6,8,10,12,14,91,65,67,69,71,73,75,77,79,96,32,34,36,38,40,42,44,46,89,16,18,20,22,24,26,28,30,97,48,50,52,54,56,58,60,62,93,80,81,82,83,84,85,86,87,94,49,51,53,55,57,59,61,63,92,17,19,21,23,25,27,29,31,98,33,35,37,39,41,43,45,47,88,64,66,68,70,72,74,76,78,95","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/beb3f622e9533b36539e7e964d42291fa9e40077ea871f5f90c6a9760108bdfb.txt"},{"canonical_hash":"867a349fa6998b39651a4b65a53bcad2fd5733edc60d5413c621bc972b80978b","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"0,3,5,7,9,65,67,69,88,1,2,4,6,8,64,66,68,89,40,42,44,46,48,50,82,84,92,22,24,26,28,30,32,76,79,90,53,55,57,59,61,63,71,87,98,11,13,15,17,19,21,73,75,94,34,35,36,37,38,39,78,81,96,10,12,14,16,18,20,72,74,95,52,54,56,58,60,62,70,86,97,23,25,27,29,31,33,77,80,91,41,43,45,47,49,51,83,85,93","comment":"F_11(10, 2) base × F_9 fiber: 11 fibers of 9. Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-23 21:26:46","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/867a349fa6998b39651a4b65a53bcad2fd5733edc60d5413c621bc972b80978b.txt"},{"canonical_hash":"a54c624655a2c2a5af219ac8ca59fb9f840f602a3b9e12e03c4c407a782fa196","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,18,28,38,48,59,69,79,88,5,15,25,35,45,56,66,76,89,6,16,26,36,46,57,67,77,93,80,81,82,83,84,85,86,87,98,1,11,20,31,41,51,61,70,96,0,10,21,30,40,52,62,72,97,3,13,23,33,43,54,64,74,92,9,19,29,39,49,50,60,71,95,7,17,27,37,47,58,68,78,91,2,12,22,32,42,53,63,73,94,4,14,24,34,44,55,65,75,90","comment":"F_11(4, 8) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/a54c624655a2c2a5af219ac8ca59fb9f840f602a3b9e12e03c4c407a782fa196.txt"},{"canonical_hash":"95b751a48b68a2f621632970f3421a3553e52ef647924d13ccb1c1f20c19d287","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"7,17,27,37,47,58,68,78,88,3,13,23,33,43,54,64,74,89,1,11,20,31,41,51,61,71,96,6,16,26,36,46,57,67,77,91,8,18,28,38,48,59,69,79,92,2,12,22,32,42,53,63,73,94,9,19,29,39,49,50,60,70,95,0,10,21,30,40,52,62,72,97,80,81,82,83,84,85,86,87,98,5,15,25,35,45,56,66,76,93,4,14,24,34,44,55,65,75,90","comment":"F_11(5, 7) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:47","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/95b751a48b68a2f621632970f3421a3553e52ef647924d13ccb1c1f20c19d287.txt"},{"canonical_hash":"0c47cf3d3f43a2c9f902b49bf9b38dbe657a95457723309323fee7c5c1d59808","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"7,17,27,37,47,58,68,78,88,8,18,28,38,48,59,69,79,89,80,81,82,83,84,85,86,87,98,3,13,23,33,43,54,64,74,93,2,12,22,32,42,53,63,73,94,5,15,25,35,45,56,66,76,91,1,11,20,31,41,51,61,71,96,9,19,29,39,49,50,60,70,95,4,14,24,34,44,55,65,75,92,6,16,26,36,46,57,67,77,90,0,10,21,30,40,52,62,72,97","comment":"F_11(6, 6) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/0c47cf3d3f43a2c9f902b49bf9b38dbe657a95457723309323fee7c5c1d59808.txt"},{"canonical_hash":"06fbc1a6ed74adb9e07f43853c4d7a503f475e128aede1b7c2f516392771e53b","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"7,17,27,37,47,58,68,78,88,8,18,28,38,48,59,69,79,89,6,16,26,36,46,57,67,77,93,3,13,23,33,43,54,64,74,90,1,11,20,30,41,51,61,70,94,4,14,24,34,44,55,65,75,97,9,19,29,39,49,50,60,71,91,2,12,22,32,42,53,63,73,92,80,81,82,83,84,85,86,87,98,5,15,25,35,45,56,66,76,96,0,10,21,31,40,52,62,72,95","comment":"F_11(10, 2) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:48","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/06fbc1a6ed74adb9e07f43853c4d7a503f475e128aede1b7c2f516392771e53b.txt"},{"canonical_hash":"fc428bb84f318e4c1c26244b107a54a3af4ddbdc16922dbd764faa363e9de0de","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,14,24,34,44,55,65,75,88,9,19,29,39,49,51,61,72,89,7,17,27,37,47,58,68,78,97,0,10,21,31,41,50,62,71,94,1,11,20,30,40,52,60,70,93,6,16,26,36,46,57,67,77,92,8,18,28,38,48,59,69,79,90,5,15,25,35,45,56,66,76,96,2,12,22,32,42,53,63,73,91,80,81,82,83,84,85,86,87,98,3,13,23,33,43,54,64,74,95","comment":"F_11(5, 7) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:49","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/fc428bb84f318e4c1c26244b107a54a3af4ddbdc16922dbd764faa363e9de0de.txt"},{"canonical_hash":"19db9b9ff88013075cd50c08e95878a5b21c7b46c92f96bdfba1d02cb4f8d3d6","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,14,24,34,44,55,65,75,88,2,12,22,32,42,53,63,73,89,6,16,26,36,46,57,67,77,92,7,17,27,37,47,58,68,78,97,3,13,23,33,43,54,64,74,95,5,15,25,35,45,56,66,76,96,1,11,20,30,40,52,60,71,93,9,19,29,39,49,51,61,72,91,80,81,82,83,84,85,86,87,98,8,18,28,38,48,59,69,79,90,0,10,21,31,41,50,62,70,94","comment":"F_11(10, 2) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:49","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/19db9b9ff88013075cd50c08e95878a5b21c7b46c92f96bdfba1d02cb4f8d3d6.txt"},{"canonical_hash":"156ec76673c2ad3b95aa6ad80b361e7bb068ea2c76c6cbb42ca2be05d0f35029","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"4,14,24,34,44,55,65,75,88,2,12,22,32,42,53,63,73,89,6,16,26,36,46,57,67,77,92,7,17,27,37,47,58,68,78,97,3,13,23,33,43,54,64,74,95,5,15,25,35,45,56,66,76,96,0,11,20,30,40,52,60,71,93,9,19,29,39,49,51,61,72,90,80,81,82,83,84,85,86,87,98,8,18,28,38,48,59,69,79,91,1,10,21,31,41,50,62,70,94","comment":"F_11(4, 8) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/156ec76673c2ad3b95aa6ad80b361e7bb068ea2c76c6cbb42ca2be05d0f35029.txt"},{"canonical_hash":"8f1c3764f569e4edb50064920621e0f087d25e36e964dac55b2ae63e13930524","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"8,18,28,38,48,59,69,79,88,9,19,29,39,49,50,61,71,89,7,17,27,37,47,58,68,78,94,4,14,24,34,44,55,65,75,97,1,11,20,30,40,52,62,72,92,0,10,21,31,41,51,60,70,93,5,15,25,35,45,56,66,76,96,3,13,23,33,43,54,64,74,95,80,81,82,83,84,85,86,87,98,6,16,26,36,46,57,67,77,90,2,12,22,32,42,53,63,73,91","comment":"F_11(6, 6) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:50","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/8f1c3764f569e4edb50064920621e0f087d25e36e964dac55b2ae63e13930524.txt"},{"canonical_hash":"46de2cb60d65ac679a381cb0718a07594cf740b1e33623e98115b824093028dc","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"7,17,27,37,47,58,68,78,88,2,12,22,32,42,53,63,73,89,3,13,23,33,43,54,64,74,93,0,11,20,30,40,52,62,72,94,9,19,29,39,49,50,60,71,92,6,16,26,36,46,57,67,77,91,5,15,25,35,45,56,66,76,96,4,14,24,34,44,55,65,75,97,8,18,28,38,48,59,69,79,90,80,81,82,83,84,85,86,87,98,1,10,21,31,41,51,61,70,95","comment":"F_11(5, 7) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/46de2cb60d65ac679a381cb0718a07594cf740b1e33623e98115b824093028dc.txt"},{"canonical_hash":"a20195a7b4c02d94fb9fc406e125955b229a87a9c9783b009b8b899ad51adc06","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"9,19,29,39,49,50,60,70,88,5,15,25,35,45,56,66,76,89,3,13,23,33,43,54,64,74,95,2,12,22,32,42,53,63,73,93,1,11,20,30,41,51,61,71,90,6,16,26,36,46,57,67,77,92,0,10,21,31,40,52,62,72,91,80,81,82,83,84,85,86,87,98,8,18,28,38,48,59,69,79,96,4,14,24,34,44,55,65,75,97,7,17,27,37,47,58,68,78,94","comment":"F_11(6, 6) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:51","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/a20195a7b4c02d94fb9fc406e125955b229a87a9c9783b009b8b899ad51adc06.txt"},{"canonical_hash":"3ec10e0f3130094455629e6582ff2efb75d44ca91c712c76da4b28ee38e971b6","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"9,19,29,39,49,50,60,70,88,5,15,25,35,45,56,66,76,89,3,13,23,33,43,54,64,74,95,2,12,22,32,42,53,63,73,92,1,11,21,30,41,51,61,71,90,6,16,26,36,46,57,67,77,93,0,10,20,31,40,52,62,72,91,80,81,82,83,84,85,86,87,98,8,18,28,38,48,59,69,79,96,4,14,24,34,44,55,65,75,97,7,17,27,37,47,58,68,78,94","comment":"F_11(10, 2) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/3ec10e0f3130094455629e6582ff2efb75d44ca91c712c76da4b28ee38e971b6.txt"},{"canonical_hash":"ceaa5cf66e9e90f9a18f98abca872d4f40876d9d61f36b41c766b39b4449cf81","size":99,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"5,15,25,35,45,56,66,76,88,6,16,26,36,46,57,67,77,89,4,14,24,34,44,55,65,75,97,3,13,23,33,43,54,64,74,92,1,11,20,30,40,52,62,72,94,7,17,27,37,47,58,68,78,90,2,12,22,32,42,53,63,73,93,80,81,82,83,84,85,86,87,98,9,19,29,39,49,50,61,71,91,0,10,21,31,41,51,60,70,95,8,18,28,38,48,59,69,79,96","comment":"F_11(4, 8) base × 9-fiber (twisted): 11 fibers of 9. Twisted fiber bundle: 11 fibers partition the carrier, and an 11-element F_11 sub-magma — with one element in each fiber — encodes the base operation. The \"base\" quotient is not well-defined element-wise; the sub-magma anchors it.","submitted_at":"2026-04-23 21:26:52","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/99/ceaa5cf66e9e90f9a18f98abca872d4f40876d9d61f36b41c766b39b4449cf81.txt"},{"canonical_hash":"f412f9ccd1f90222991c0b5f9ad3840e5cc8d82953f8de5e591e4db015d3f24c","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,90,30,42,93,39,59,35,54,27,60,76,70,87,34,8,48,23,80,17,88,22,92,40,95,83,37,63,62,33,89,12,25,71,19,99,94,75,85,50,64,6,14,18,21,53,77,15,66,43,20,11,79,38,45,3,81,44,5,61,7,29,31,72,100,10,84,82,69,24,67,97,28,65,98,91,26,73,57,96,4,52,49,16,58,55,51,68,2,13,32,47,41,46,56,9,78,74,36,86","comment":"Linear magma over Z/101Z (the prime field F_101): x ◇ y = 37x + 65y (mod 101).","submitted_at":"2026-04-28 16:07:07","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/101/f412f9ccd1f90222991c0b5f9ad3840e5cc8d82953f8de5e591e4db015d3f24c.txt"},{"canonical_hash":"763eb91860d7292823ef48364f1f09e2d1f7395fe9b6c5ca2e7cad52db436c56","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,98,20,14,95,78,66,42,63,82,10,31,28,72,90,5,100,30,65,97,3,6,35,57,88,17,91,53,70,39,45,73,26,25,52,34,29,27,41,19,8,32,74,84,80,50,11,46,61,23,60,83,40,24,69,56,64,71,62,13,76,43,54,47,93,37,67,92,12,68,22,79,18,51,38,87,96,89,81,94,49,15,58,85,48,86,21,36,75,55,59,99,7,33,44,16,2,4,9,77","comment":"Linear magma over Z/101Z (the prime field F_101): x ◇ y = 85x + 17y (mod 101).","submitted_at":"2026-04-28 16:07:08","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/101/763eb91860d7292823ef48364f1f09e2d1f7395fe9b6c5ca2e7cad52db436c56.txt"},{"canonical_hash":"665cee59bd008da0e9a3efc886415205d33f966714026ae4227ca167527385a3","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,40,51,53,13,37,67,10,87,7,52,74,83,100,15,45,48,75,19,78,38,66,81,49,47,69,94,93,27,24,88,72,6,79,96,77,89,2,23,60,50,59,64,82,4,29,80,54,42,5,16,36,63,70,44,62,90,68,85,55,76,32,86,28,57,18,61,8,26,17,39,22,33,73,41,34,65,84,98,71,25,12,58,97,14,35,30,46,31,91,95,21,9,3,11,99,43,20,92,56","comment":"Linear magma over Z/101Z (the prime field F_101): x ◇ y = 88x + 14y (mod 101).","submitted_at":"2026-04-28 16:07:09","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/101/665cee59bd008da0e9a3efc886415205d33f966714026ae4227ca167527385a3.txt"},{"canonical_hash":"67d9a5a542d8d4a2caa9eff8dd57a4b2fb5e69f8f65fbb295abce2f378a9d9b8","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,8,62,70,45,100,20,95,87,33,26,25,97,58,17,51,73,50,49,35,93,46,15,92,44,39,27,11,29,38,32,74,84,60,80,31,16,71,3,90,53,30,34,69,66,64,81,52,43,86,23,54,47,63,37,57,82,12,88,22,79,48,61,18,77,56,89,91,94,9,5,78,65,28,96,41,6,55,85,59,99,7,13,4,36,2,14,19,67,40,21,68,10,24,75,98,76,42,83,72","comment":"Linear magma over Z/101Z (the prime field F_101): x ◇ y = 96x + 6y (mod 101).","submitted_at":"2026-04-28 16:07:11","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/101/67d9a5a542d8d4a2caa9eff8dd57a4b2fb5e69f8f65fbb295abce2f378a9d9b8.txt"},{"canonical_hash":"2b36cdbafcbe170eb224c4b19fee9c880ae30e2a5b9d896e35095c24fa7dce95","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,82,20,14,89,62,90,42,97,86,10,31,28,76,84,5,100,30,59,51,3,6,35,61,72,17,65,87,64,39,45,57,26,25,56,34,29,27,41,19,8,32,88,98,74,94,11,46,85,23,54,67,40,24,83,80,78,95,66,13,50,43,68,47,77,37,71,96,12,52,22,93,18,75,38,91,70,53,55,58,49,15,92,79,48,60,21,36,69,99,73,63,7,33,44,16,2,4,9,81","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0 and cycle structure (10^10, 1) on F_101* — 10 orbits of size 10, fixed point at 0.\n\nDecomposition: with respect to the order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets. δ acts as:\n  • multiplication by α₀ = 17 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by α₁ = 6 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are with respect to the F_101* generator g = 2.\n\nBoth α₀ = 17 and α₁ = 6 are primitive 10th roots of unity in F_101* (= roots of Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 101), namely from the 4-element set {6, 14, 17, 65}. Because these ratios lie IN H, multiplication by them keeps each element in its coset, giving the 10 separate cycles of length 10. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0 mod 101. The magma is globally NOT medial (since α₀ ≠ α₁).\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nCompare ee5b34c8 (the one size-101 b-reinke outlier): same template but with α₀, α₁ taken from primitive ROOTS of F_101* (order 100), not 10th roots.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:21:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/2b36cdbafcbe170eb224c4b19fee9c880ae30e2a5b9d896e35095c24fa7dce95.txt"},{"canonical_hash":"5919e6d1e3fd34d751a7f477f8a98e6b14d1952976913c53a20674a38568d0d5","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,97,80,68,13,65,84,10,35,7,74,92,31,100,15,67,99,48,19,26,59,90,29,93,55,72,42,41,75,24,36,54,6,27,44,25,37,2,23,76,86,82,52,30,4,63,28,62,85,5,16,71,58,66,73,64,38,78,33,56,49,95,34,69,94,18,70,8,81,17,53,22,89,98,91,83,96,32,46,60,87,12,88,45,14,77,57,61,51,39,43,21,9,3,11,47,79,20,40,50","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0 and cycle structure (10^10, 1) on F_101* — 10 orbits of size 10, fixed point at 0.\n\nDecomposition: with respect to the order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets. δ acts as:\n  • multiplication by α₀ = 14 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by α₁ = 17 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are with respect to the F_101* generator g = 2.\n\nBoth α₀ = 14 and α₁ = 17 are primitive 10th roots of unity in F_101* (= roots of Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 101), namely from the 4-element set {6, 14, 17, 65}. Because these ratios lie IN H, multiplication by them keeps each element in its coset, giving the 10 separate cycles of length 10. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0 mod 101. The magma is globally NOT medial (since α₀ ≠ α₁).\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nCompare ee5b34c8 (the one size-101 b-reinke outlier): same template but with α₀, α₁ taken from primitive ROOTS of F_101* (order 100), not 10th roots.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:21:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/5919e6d1e3fd34d751a7f477f8a98e6b14d1952976913c53a20674a38568d0d5.txt"},{"canonical_hash":"5175434b5ac7f33a92aef548a737a5e09b80a4c3ea0bf4aed013cc46f3c88bde","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,71,68,66,83,54,35,88,30,56,36,65,46,59,84,8,90,23,81,17,63,22,79,58,91,93,96,39,38,80,67,12,98,47,19,57,87,61,51,26,40,6,14,18,21,29,69,15,42,70,20,11,77,50,78,3,85,74,5,37,7,64,72,48,100,10,97,89,45,24,43,99,60,41,53,75,52,49,33,95,4,28,94,16,34,31,27,44,2,13,76,86,62,82,32,9,73,25,92,55","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0 and cycle structure (10^10, 1) on F_101* — 10 orbits of size 10, fixed point at 0.\n\nDecomposition: with respect to the order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets. δ acts as:\n  • multiplication by α₀ = 65 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by α₁ = 6 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are with respect to the F_101* generator g = 2.\n\nBoth α₀ = 65 and α₁ = 6 are primitive 10th roots of unity in F_101* (= roots of Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 101), namely from the 4-element set {6, 14, 17, 65}. Because these ratios lie IN H, multiplication by them keeps each element in its coset, giving the 10 separate cycles of length 10. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0 mod 101. The magma is globally NOT medial (since α₀ ≠ α₁).\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nCompare ee5b34c8 (the one size-101 b-reinke outlier): same template but with α₀, α₁ taken from primitive ROOTS of F_101* (order 100), not 10th roots.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:21:51","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/5175434b5ac7f33a92aef548a737a5e09b80a4c3ea0bf4aed013cc46f3c88bde.txt"},{"canonical_hash":"b816ef73776ef27e8aedf9b7d056cf3c6a0814e0b1260007ea2b293e2e1a6c9e","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,53,90,98,55,96,46,60,41,88,47,77,32,51,76,8,52,23,63,17,85,22,71,80,73,65,78,25,49,92,69,12,70,33,19,59,89,93,83,37,26,6,14,18,21,40,61,15,28,82,20,11,79,62,50,3,97,66,5,48,7,56,74,34,100,10,99,81,31,24,29,91,72,27,75,87,54,35,44,57,4,39,86,16,45,42,38,30,2,13,58,68,64,84,43,9,95,36,94,67","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0 and cycle structure (10^10, 1) on F_101* — 10 orbits of size 10, fixed point at 0.\n\nDecomposition: with respect to the order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets. δ acts as:\n  • multiplication by α₀ = 65 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by α₁ = 17 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are with respect to the F_101* generator g = 2.\n\nBoth α₀ = 65 and α₁ = 17 are primitive 10th roots of unity in F_101* (= roots of Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 101), namely from the 4-element set {6, 14, 17, 65}. Because these ratios lie IN H, multiplication by them keeps each element in its coset, giving the 10 separate cycles of length 10. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0 mod 101. The magma is globally NOT medial (since α₀ ≠ α₁).\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nCompare ee5b34c8 (the one size-101 b-reinke outlier): same template but with α₀, α₁ taken from primitive ROOTS of F_101* (order 100), not 10th roots.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:22:17","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/b816ef73776ef27e8aedf9b7d056cf3c6a0814e0b1260007ea2b293e2e1a6c9e.txt"},{"canonical_hash":"ee5b34c8ad3ad05be20c20491c3eb5771980f48b2d4859be9b262f7b0d656d36","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,60,14,61,66,21,11,13,33,93,55,62,76,58,82,67,47,84,71,20,74,52,31,10,4,88,15,12,54,81,70,32,16,69,100,94,41,7,95,56,79,37,40,63,29,35,6,77,99,45,96,59,22,92,57,83,51,87,80,68,8,38,36,46,91,86,39,85,26,25,64,72,43,24,28,19,2,65,34,75,48,73,5,53,17,42,78,30,98,23,50,9,90,27,44,3,49,18,97,89","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation: x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0.\n\nUnlike the size-151 RC sibling family (whose δ has cycle structure (10^15, 1) with ratios in the order-10 subgroup H ⊂ F_151*), here δ has a SINGLE cycle of length 100 — i.e. δ is a primitive permutation of F_101*, of order 100.\n\nDecomposition: with respect to the unique order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets, and δ acts as:\n  • multiplication by 35 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by 67 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are taken with respect to the F_101* generator g = 2.\n\nBoth 35 and 67 are primitive roots of F_101* (multiplicative order 100), NOT roots of Φ_10. Because multiplication by either ratio shifts an element by an ODD number of cosets, and the two ratios alternate, δ produces a single long orbit instead of the 15 small orbits seen in the size-151 family.\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nADDENDUM (post-classification of the full size-101 family): the 7 size-101 b-reinke magmas all follow the F_101-translation-invariant template x ◇ y = x + δ(y - x), with δ acting as multiplication by α₀ on even-index cosets and α₁ on odd-index cosets of the order-10 subgroup H ⊂ F_101*. The other 6 (2b36cdba, 5919e6d1, 5175434b, b816ef73, 313eaa7b, 7505447f) draw (α₀, α₁) from the 4 primitive 10th roots {6, 14, 17, 65} — covering all C(4,2) = 6 unordered pairs. This one (ee5b34c8) is the unique outlier drawing (α₀, α₁) = (35, 67) from primitive roots of F_101* (order 100). The eq677 constraint is therefore satisfied by a broader α-set than just the 10th roots of unity. Notably 35 + 67 ≡ 1 (mod 101), so the two primitive-root ratios are 'complementary' in the idempotent-linear sense (α + α' = 1) — a brute-force enumeration over all of F_101* × F_101* finds that (35, 67) is the UNIQUE non-10th-root alternating pair satisfying eq677.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:22:19","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/ee5b34c8ad3ad05be20c20491c3eb5771980f48b2d4859be9b262f7b0d656d36.txt"},{"canonical_hash":"313eaa7bfc4d92cb984ff9e4525253ff163b69bd3257fc4185fd3cd09b6bd457","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,85,58,86,13,93,82,10,48,7,72,80,44,100,15,55,97,36,19,39,57,68,42,61,83,60,30,29,53,24,49,52,6,40,32,38,25,2,23,84,94,70,90,43,4,81,41,50,63,5,16,79,76,74,91,62,26,96,46,64,37,73,47,67,92,18,98,8,89,17,71,22,87,66,99,51,54,45,34,88,75,12,56,33,14,65,95,69,59,27,31,21,9,3,11,35,77,20,28,78","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0 and cycle structure (10^10, 1) on F_101* — 10 orbits of size 10, fixed point at 0.\n\nDecomposition: with respect to the order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets. δ acts as:\n  • multiplication by α₀ = 14 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by α₁ = 6 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are with respect to the F_101* generator g = 2.\n\nBoth α₀ = 14 and α₁ = 6 are primitive 10th roots of unity in F_101* (= roots of Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 101), namely from the 4-element set {6, 14, 17, 65}. Because these ratios lie IN H, multiplication by them keeps each element in its coset, giving the 10 separate cycles of length 10. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0 mod 101. The magma is globally NOT medial (since α₀ ≠ α₁).\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nCompare ee5b34c8 (the one size-101 b-reinke outlier): same template but with α₀, α₁ taken from primitive ROOTS of F_101* (order 100), not 10th roots.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:22:20","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/313eaa7bfc4d92cb984ff9e4525253ff163b69bd3257fc4185fd3cd09b6bd457.txt"},{"canonical_hash":"7505447f731ceccf9c409d4667dfcec484e9a63e74f93f2642f8bd62fca8f189","size":101,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,32,52,59,40,51,75,57,95,69,76,28,86,49,71,8,50,23,47,17,35,22,29,62,37,30,54,79,78,60,46,12,72,87,19,31,26,42,27,91,80,6,14,18,21,94,39,15,82,70,20,11,36,65,67,3,33,56,5,77,7,66,63,88,100,10,41,44,85,24,83,34,55,81,45,43,58,89,98,48,4,93,61,16,99,96,92,84,2,13,74,64,73,53,97,9,25,90,68,38","comment":"Size-101 idempotent right-cancellative translation-invariant magma on F_101 (= Z/101 additively). Operation x ◇ y = x + δ(y - x) where δ : F_101 → F_101 is a permutation with δ(0) = 0 and cycle structure (10^10, 1) on F_101* — 10 orbits of size 10, fixed point at 0.\n\nDecomposition: with respect to the order-10 subgroup H ⊂ F_101* ({1, 6, 14, 17, 36, 65, 84, 87, 95, 100}), F_101* has 10 cosets. δ acts as:\n  • multiplication by α₀ = 65 on cosets {0, 2, 4, 6, 8} (5 even-index cosets)\n  • multiplication by α₁ = 14 on cosets {1, 3, 5, 7, 9} (5 odd-index cosets)\nwhere coset indices are with respect to the F_101* generator g = 2.\n\nBoth α₀ = 65 and α₁ = 14 are primitive 10th roots of unity in F_101* (= roots of Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 101), namely from the 4-element set {6, 14, 17, 65}. Because these ratios lie IN H, multiplication by them keeps each element in its coset, giving the 10 separate cycles of length 10. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0 mod 101. The magma is globally NOT medial (since α₀ ≠ α₁).\n\nDisplay reorder: relabel points so that the magma's order-101 translation auto acts as i ↦ i + 1, making T[i+1][j+1] ≡ T[i][j] + 1 (mod 101) directly visible.\n\nCompare ee5b34c8 (the one size-101 b-reinke outlier): same template but with α₀, α₁ taken from primitive ROOTS of F_101* (order 100), not 10th roots.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:22:22","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/101/7505447f731ceccf9c409d4667dfcec484e9a63e74f93f2642f8bd62fca8f189.txt"},{"canonical_hash":"ce04ffa0709cb58284f51f33c4ce5dee9ed8ee6a2af61e48535d551f0a0227c3","size":103,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"102,0,29,45,25,67,41,76,21,60,63,43,37,42,72,82,17,70,56,101,59,91,39,3,33,5,38,75,68,50,78,99,13,58,66,14,52,6,31,57,55,44,87,26,35,97,98,16,32,23,100,85,34,49,71,80,64,47,46,86,74,36,95,7,9,79,54,4,62,18,10,61,48,30,2,20,27,89,53,84,51,90,40,11,83,8,22,65,1,24,93,88,94,15,12,69,28,92,19,73,96,77,81","comment":"Linear magma over Z/103Z (the prime field F_103): x ◇ y = 46x + 59y (mod 103).","submitted_at":"2026-04-28 16:07:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/103/ce04ffa0709cb58284f51f33c4ce5dee9ed8ee6a2af61e48535d551f0a0227c3.txt"},{"canonical_hash":"f4bef13c0c24227f19fa334b7961cb31de9d7023c415da42b091c6f59a3c9748","size":103,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"102,0,46,58,38,51,50,44,30,12,94,54,93,27,36,101,22,32,2,7,86,99,97,45,85,49,19,67,28,43,48,64,14,8,24,92,47,76,3,82,78,31,91,65,89,60,37,96,77,34,41,87,11,66,59,5,20,62,35,13,40,15,56,1,6,75,4,72,16,100,84,90,39,73,68,53,42,95,74,9,70,21,23,10,83,80,57,98,81,61,52,17,29,18,88,55,69,25,26,63,33,71,79","comment":"Linear magma over Z/103Z (the prime field F_103): x ◇ y = 46x + 90y (mod 103).","submitted_at":"2026-04-28 16:07:13","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/103/f4bef13c0c24227f19fa334b7961cb31de9d7023c415da42b091c6f59a3c9748.txt"},{"canonical_hash":"ad12489b834482ea774a64d61761a25b0ee3c39a02221631feed91ea4b2b8604","size":103,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"102,0,31,82,15,8,6,27,63,91,26,101,24,57,11,77,47,67,75,81,74,36,32,29,72,3,41,100,59,25,35,94,95,83,51,22,33,54,5,66,58,65,20,96,16,86,13,30,56,71,21,12,89,98,84,9,43,90,73,93,19,97,78,2,79,52,7,46,99,4,70,18,17,48,38,1,23,28,50,85,42,45,49,87,68,62,80,34,64,88,10,37,61,39,14,76,40,53,55,92,69,44,60","comment":"Linear magma over Z/103Z (the prime field F_103): x ◇ y = 56x + 24y (mod 103).","submitted_at":"2026-04-28 16:07:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/103/ad12489b834482ea774a64d61761a25b0ee3c39a02221631feed91ea4b2b8604.txt"},{"canonical_hash":"a8e1368c87358b8ea19249e3a08c8e0b91a3a4a0167906f685d8fc4b9c981609","size":103,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"102,0,37,90,24,85,77,21,11,20,72,58,64,38,8,15,49,27,101,31,59,61,96,29,51,10,25,60,46,13,4,87,36,39,14,56,45,81,18,78,97,19,99,95,83,55,16,88,89,43,48,67,12,52,98,34,33,71,2,28,40,44,74,42,23,73,26,100,3,69,94,91,32,57,68,50,7,80,65,47,84,41,1,6,86,62,82,53,70,63,93,9,5,17,75,66,76,22,30,79,35,92,54","comment":"Linear magma over Z/103Z (the prime field F_103): x ◇ y = 56x + 32y (mod 103).","submitted_at":"2026-04-28 16:07:16","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/103/a8e1368c87358b8ea19249e3a08c8e0b91a3a4a0167906f685d8fc4b9c981609.txt"},{"canonical_hash":"de38b055420d2dc78d72cab1c5efbdc5be7694caaa29d1542ee194723d9ebdf2","size":109,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"108,0,1,106,2,98,105,74,3,43,97,68,104,83,73,35,4,16,42,7,96,47,67,26,103,63,82,13,72,76,70,37,5,28,15,39,41,58,8,56,95,22,46,19,66,31,25,54,102,51,62,93,81,89,12,107,71,99,75,44,69,84,36,17,6,48,27,64,14,77,38,29,40,59,57,23,20,32,55,52,94,90,34,100,45,85,18,49,65,78,30,60,24,33,53,91,101,86,50,79,61,21,92,87,80,9,88,10,11","comment":"Linear magma over Z/109Z (the prime field F_109): x ◇ y = 45x + 20y (mod 109).","submitted_at":"2026-04-28 16:07:17","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/109/de38b055420d2dc78d72cab1c5efbdc5be7694caaa29d1542ee194723d9ebdf2.txt"},{"canonical_hash":"f62c73efc49b423e465b4dd137efc14fc476131258516965bfec71b5f0e79aa1","size":109,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"108,0,72,101,87,13,16,49,102,45,28,94,31,22,1,57,17,44,4,6,43,85,9,60,46,61,37,81,71,19,64,27,32,38,3,97,67,36,69,107,58,20,100,99,24,93,75,88,5,33,76,80,52,40,96,50,86,98,34,30,79,7,42,29,47,70,53,54,66,104,12,23,82,21,51,105,84,78,73,18,65,25,35,83,15,92,14,2,39,89,8,106,90,63,103,10,68,77,48,74,91,56,95,62,59,41,55,26,11","comment":"Linear magma over Z/109Z (the prime field F_109): x ◇ y = 45x + 25y (mod 109).","submitted_at":"2026-04-28 16:07:18","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/109/f62c73efc49b423e465b4dd137efc14fc476131258516965bfec71b5f0e79aa1.txt"},{"canonical_hash":"bb54efccb01a6693da6fe7fa5911dfb34357e705bbecdb05a2adcd645e999db5","size":117,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"116,96,107,98,101,106,105,103,104,97,100,102,99,108,26,32,18,62,40,3,76,92,10,70,84,54,111,14,44,30,50,0,36,88,80,22,58,72,66,109,29,35,21,65,43,1,79,71,13,49,87,57,114,23,4,15,59,37,45,73,89,7,67,81,51,115,20,5,12,56,34,42,94,86,28,64,78,48,113,17,6,9,53,31,39,91,83,25,61,75,69,112,8,38,24,68,46,95,82,74,16,52,90,60,110,11,41,27,47,2,33,85,77,19,55,93,63","comment":"Direct product of two linear magmas: F_9 × F_13(9,11).","submitted_at":"2026-04-28 16:08:11","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/117/bb54efccb01a6693da6fe7fa5911dfb34357e705bbecdb05a2adcd645e999db5.txt"},{"canonical_hash":"ee53a960fcb4822fb3ece18b2952f472cacf55c57f3a61d2020f7406386ce92e","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"115,2,5,9,8,4,6,3,0,1,7,114,15,19,13,14,16,12,18,10,11,17,120,87,82,89,85,88,84,80,81,86,83,117,56,52,58,59,57,54,50,51,55,53,110,35,37,39,36,30,31,33,32,38,34,119,76,73,74,70,71,78,77,79,72,75,111,23,26,20,21,24,28,25,27,22,29,113,97,98,93,92,90,91,96,94,99,95,118,48,44,40,41,43,45,49,47,46,42,116,65,69,62,63,60,61,68,66,64,67,112,108,104,103,105,102,107,100,101,106,109","comment":"Size-121 (= 11²) non-right-cancellative magma, all elements idempotent, satisfies eq255. Decomposes as a fiber-bundle-like structure: F_11(10,2) base × F_11(4,8) fiber. The 121 elements partition into 11 fibers of 11 elements (an F_11-quotient congruence), and EVERY fiber is itself an F_11(4,8) sub-magma. In addition, there is exactly one extra 11-element sub-magma — a transversal that hits each fiber in exactly one element — and this transversal is isomorphic to F_11(10,2) (matching the base operation). The 12 size-11 sub-magmas (11 fibers + 1 transversal) form an AG(2,11)-pencil-like configuration. The magma is left-cancellative but not right-cancellative, distinguishing it from the direct product F_11(10,2) × F_11(4,8) (which would be both LC and RC). Each pair of distinct elements is contained in exactly one of the 12 size-11 sub-magmas (covering 660 = 12·C(11,2) of the 7260 = C(121,2) total pairs); pairs across two distinct fibers and not on the transversal lie in no sub-magma.","submitted_at":"2026-04-23 22:00:49","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/121/ee53a960fcb4822fb3ece18b2952f472cacf55c57f3a61d2020f7406386ce92e.txt"},{"canonical_hash":"d4b8c23f26f1d9c94149853148c7aaf02f4b1b5b886ef5fae4841ac0eb3f626c","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"1,2,108,104,0,120,105,109,103,107,106,89,62,76,35,3,70,112,98,47,14,31,53,77,15,48,90,71,36,4,99,32,113,78,16,23,100,54,72,49,91,5,114,37,17,24,115,6,79,63,101,55,92,38,50,25,116,39,83,18,64,7,80,56,51,102,117,40,52,57,26,65,84,19,81,93,8,41,43,94,82,118,66,58,27,20,9,85,44,95,10,21,42,67,73,119,28,86,59,96,11,87,29,45,68,22,33,110,60,74,12,88,61,111,97,69,30,46,34,75,13","comment":"Direct product of two linear magmas: F_11 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (10x₁ + 2y₁ (mod 11), 10x₂ + 2y₂ (mod 11)).","submitted_at":"2026-04-28 16:31:03","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/121/d4b8c23f26f1d9c94149853148c7aaf02f4b1b5b886ef5fae4841ac0eb3f626c.txt"},{"canonical_hash":"199764ee94ba2f149d8c3bc961066b7e83381b8c4aa8881608a66d78e16f386e","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,32,6,20,117,1,107,105,82,98,3,81,5,31,106,97,4,108,19,109,116,2,28,12,110,33,99,78,21,83,7,104,16,8,111,11,84,103,15,22,34,27,100,77,44,25,94,119,101,62,75,66,48,9,23,47,93,26,65,10,24,76,118,43,102,61,17,74,42,13,95,79,60,92,115,29,46,114,41,73,91,30,45,59,14,18,96,80,86,67,68,50,36,63,120,49,85,35,64,55,90,37,58,72,54,51,40,69,87,112,70,38,89,39,88,113,52,57,56,71,53","comment":"Direct product of two linear magmas: F_11 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (6x₁ + 6y₁ (mod 11), 6x₂ + 6y₂ (mod 11)).","submitted_at":"2026-04-28 18:08:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/121/199764ee94ba2f149d8c3bc961066b7e83381b8c4aa8881608a66d78e16f386e.txt"},{"canonical_hash":"65eed5985265ba99e1da5830688bb83ad3e2d7bdac34bb418b5abcd2564e6cd2","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"78,1,111,95,25,42,92,45,79,0,66,112,109,80,46,93,26,96,43,2,67,74,81,32,3,39,97,89,47,22,68,75,113,4,33,64,23,48,98,40,90,76,114,82,65,11,77,91,41,44,24,94,110,83,5,102,104,63,6,52,117,85,18,37,54,13,59,105,38,19,86,53,7,118,55,14,103,34,106,56,119,8,87,20,49,15,99,60,57,107,16,50,21,9,115,88,100,61,35,12,108,101,84,116,17,51,10,62,36,58,29,120,28,72,69,70,73,71,27,31,30","comment":"Direct product of two linear magmas: F_11 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (5x₁ + 7y₁ (mod 11), 5x₂ + 7y₂ (mod 11)).","submitted_at":"2026-04-28 18:08:07","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/121/65eed5985265ba99e1da5830688bb83ad3e2d7bdac34bb418b5abcd2564e6cd2.txt"},{"canonical_hash":"c3819eedb211f3d9ce11761a715059518713bc8c50f06c8cb3b5672b39f55317","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"106,107,104,12,109,120,105,108,1,0,13,71,92,94,47,119,57,75,83,2,49,40,76,72,79,115,50,58,95,93,41,3,48,96,77,89,51,4,54,80,73,44,42,116,81,97,69,5,43,55,90,78,117,45,52,91,82,74,39,46,56,70,98,53,118,6,101,112,59,15,7,33,65,88,23,25,36,66,102,84,8,26,29,60,113,37,19,16,61,67,114,27,20,30,85,103,17,38,9,86,62,99,21,34,31,110,68,10,18,28,111,87,64,35,14,32,100,63,24,11,22","comment":"Direct product of two linear magmas: F_11 × F_11. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 8y₁ (mod 11), 4x₂ + 8y₂ (mod 11)).","submitted_at":"2026-04-28 18:08:09","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/121/c3819eedb211f3d9ce11761a715059518713bc8c50f06c8cb3b5672b39f55317.txt"},{"canonical_hash":"74c24c4dbe554f336d0d031d9a6ea9217fedbc0ac93bd945b82546cb09a054f9","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,91,64,117,101,59,96,118,67,87,1,110,15,99,83,32,28,78,98,17,113,76,43,5,68,29,89,31,63,9,44,73,18,45,108,48,60,71,58,115,42,14,24,54,114,39,12,30,20,36,109,52,65,66,62,11,37,82,79,38,3,69,25,95,35,105,21,116,7,119,23,104,72,34,26,77,70,85,8,6,93,61,112,102,53,107,111,51,81,16,80,55,88,106,41,46,103,90,13,92,86,19,50,27,10,120,4,33,56,74,22,75,57,84,97,40,47,100,94,49","comment":"Size-121 RC idempotent magma on F_121 — \"order-20 multiplier\" outlier.\n\nSize 121, fully idempotent, right-cancellative. NO size-11 sub-magmas.\n\nL_0 and R_0 cycle structure **1 + 6·20** — multiplier in the F_121 linear operation has order **20**, not 10. This places the magma outside Pace Nielsen's standard Type-1 / Type-2 classification (both of which use multiplier orders related to Phi_10 = 10).\n\nThe order-20 subgroup of F_121* has 8 elements (= phi(20)·2 / 2 for primitive 20th roots). The multiplier here is a primitive 20th root of unity in F_121. Note that the (F_121*)-subgroup of order 20 contains Phi_10 roots as a subgroup (the order-10 elements), but this construction uses a primitive 20-th root instead.\n\nThe additive structure is F_11² (= F_121 additively). The suggested reorder uses two commuting order-11 fix-free auts as F_11 × F_11 grid generators (positions 11·a + b = t1^a(t2^b(0))). Cayley table shows 11×11 grid of 11×11 sub-blocks, diagonal-stripe structure within each block reflecting the order-11 translation action.\n\nCompanion to the \"order-8 multiplier\" family (5 magmas: magma#70e5572a, magma#873c2695, magma#58669675, magma#af70b7bb, magma#fdc7e335) and the Zassenhaus near-field magma#5ebfbb80 (order-30 multiplier). All four \"sub-11=0\" families share the F_11² additive structure but use different multiplicative orders.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:22:24","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/74c24c4dbe554f336d0d031d9a6ea9217fedbc0ac93bd945b82546cb09a054f9.txt"},{"canonical_hash":"83a10ff448e020055ba954f21047deb23d4965798dd069bcd1f5a2550f10bfa9","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"61,26,9,27,120,1,60,5,0,4,8,2,13,88,99,90,79,119,6,106,28,23,111,73,22,12,35,30,3,29,95,7,42,51,58,20,47,34,41,94,67,10,110,72,78,48,103,59,89,11,105,118,87,66,21,70,49,24,97,37,54,53,14,64,44,113,52,76,116,108,92,65,101,85,55,15,25,40,114,31,18,33,71,38,98,16,50,45,39,19,46,117,93,17,86,104,102,77,32,62,43,96,57,36,112,68,81,83,74,109,69,56,107,84,91,82,63,100,115,80,75","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines split EVENLY into two line-operation types (in the natural F_11 parameterization x ◇ y = (1-α)x + αy):\n\n  • 6 parallel classes use α = 6 (the F_11 midpoint quasigroup x ◇ y = 6(x+y) mod 11, which is commutative).\n  • 6 parallel classes use α = 7 (the non-commutative operation x ◇ y = 5x + 7y mod 11).\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. The display reorder presents points as (h, v) ∈ F_11 × F_11; all 11 diagonal 11×11 blocks render as the identical F_11(α=6) Cayley table, and the 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation. Compare 985e14d6, which has the same combinatorial AG(2, 11) structure but an uneven 8 × α=6 / 4 × α=8 split.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:37","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/83a10ff448e020055ba954f21047deb23d4965798dd069bcd1f5a2550f10bfa9.txt"},{"canonical_hash":"3f8367e97c9b882f7d98f5659f4b8a1ee5bbea26f3d1a603df5f2afcb76cac2d","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,2,103,77,57,18,87,94,56,109,76,1,60,84,12,96,108,120,48,36,72,24,62,59,16,49,116,34,27,78,117,17,43,37,5,104,31,22,50,15,47,66,4,105,20,21,83,58,41,40,51,67,73,102,86,19,112,10,93,38,25,3,113,35,92,54,30,106,118,11,115,69,99,68,88,14,89,46,90,29,74,28,8,39,9,55,71,61,52,79,114,32,95,53,63,85,98,33,70,81,80,26,42,13,7,111,100,101,119,23,65,97,45,64,6,107,75,110,82,91,44","comment":"Size-121 NON-right-cancellative idempotent outlier at sub-11 = 0.\n\nSize 121, fully idempotent, NOT right-cancellative — the only sub-11=0 magma in the DB that fails RC. NO size-11 sub-magmas. Left-multiplication L_0 is a permutation (cycle structure 1 + 2·60: 1 fixed point + 2 cycles of length 60), but right-multiplication R_0 is NOT a permutation (only 81 distinct values out of 121), confirming the non-RC failure. The image of R_0 has 81 elements; 40 elements appear as repeated outputs.\n\nThe asymmetric L_0/R_0 structure (L_0 cycle 1+2·60 vs. R_0 only 81-element image) is distinctive — for an RC magma at size 121 we'd expect L_0 and R_0 to have matching cycle structures. Here L_0 has cycles of length 60 (= order of multiplier in F_121*? F_121* has order 120, and 60 | 120, so order-60 elements exist).\n\nThe additive structure is still F_11² (the magma admits a Z_11 × Z_11 regular sub-action). The suggested reorder uses two commuting order-11 fix-free auts as grid generators, displaying the magma as an 11×11 grid of 11×11 sub-blocks (positions 11·a + b = t1^a(t2^b(0))).\n\nThis is the only non-RC sub-11=0 magma at size 121. Companion non-RC magmas at size 121 sit in other sub-11 buckets: magma#ee53a960 at sub-11=12 (fiber bundle), the 4-class and 8-class twisted AG(2, 11) families at sub-11 ∈ {44, 88}.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:39","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/3f8367e97c9b882f7d98f5659f4b8a1ee5bbea26f3d1a603df5f2afcb76cac2d.txt"},{"canonical_hash":"70ad4c3322b3bd28fd0cfb48595a85ac48d0aa988849d4dec29f849141317798","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"107,1,108,104,103,0,106,105,2,120,109,69,81,84,3,40,117,55,58,93,28,24,113,4,25,90,65,59,77,99,41,34,51,60,86,57,26,119,95,5,42,71,30,73,101,27,79,53,61,38,92,67,115,36,6,39,49,7,75,97,63,23,111,62,32,88,56,94,70,18,15,82,8,43,85,29,118,78,19,114,66,52,44,100,91,16,35,9,45,72,10,110,74,87,20,17,48,31,96,83,116,102,11,46,13,68,54,80,37,21,14,12,22,98,89,50,112,76,47,33,64","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=2 / 4×α=8.\n\n  • α = 2 on 8 parallel classes (slopes {2, 4, 5, 6, 7, 9, 10, INF})\n  • α = 8 on 4 parallel classes (slopes {0, 1, 3, 8})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=2) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:41","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/70ad4c3322b3bd28fd0cfb48595a85ac48d0aa988849d4dec29f849141317798.txt"},{"canonical_hash":"6cced9128206e81c8a24efc12ee2c4f73c4bc93856f33dc61a29ae4f8583f983","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"120,39,40,2,3,1,42,4,41,0,38,71,24,5,116,93,11,18,59,80,89,63,56,77,117,48,17,81,36,6,94,44,31,68,20,65,8,91,95,7,118,26,61,82,69,78,21,62,9,114,27,92,66,101,107,70,103,84,97,58,88,67,10,22,110,23,72,64,25,90,112,60,86,99,105,12,19,57,32,73,45,49,106,100,13,113,87,37,53,33,28,83,46,14,119,50,74,109,96,54,102,34,108,79,51,75,47,29,15,115,55,111,98,16,104,43,30,85,35,52,76","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 8×α=8.\n\n  • α = 2 on 4 parallel classes (slopes {0, 5, 7, 8})\n  • α = 8 on 8 parallel classes (slopes {1, 2, 3, 4, 6, 9, 10, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=8) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:44","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/6cced9128206e81c8a24efc12ee2c4f73c4bc93856f33dc61a29ae4f8583f983.txt"},{"canonical_hash":"d0e8100118d7fb2c967447ff2e847afb81b4518e117af6fbf16d121199607a0b","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"30,120,4,0,29,1,31,28,32,3,2,95,58,5,116,44,39,50,71,91,107,65,47,61,105,42,72,6,93,89,51,63,114,68,59,66,7,87,103,45,52,101,112,40,85,62,110,17,48,64,69,99,43,38,8,49,60,41,67,97,118,83,46,70,9,15,115,76,90,27,21,53,78,34,106,10,94,19,74,11,54,35,88,113,104,81,102,25,36,77,100,86,109,12,22,79,111,23,55,16,75,26,13,82,98,37,119,20,56,84,80,73,57,96,117,24,108,18,33,92,14","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 4×α=7 / 4×α=8.\n\n  • α = 2 on 4 parallel classes (slopes {1, 3, 8, 9})\n  • α = 7 on 4 parallel classes (slopes {2, 4, 6, INF})\n  • α = 8 on 4 parallel classes (slopes {0, 5, 7, 10})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=7) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/d0e8100118d7fb2c967447ff2e847afb81b4518e117af6fbf16d121199607a0b.txt"},{"canonical_hash":"4513afb2cc29dc2099571458ccd6bcb7e98920bc4fcca4b9fb975826285d48b2","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"69,0,43,98,22,42,51,10,7,116,1,2,70,92,8,9,111,106,67,93,72,33,64,60,89,3,113,35,95,74,25,108,48,61,19,45,26,39,103,49,118,4,53,100,76,96,46,50,5,20,114,29,54,56,40,101,77,90,36,30,57,75,6,104,65,119,110,41,47,21,105,102,24,55,14,11,15,71,115,91,13,37,12,16,17,66,97,23,52,107,44,38,94,32,27,62,112,59,18,109,34,88,117,63,58,68,99,73,31,28,78,83,120,85,81,79,82,86,80,84,87","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 4×α=6 / 4×α=8.\n\n  • α = 2 on 4 parallel classes (slopes {0, 1, 3, 7})\n  • α = 6 on 4 parallel classes (slopes {4, 5, 10, INF})\n  • α = 8 on 4 parallel classes (slopes {2, 6, 8, 9})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/4513afb2cc29dc2099571458ccd6bcb7e98920bc4fcca4b9fb975826285d48b2.txt"},{"canonical_hash":"e728039473d8281487717462e92cda34e4044cdc5512902c689f976a56d2229d","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"38,75,102,44,115,59,0,27,30,1,68,97,80,33,64,29,49,28,2,110,67,106,47,78,62,5,20,118,3,104,24,41,95,57,73,52,113,23,6,65,4,19,100,36,7,79,9,105,96,16,48,63,42,119,26,10,74,8,15,37,66,58,43,101,25,114,14,81,111,17,107,11,98,34,54,50,55,116,76,13,12,53,18,39,93,109,60,45,108,82,71,35,56,99,21,112,51,32,70,72,77,103,94,46,40,117,22,61,69,31,83,120,88,90,92,85,84,89,87,86,91","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=2 / 4×α=6.\n\n  • α = 2 on 8 parallel classes (slopes {0, 1, 2, 4, 5, 7, 8, 10})\n  • α = 6 on 4 parallel classes (slopes {3, 6, 9, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:53","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/e728039473d8281487717462e92cda34e4044cdc5512902c689f976a56d2229d.txt"},{"canonical_hash":"c8dcedeb66e0d3938358cbc800c5c87189642160f1774fe6ecdb0d569e7825ef","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"37,3,65,0,103,39,109,91,72,8,54,108,77,1,60,43,102,36,7,29,90,49,2,9,44,82,92,32,105,34,61,68,50,104,66,83,38,33,93,19,73,10,4,55,35,45,99,17,21,111,69,62,95,5,51,74,94,18,98,110,20,22,6,40,67,56,26,23,112,30,75,11,58,41,88,96,57,63,89,31,113,12,70,25,97,24,46,52,42,87,76,16,116,59,106,114,27,13,48,107,28,15,71,64,117,47,14,86,115,53,78,100,81,80,84,85,79,119,101,118,120","comment":"Size-121 non-right-cancellative idempotent magma built on the point set of the affine plane AG(2, 11), but with only 8 out of 12 parallel classes of lines preserved by the operation. These 88 'kept' lines are exactly the size-11 sub-quasigroups of the magma; pairs lying on a 'removed' line (slopes in F_11 P¹ where the line is NOT a sub-quasigroup) instead generate the whole magma under the closure of ◇.\n\nPer-class α (in F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 4×α=6.\n\n  • α = 2: parallel classes with F_11 slopes {0, 1, 3, 7}\n  • α = 6: parallel classes with F_11 slopes {4, 5, 10, INF}\n\nKept slopes (8): {0, 1, 3, 4, 5, 7, 10, INF}.\nRemoved slopes (4): {2, 6, 8, 9}.\n\nEach column of the Cayley table is non-injective (collapse fibers), hence the magma is non-right-cancellative; nevertheless it is left-cancellative and every element is idempotent. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:55","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/c8dcedeb66e0d3938358cbc800c5c87189642160f1774fe6ecdb0d569e7825ef.txt"},{"canonical_hash":"fdc3bc3fe5e609f46272fb80974e4cfce83a35a9a8d17cb71cd232542ddc7c59","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"80,29,1,109,0,24,45,107,48,96,54,95,101,23,93,47,36,104,33,56,50,2,78,89,44,52,113,18,9,17,3,53,84,91,57,27,4,21,119,11,43,110,98,51,81,5,30,34,108,70,97,58,106,64,25,114,49,87,55,12,46,6,15,103,117,82,115,86,59,13,71,83,116,102,8,7,65,90,28,68,20,31,61,99,111,67,10,118,79,63,88,112,62,85,69,14,16,26,19,94,22,100,66,92,35,60,72,32,105,37,120,39,75,41,73,77,76,74,42,38,40","comment":"Size-121 non-right-cancellative idempotent magma built on the point set of the affine plane AG(2, 11), but with only 8 out of 12 parallel classes of lines preserved by the operation. These 88 'kept' lines are exactly the size-11 sub-quasigroups of the magma; pairs lying on a 'removed' line (slopes in F_11 P¹ where the line is NOT a sub-quasigroup) instead generate the whole magma under the closure of ◇.\n\nPer-class α (in F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6 / 4×α=8.\n\n  • α = 6: parallel classes with F_11 slopes {4, 6, 8, INF}\n  • α = 8: parallel classes with F_11 slopes {0, 3, 5, 10}\n\nKept slopes (8): {0, 3, 4, 5, 6, 8, 10, INF}.\nRemoved slopes (4): {1, 2, 7, 9}.\n\nEach column of the Cayley table is non-injective (collapse fibers), hence the magma is non-right-cancellative; nevertheless it is left-cancellative and every element is idempotent. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:57","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/fdc3bc3fe5e609f46272fb80974e4cfce83a35a9a8d17cb71cd232542ddc7c59.txt"},{"canonical_hash":"014291bf591068236bbc4abf57aa75c6a93c8beb6e63f68352f53280cbad0e14","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"34,75,71,35,107,0,74,76,70,106,1,4,99,53,5,13,3,98,112,52,12,2,61,96,62,60,16,6,97,113,63,17,7,33,45,72,32,104,8,44,77,73,105,9,59,69,41,58,10,94,68,110,40,11,95,54,15,83,55,116,19,14,108,82,117,18,84,64,20,85,30,47,65,119,21,31,46,87,25,38,86,36,23,24,118,39,37,22,26,66,29,27,51,93,67,111,28,50,92,56,48,80,57,114,42,49,109,81,115,43,102,88,79,103,101,90,89,120,78,100,91","comment":"Size-121 non-right-cancellative idempotent magma built on the point set of the affine plane AG(2, 11), but with only 4 out of 12 parallel classes of lines preserved by the operation. These 44 'kept' lines are exactly the size-11 sub-quasigroups of the magma; pairs lying on a 'removed' line (slopes in F_11 P¹ where the line is NOT a sub-quasigroup) instead generate the whole magma under the closure of ◇.\n\nPer-class α (in F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6.\n\n  • α = 6: parallel classes with F_11 slopes {0, 4, 7, INF}\n\nKept slopes (4): {0, 4, 7, INF}.\nRemoved slopes (8): {1, 2, 3, 5, 6, 8, 9, 10}.\n\nEach column of the Cayley table is non-injective (collapse fibers), hence the magma is non-right-cancellative; nevertheless it is left-cancellative and every element is idempotent. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:24:59","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/014291bf591068236bbc4abf57aa75c6a93c8beb6e63f68352f53280cbad0e14.txt"},{"canonical_hash":"d7e85eadbf36415ab80a8afa93504a8062229e3cfdc14cd3e03eb834f1c7fd62","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"1,3,54,59,69,96,2,0,119,107,77,41,65,105,49,12,87,44,117,4,103,37,67,22,39,5,51,33,97,27,46,106,118,30,79,17,31,61,71,56,74,6,98,111,45,100,35,88,24,10,66,7,42,85,50,89,8,25,76,34,58,9,101,53,84,68,32,43,64,11,18,48,40,78,110,99,26,28,55,82,81,73,20,13,70,16,115,60,80,38,47,29,83,14,19,52,63,114,15,57,116,23,72,104,75,86,62,36,102,21,94,93,109,95,108,112,113,92,91,120,90","comment":"Size-121 non-right-cancellative idempotent magma built on the point set of the affine plane AG(2, 11), but with only 8 out of 12 parallel classes of lines preserved by the operation. These 88 'kept' lines are exactly the size-11 sub-quasigroups of the magma; pairs lying on a 'removed' line (slopes in F_11 P¹ where the line is NOT a sub-quasigroup) instead generate the whole magma under the closure of ◇.\n\nPer-class α (in F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6 / 4×α=7.\n\n  • α = 6: parallel classes with F_11 slopes {2, 5, 8, INF}\n  • α = 7: parallel classes with F_11 slopes {0, 6, 7, 9}\n\nKept slopes (8): {0, 2, 5, 6, 7, 8, 9, INF}.\nRemoved slopes (4): {1, 3, 4, 10}.\n\nEach column of the Cayley table is non-injective (collapse fibers), hence the magma is non-right-cancellative; nevertheless it is left-cancellative and every element is idempotent. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:01","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/d7e85eadbf36415ab80a8afa93504a8062229e3cfdc14cd3e03eb834f1c7fd62.txt"},{"canonical_hash":"ab07f9801f4167faea23486a9b4224c2ba8ceca89c3bb69b5058825efc89286e","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"1,22,23,3,24,20,0,4,120,2,21,16,5,65,82,87,46,37,112,102,50,10,110,11,6,48,63,85,17,80,100,35,108,78,106,12,43,7,71,118,56,98,18,83,54,91,104,19,13,8,76,41,96,116,69,39,67,89,114,109,14,52,15,94,74,9,86,49,81,25,111,58,45,64,101,30,36,72,44,57,31,79,119,84,26,99,107,59,27,60,42,105,55,77,70,32,97,92,117,33,115,61,90,40,53,28,103,95,68,75,47,73,113,66,62,38,34,88,93,29,51","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=2 / 4×α=7.\n\n  • α = 2 on 8 parallel classes (slopes {1, 3, 6, 7, 8, 9, 10, INF})\n  • α = 7 on 4 parallel classes (slopes {0, 2, 4, 5})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=2) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:04","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/ab07f9801f4167faea23486a9b4224c2ba8ceca89c3bb69b5058825efc89286e.txt"},{"canonical_hash":"8b0e368b8f3290fc9aa0bd820f6265e3ae7023c999ea8a783a99388f9dea3fd5","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,108,47,7,116,1,49,38,81,79,45,52,112,75,54,88,94,35,56,2,12,37,41,31,71,68,110,101,64,3,84,17,24,114,21,67,91,63,10,86,4,58,42,33,26,14,50,76,92,25,61,5,99,105,72,104,77,51,13,73,60,28,98,6,27,93,18,69,70,30,8,65,100,85,36,40,111,43,90,66,22,32,87,9,59,23,115,62,11,55,74,113,16,34,95,15,57,53,89,78,20,46,109,44,48,29,80,39,19,117,118,97,120,96,107,82,83,103,102,119,106","comment":"Size-121 non-right-cancellative idempotent magma built on the point set of the affine plane AG(2, 11), but with only 8 out of 12 parallel classes of lines preserved by the operation. These 88 'kept' lines are exactly the size-11 sub-quasigroups of the magma; pairs lying on a 'removed' line (slopes in F_11 P¹ where the line is NOT a sub-quasigroup) instead generate the whole magma under the closure of ◇.\n\nPer-class α (in F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=6.\n\n  • α = 6: parallel classes with F_11 slopes {0, 1, 3, 4, 5, 8, 10, INF}\n\nKept slopes (8): {0, 1, 3, 4, 5, 8, 10, INF}.\nRemoved slopes (4): {2, 6, 7, 9}.\n\nEach column of the Cayley table is non-injective (collapse fibers), hence the magma is non-right-cancellative; nevertheless it is left-cancellative and every element is idempotent. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:06","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/8b0e368b8f3290fc9aa0bd820f6265e3ae7023c999ea8a783a99388f9dea3fd5.txt"},{"canonical_hash":"80bb735bf82bd5a19caa80aa9af6a8a9ed18a8f1cc3a4e8d7e066bb6e5c25669","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,120,17,30,33,16,29,34,1,23,22,56,27,83,94,53,18,78,91,2,117,104,3,67,19,46,70,43,99,52,61,81,112,116,65,4,32,74,73,41,55,103,49,93,108,25,89,86,60,5,31,75,111,98,76,97,68,59,6,110,8,71,107,47,15,44,79,28,9,92,109,54,7,115,102,84,14,42,66,39,63,101,114,10,45,36,12,69,35,26,119,11,77,106,58,96,87,90,13,37,24,100,113,51,80,82,85,88,20,62,72,64,48,105,40,95,118,50,38,57,21","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 4×α=6 / 4×α=7.\n\n  • α = 2 on 4 parallel classes (slopes {3, 4, 6, 8})\n  • α = 6 on 4 parallel classes (slopes {2, 5, 10, INF})\n  • α = 7 on 4 parallel classes (slopes {0, 1, 7, 9})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:09","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/80bb735bf82bd5a19caa80aa9af6a8a9ed18a8f1cc3a4e8d7e066bb6e5c25669.txt"},{"canonical_hash":"504d874c86f36ef2c5e84f3b4ecaf75aa0d1d9b76d3756aeba9f68e47e06b864","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"14,12,1,3,0,11,10,13,2,120,4,18,56,111,61,43,90,35,102,103,42,5,100,88,6,27,119,36,19,57,44,38,62,53,37,58,45,7,15,98,86,117,39,25,84,16,107,115,59,96,54,33,8,40,46,34,94,47,9,105,55,92,17,60,41,113,20,65,83,68,78,30,106,114,95,73,52,112,31,48,93,91,104,21,66,79,74,69,67,109,70,80,49,22,110,32,89,75,101,28,23,99,87,71,118,63,26,50,76,81,108,116,82,51,97,64,29,24,72,77,85","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 8×α=7.\n\n  • α = 2 on 4 parallel classes (slopes {0, 1, 2, 5})\n  • α = 7 on 8 parallel classes (slopes {3, 4, 6, 7, 8, 9, 10, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=7) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:11","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/504d874c86f36ef2c5e84f3b4ecaf75aa0d1d9b76d3756aeba9f68e47e06b864.txt"},{"canonical_hash":"fa0f52cd7d47d051054a76937e03482f38e8aacf9cbfc7c8be0b04c144c7789f","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"35,43,91,39,13,0,1,9,67,99,83,44,36,94,40,88,106,2,68,10,92,14,79,27,65,29,95,15,5,107,7,3,45,28,84,4,30,46,6,16,8,109,66,100,105,73,87,69,11,37,41,53,93,59,89,74,34,60,70,90,42,38,98,54,82,12,21,101,103,17,77,63,85,25,47,31,49,96,22,32,18,50,80,64,48,26,108,78,23,55,51,57,19,97,61,81,71,75,33,56,24,76,58,104,62,102,72,86,52,20,110,115,118,120,119,111,116,112,117,113,114","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 8×α=6.\n\n  • α = 2 on 4 parallel classes (slopes {0, 1, 3, 8})\n  • α = 6 on 8 parallel classes (slopes {2, 4, 5, 6, 7, 9, 10, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:14","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/fa0f52cd7d47d051054a76937e03482f38e8aacf9cbfc7c8be0b04c144c7789f.txt"},{"canonical_hash":"e5ec2793fb38d2870818a449abc1611b93d9832248e8f38cc260d4b1bf8df614","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"120,11,40,39,7,10,77,1,6,78,0,60,82,110,4,45,88,69,2,106,22,72,101,58,5,117,20,48,21,89,98,34,3,100,97,8,33,116,29,17,47,19,93,57,64,105,68,9,18,44,76,87,114,16,81,103,66,55,50,91,31,95,119,53,27,12,62,71,79,85,54,65,108,13,74,42,112,99,52,35,92,32,115,56,28,14,46,96,63,113,75,36,15,51,80,43,67,86,104,61,73,107,41,84,23,111,38,83,25,70,102,24,94,109,49,90,26,30,59,118,37","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6 / 8×α=8.\n\n  • α = 6 on 4 parallel classes (slopes {1, 5, 9, INF})\n  • α = 8 on 8 parallel classes (slopes {0, 2, 3, 4, 6, 7, 8, 10})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:17","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/e5ec2793fb38d2870818a449abc1611b93d9832248e8f38cc260d4b1bf8df614.txt"},{"canonical_hash":"b62e800066c2296f62aab257741b2ac079466d77da576d6b621ea73b2403ff7c","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"120,18,36,19,71,17,1,35,70,0,16,97,66,78,21,56,52,93,82,2,116,104,27,20,63,37,3,45,114,102,86,50,51,29,101,11,62,39,49,85,4,7,14,111,94,81,5,77,6,118,15,106,68,55,92,28,110,8,47,10,38,99,88,24,60,58,98,90,53,117,25,59,79,9,105,75,67,95,43,12,57,119,74,107,69,89,33,83,30,87,40,42,46,64,34,13,112,109,103,26,73,48,44,61,32,22,113,100,41,84,96,108,115,72,76,54,65,91,80,23,31","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6 / 4×α=7 / 4×α=8.\n\n  • α = 6 on 4 parallel classes (slopes {5, 6, 7, INF})\n  • α = 7 on 4 parallel classes (slopes {1, 2, 4, 9})\n  • α = 8 on 4 parallel classes (slopes {0, 3, 8, 10})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:20","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/b62e800066c2296f62aab257741b2ac079466d77da576d6b621ea73b2403ff7c.txt"},{"canonical_hash":"aac04c7b85d4c8a45953449af4dd8d1d6fb29c68e3212ab01404e90d31250f65","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"63,119,1,46,26,99,90,0,30,67,97,2,31,109,64,48,92,27,115,98,100,60,116,94,23,101,66,28,45,32,62,89,3,33,59,16,91,102,47,68,95,4,24,117,96,5,17,25,93,65,103,61,118,44,29,83,57,108,73,85,51,114,15,6,40,36,7,79,106,112,49,71,41,34,11,88,55,12,8,104,42,69,110,86,58,37,52,80,35,13,107,84,113,43,50,81,56,72,9,54,38,105,53,39,87,70,10,82,111,14,74,77,120,18,19,21,20,78,76,22,75","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=7 / 8×α=8.\n\n  • α = 7 on 4 parallel classes (slopes {0, 1, 5, 9})\n  • α = 8 on 8 parallel classes (slopes {2, 3, 4, 6, 7, 8, 10, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=8) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:23","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/aac04c7b85d4c8a45953449af4dd8d1d6fb29c68e3212ab01404e90d31250f65.txt"},{"canonical_hash":"985e14d62209bb98ad27437d2549964de71b46b741b163844319d67972fef3c3","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"37,66,67,19,36,120,18,1,62,0,63,110,93,79,32,56,84,8,14,88,2,71,57,80,99,9,117,104,33,3,43,15,89,21,65,4,50,51,85,94,72,111,16,86,52,5,64,100,20,105,49,17,87,44,118,95,39,73,55,6,53,34,30,27,112,78,7,40,38,35,101,106,54,119,77,31,26,60,10,47,22,70,83,114,12,97,92,29,42,48,11,116,61,108,23,103,28,13,98,69,113,90,74,46,109,24,58,96,81,75,45,91,115,25,68,107,41,82,76,59,102","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines carry only TWO line-operation types (in the natural F_11 parameterization x ◇ y = (1-α)x + αy):\n\n  • 8 parallel classes use α = 6 (the F_11 midpoint quasigroup x ◇ y = 6(x+y) mod 11, which is commutative).\n  • 4 parallel classes use α = 8 (the operation x ◇ y = 4x + 8y mod 11, non-commutative).\n\nGlobally the magma is NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. The display reorder presents points as (h, v) ∈ F_11 × F_11 where rows/cols of each 11×11 diagonal block correspond to the α=6 'horizontal' parallel class, so all 11 diagonal blocks render as the identical F_11(6,6) Cayley table.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:26","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/985e14d62209bb98ad27437d2549964de71b46b741b163844319d67972fef3c3.txt"},{"canonical_hash":"61c16114c7b2423f3ff97def48877e88f993e5cb313f2d85864755a8bd784b92","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"1,80,44,70,0,23,111,87,50,96,45,92,24,101,46,116,75,2,106,49,43,69,17,5,56,65,94,119,28,78,8,3,85,73,114,4,90,27,6,99,18,7,55,104,64,108,68,93,48,84,77,9,31,118,57,10,89,113,58,82,103,47,63,32,67,98,117,102,107,11,29,54,22,59,62,83,76,60,53,88,81,21,97,30,112,61,109,12,95,51,79,72,66,16,86,13,19,26,110,14,15,25,115,91,52,105,100,20,74,71,33,40,39,41,42,35,37,38,120,34,36","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 6×α=2 / 6×α=6.\n\n  • α = 2 on 6 parallel classes (slopes {0, 1, 4, 5, 7, 9})\n  • α = 6 on 6 parallel classes (slopes {2, 3, 6, 8, 10, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:28","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/61c16114c7b2423f3ff97def48877e88f993e5cb313f2d85864755a8bd784b92.txt"},{"canonical_hash":"d2ea11ab0d0513122e5e98515a73964b27348d2d0356c2250e1513a47ba2ca05","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"108,106,105,109,8,0,120,1,2,107,104,102,27,114,86,32,56,71,83,53,15,3,18,112,4,51,87,81,72,33,57,28,103,24,5,99,58,49,29,73,88,79,110,16,113,100,14,82,54,84,69,52,30,6,25,7,17,26,31,80,50,70,55,85,101,111,78,66,23,117,59,46,98,42,37,89,9,90,19,10,38,115,40,94,60,47,64,76,67,11,74,48,34,61,95,118,43,20,91,21,77,92,41,44,116,96,35,62,12,65,13,93,68,63,39,36,97,45,119,75,22","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=7 / 4×α=8.\n\n  • α = 7 on 8 parallel classes (slopes {2, 3, 4, 5, 6, 8, 9, INF})\n  • α = 8 on 4 parallel classes (slopes {0, 1, 7, 10})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=7) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:31","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/d2ea11ab0d0513122e5e98515a73964b27348d2d0356c2250e1513a47ba2ca05.txt"},{"canonical_hash":"b62281e320c092a243c78e8473cb6faa2b70ef055297d73876acd0f4fa417ee1","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,120,58,12,1,13,42,10,59,43,11,87,77,2,45,102,113,23,64,15,74,94,36,78,14,116,52,89,41,68,3,106,82,114,9,109,4,46,26,95,103,75,60,88,90,8,37,27,117,5,83,53,107,69,32,98,31,112,101,63,86,16,73,44,6,22,81,30,93,51,67,35,7,105,115,17,40,57,18,96,76,28,20,84,47,61,99,110,29,19,79,108,56,38,33,118,70,54,91,21,25,85,62,72,97,111,49,100,48,65,39,24,34,71,104,80,92,66,55,119,50","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=6 / 8×α=7.\n\n  • α = 6 on 4 parallel classes (slopes {3, 4, 5, INF})\n  • α = 7 on 8 parallel classes (slopes {0, 1, 2, 6, 7, 8, 9, 10})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:36","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/b62281e320c092a243c78e8473cb6faa2b70ef055297d73876acd0f4fa417ee1.txt"},{"canonical_hash":"fd4053a18b9bb75d2e0227fe7be95f0dc5edc60a7284fd8c21c333703d038b8d","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"67,4,15,62,14,68,61,120,0,1,5,70,44,9,105,29,111,78,2,7,92,91,119,90,28,100,8,69,86,3,58,6,45,42,74,107,20,75,94,24,65,10,97,113,60,116,102,25,109,43,21,66,98,11,73,32,76,95,89,18,38,53,12,30,114,108,39,84,19,52,56,33,88,13,117,31,103,79,63,112,93,54,106,36,47,82,50,16,87,17,55,37,115,101,59,46,51,83,64,35,57,71,27,81,22,118,40,85,99,49,23,48,80,110,72,34,26,41,77,104,96","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 8×α=6 / 4×α=7.\n\n  • α = 6 on 8 parallel classes (slopes {1, 4, 5, 6, 8, 9, 10, INF})\n  • α = 7 on 4 parallel classes (slopes {0, 2, 3, 7})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:39","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/fd4053a18b9bb75d2e0227fe7be95f0dc5edc60a7284fd8c21c333703d038b8d.txt"},{"canonical_hash":"6fec6f96bcd08257200e24bf65029d536066debcfd3c186f35cf51e44e6f4c79","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"28,0,1,29,120,80,41,32,33,81,40,36,85,50,27,2,109,116,88,23,75,44,26,49,101,37,3,59,55,22,94,107,114,73,47,119,78,57,91,4,83,21,42,34,105,112,53,62,56,43,35,20,99,97,5,64,8,69,89,14,86,71,45,117,6,76,95,70,9,63,15,7,108,110,51,102,60,52,31,96,111,39,17,103,61,104,19,10,118,90,30,46,38,18,11,77,72,16,82,68,79,74,84,25,48,93,65,12,115,87,100,58,106,67,24,113,98,13,66,54,92","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 6×α=6 / 6×α=8.\n\n  • α = 6 on 6 parallel classes (slopes {3, 4, 5, 6, 10, INF})\n  • α = 8 on 6 parallel classes (slopes {0, 1, 2, 7, 8, 9})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=6) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:42","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/6fec6f96bcd08257200e24bf65029d536066debcfd3c186f35cf51e44e6f4c79.txt"},{"canonical_hash":"ce5d89d56c9069c6008cb2e1d6d3a96f65c626e1528fda77c4c5dc9ec8e50791","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"104,108,107,120,109,2,3,106,1,0,105,110,50,26,93,64,32,10,87,99,4,47,53,27,85,91,5,102,33,48,65,13,113,28,88,44,89,11,66,100,111,6,29,51,86,45,114,92,30,7,67,49,9,103,24,46,112,52,90,101,12,8,25,31,68,84,42,19,72,78,61,14,115,96,56,36,81,69,97,83,74,116,62,58,43,38,15,21,80,39,23,75,55,117,35,71,16,63,98,20,73,94,76,37,57,17,82,59,118,40,95,79,41,77,18,34,60,22,119,54,70","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 6×α=7 / 6×α=8.\n\n  • α = 7 on 6 parallel classes (slopes {1, 2, 3, 5, 10, INF})\n  • α = 8 on 6 parallel classes (slopes {0, 4, 6, 7, 8, 9})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=7) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=8) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:45","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/ce5d89d56c9069c6008cb2e1d6d3a96f65c626e1528fda77c4c5dc9ec8e50791.txt"},{"canonical_hash":"d31e0c93a8527e2728dc01cd3ed2f520e44303c78e51949596be178e6014d470","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"9,4,1,2,8,120,0,6,7,3,5,73,108,114,81,89,18,26,46,93,10,32,85,11,104,27,99,19,110,33,52,82,69,95,78,12,116,48,15,30,75,34,28,91,44,29,79,106,35,16,13,87,71,112,101,36,118,25,14,77,17,80,97,83,109,50,67,88,72,45,39,57,20,107,113,102,62,40,98,84,21,119,53,68,58,103,51,63,115,47,94,74,37,54,90,64,59,22,41,105,23,43,86,60,55,100,42,65,70,111,61,76,24,96,66,56,49,117,38,92,31","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 6×α=2 / 6×α=8.\n\n  • α = 2 on 6 parallel classes (slopes {0, 1, 2, 3, 5, 9})\n  • α = 8 on 6 parallel classes (slopes {4, 6, 7, 8, 10, INF})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=8) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:48","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/d31e0c93a8527e2728dc01cd3ed2f520e44303c78e51949596be178e6014d470.txt"},{"canonical_hash":"90626b88af6c2533483bee5758fe19d239b8b14a69995f3f111e70807bee1be7","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"107,22,109,106,108,1,105,103,0,104,120,15,114,27,84,77,42,36,19,2,99,69,112,38,97,75,3,20,16,37,25,92,70,39,21,90,4,23,33,110,12,95,73,71,17,34,81,31,93,13,40,118,88,5,72,35,14,6,101,86,116,18,41,79,29,68,61,24,7,111,64,96,74,91,54,50,47,32,94,51,65,55,89,62,82,8,119,43,102,87,117,56,9,80,30,58,52,66,44,85,78,67,10,48,59,100,28,115,57,45,76,60,53,49,113,26,83,98,63,11,46","comment":"Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 6×α=2 / 6×α=7.\n\n  • α = 2 on 6 parallel classes (slopes {1, 3, 4, 5, 7, INF})\n  • α = 7 on 6 parallel classes (slopes {0, 2, 6, 8, 9, 10})\n\nGlobally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=2) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/90626b88af6c2533483bee5758fe19d239b8b14a69995f3f111e70807bee1be7.txt"},{"canonical_hash":"5ebfbb802eeb70dd54088b43b701e3a350898bc1d820fb30bbaf1ac7e5d84520","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,34,19,102,75,111,110,106,49,94,1,32,56,61,29,54,65,98,21,66,83,16,108,46,14,99,107,91,31,87,118,12,79,85,42,82,120,36,88,39,33,30,76,41,77,15,74,23,50,10,60,92,48,70,97,22,113,3,90,109,5,78,52,37,114,73,62,63,44,26,95,80,53,51,18,13,71,7,45,89,20,72,67,27,47,104,38,86,64,101,4,17,24,35,57,69,59,68,117,6,81,100,93,55,25,112,40,116,8,11,103,115,105,96,43,9,58,119,84,28","comment":"Constructed using the exceptional near-field II (https://en.wikipedia.org/wiki/Near-field_(mathematics)) of size 121. In particular, this model admits as symmetry group the sharply 2-transitive group (Z_11)^2 ⋊ (Z5 x SL(2,3)). This model satisfies Eq3345: x ◇ y = y ◇ (x ◇ (y ◇ x)).","submitted_at":"2026-05-14 05:46:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/5ebfbb802eeb70dd54088b43b701e3a350898bc1d820fb30bbaf1ac7e5d84520.txt"},{"canonical_hash":"70e5572af7954a2ea2993e55013acaa29f420c8b1bbb8322ca4b43c7902939fe","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,85,75,107,108,67,39,77,16,57,1,44,23,90,43,21,115,103,69,49,98,81,70,28,14,116,33,45,76,117,83,12,47,56,68,59,120,74,53,71,62,65,50,32,95,60,118,31,17,10,55,100,15,102,54,84,30,3,113,86,5,114,19,79,64,96,109,52,38,37,94,104,20,18,72,13,112,7,27,101,40,58,93,63,29,91,41,92,99,97,4,34,66,35,24,46,26,106,61,6,105,51,119,22,78,80,88,36,8,11,48,89,73,110,82,9,25,42,111,87","comment":"Size-121 RC idempotent magma on F_121 = F_11² with NO size-11 sub-magmas — an \"order-8 multiplier\" construction outside the standard Phi_10 family.\n\nSize 121, fully idempotent, right-cancellative. Sub-magma count by size: only 0 (singletons) and 121 (the whole magma). Every pair of distinct points generates the entire 121-element magma — there are NO non-trivial sub-magmas.\n\nL_0 and R_0 each have cycle structure **1 + 15·8** — the multiplier in the F_121 linear operation has order **8**, not 10. This places the magma outside Pace Nielsen's standard Type-1 (Phi_10 roots, multiplier order 10) and Type-2 (Phi_2_5 roots) classification. Instead, the construction uses an element of the order-8 subgroup of F_121* = (F_121*)^15.\n\nThe additive structure is F_11² (= F_121 additively). In the suggested reorder, two commuting order-11 fix-free automorphisms t1, t2 of M are chosen as grid generators; position 11·a + b corresponds to the point t1^a(t2^b(0)). The resulting Cayley table shows a clean 11×11 grid of 11×11 sub-blocks, each block showing diagonal-stripe structure characteristic of the F_11² translation action.\n\nFamily at size 121 sharing this fingerprint (1 + 15·8 cycle): 5 RC idempotent iso classes — magma#873c2695, magma#58669675, magma#af70b7bb, magma#fdc7e335. They likely correspond to different (α, β) choices among the F_121 multipliers of order 8, modulo Galois conjugacy.\n\nThis is one of the \"sub-11 = 0\" magmas distinct from the F_121 affine line (Phi_10 multiplier, would have sub-11 = 132 if used) and the Zassenhaus near-field (magma#5ebfbb80, multiplier order 30).\n\n[text written by Claude]","submitted_at":"2026-05-17 12:41:20","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/70e5572af7954a2ea2993e55013acaa29f420c8b1bbb8322ca4b43c7902939fe.txt"},{"canonical_hash":"6c5e9b39f87eb5593826d732f81ef984d064f4f91f25234fd56e2893490e373b","size":121,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"80,30,55,110,0,85,107,46,88,2,5,54,91,37,12,73,63,106,103,68,99,1,3,18,95,76,51,31,17,102,62,96,81,71,32,66,4,112,16,8,61,36,52,109,49,28,60,6,15,74,98,44,79,105,108,7,34,77,111,39,45,58,72,114,47,89,35,38,19,9,113,116,53,83,43,78,64,33,90,101,67,82,48,100,97,57,104,10,11,120,13,20,22,26,86,14,25,87,23,119,42,92,50,27,41,84,21,115,69,59,93,40,118,65,56,117,75,94,29,24,70","comment":"Twisted AG(2, 11) magma with exactly 4 of 12 parallel classes preserved (NON-right-cancellative).\n\nSize 121 = 11², fully idempotent, NOT right-cancellative. Exactly 44 size-11 sub-magmas in M, partitioning into 4 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; the other 8 parallel classes of AG(2, 11) are NOT closed under the operation.\n\nThis is the \"4-class\" sub-family of twisted AG(2, 11) magmas — one of 2 iso classes at size 121 sharing this fingerprint (the other: magma#014291bf). The non-RC property distinguishes it from the \"2-class\" sub-family (sub-11 = 22, 8 RC iso classes including magma#6bab1ff9) and from the full AG(2, 11) line family (sub-11 = 132, all RC).\n\nIn the suggested reorder, positions 11·r + c correspond to grid points at the intersection of P1-row r and P2-column c (using 2 of the 4 preserved parallel classes as grid axes). Diagonal 11×11 blocks reveal the row sub-magma operations.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:41:22","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/6c5e9b39f87eb5593826d732f81ef984d064f4f91f25234fd56e2893490e373b.txt"},{"canonical_hash":"3c3384aae3864e46ea7ba61537096fe049c4c830be379b7e95c4a8892e63ec1b","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"44,9,82,1,10,120,45,53,54,81,0,64,2,112,8,17,79,46,83,29,14,94,21,22,28,63,114,71,103,96,3,87,24,108,119,51,25,23,76,66,4,101,37,88,26,100,61,118,56,75,85,107,19,5,36,49,55,6,35,95,80,40,69,109,91,113,47,67,13,99,106,74,89,38,52,117,7,97,90,104,48,11,72,16,115,31,68,39,15,12,18,30,65,77,102,32,110,57,84,116,86,60,20,27,73,42,34,62,98,105,43,41,93,58,50,78,111,92,33,59,70","comment":null,"submitted_at":"2026-05-17 12:41:25","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/3c3384aae3864e46ea7ba61537096fe049c4c830be379b7e95c4a8892e63ec1b.txt"},{"canonical_hash":"402e4f52d6e4b17256dd7345042f72ca27b57f96d635fac0a56855b1bb29cd2a","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,107,109,103,120,105,2,104,108,106,1,73,87,79,99,114,43,70,48,91,3,27,23,76,56,44,112,85,80,4,68,89,97,95,24,5,83,110,74,54,92,81,71,45,46,93,90,77,118,25,6,69,52,82,86,84,47,72,26,116,101,88,78,7,50,75,20,34,60,66,115,49,40,100,32,14,8,63,9,16,36,111,21,96,28,62,41,55,33,51,42,10,117,65,29,59,13,102,22,11,18,98,57,113,35,61,15,38,30,67,53,64,31,19,119,12,17,39,94,58,37","comment":null,"submitted_at":"2026-05-17 12:41:29","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/402e4f52d6e4b17256dd7345042f72ca27b57f96d635fac0a56855b1bb29cd2a.txt"},{"canonical_hash":"97a4deb63926e9d620aded2eade2da15f0c95fd974ffd9324b09b3dc924382b7","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"19,36,0,1,37,18,120,4,5,12,13,104,16,54,38,2,58,110,76,82,94,72,89,3,61,84,17,20,115,81,33,67,99,43,39,100,68,55,30,116,59,21,6,77,29,85,73,95,62,44,111,105,90,34,7,102,79,109,56,27,70,118,41,52,8,50,75,28,92,107,31,97,113,87,64,49,9,63,101,35,14,69,86,117,48,10,91,22,51,74,15,78,96,40,112,11,47,106,60,23,57,25,46,108,80,114,66,98,53,42,32,103,45,26,88,24,119,93,71,65,83","comment":null,"submitted_at":"2026-05-17 12:41:32","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/97a4deb63926e9d620aded2eade2da15f0c95fd974ffd9324b09b3dc924382b7.txt"},{"canonical_hash":"f9590a52ef08d98331d1f5061a0297d2ded8fafc0d2047350ffdc238d9f8059f","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"93,1,36,98,112,30,88,0,42,27,15,31,51,76,106,16,10,2,60,79,37,119,95,85,113,3,78,9,45,28,43,34,90,108,4,35,62,12,53,72,46,80,115,77,19,5,22,29,7,87,114,70,44,92,97,64,73,14,6,55,20,71,116,81,21,105,47,18,86,91,33,111,8,96,41,24,26,50,56,52,117,39,74,11,58,82,107,61,118,13,23,17,75,48,54,104,83,63,32,25,110,109,57,84,49,59,89,40,94,38,69,99,102,68,101,100,103,67,120,66,65","comment":null,"submitted_at":"2026-05-17 12:41:35","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/f9590a52ef08d98331d1f5061a0297d2ded8fafc0d2047350ffdc238d9f8059f.txt"},{"canonical_hash":"f71bc399aff9a4f72104ef5ba6b9750a6f7936b23343683791d4ae87dc8b276e","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"51,1,101,61,81,0,71,41,91,19,29,36,86,96,14,30,66,2,46,106,56,76,59,3,99,89,39,79,7,17,69,25,49,12,64,94,104,44,8,74,54,4,84,34,65,35,95,5,105,13,55,27,45,75,85,28,50,100,80,90,60,18,70,40,6,26,9,11,93,43,23,103,83,73,53,33,63,78,58,98,38,68,88,108,10,16,48,24,87,77,97,67,15,37,47,107,21,31,57,109,22,102,32,62,52,42,92,82,72,20,111,110,120,113,114,112,117,116,115,118,119","comment":null,"submitted_at":"2026-05-17 12:41:39","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/f71bc399aff9a4f72104ef5ba6b9750a6f7936b23343683791d4ae87dc8b276e.txt"},{"canonical_hash":"062a3fc50fec0eb95fe9daba285d193947abdf086e97f0b27f4bf87b79dd6976","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"108,103,104,109,106,120,12,107,105,0,1,8,70,62,47,35,76,2,89,98,112,14,22,96,33,60,9,74,110,3,87,68,45,43,85,10,41,20,82,66,118,4,94,58,56,5,18,11,51,80,102,64,116,83,39,37,114,49,16,54,78,91,100,72,6,7,27,61,97,69,88,75,13,28,34,46,111,90,48,71,113,99,77,32,36,53,15,26,101,17,115,25,63,79,38,55,50,31,92,65,30,24,84,117,81,57,52,19,40,93,119,42,86,95,23,73,44,21,29,59,67","comment":null,"submitted_at":"2026-05-17 12:41:42","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/062a3fc50fec0eb95fe9daba285d193947abdf086e97f0b27f4bf87b79dd6976.txt"},{"canonical_hash":"4490b18769929a280d7f44eb699f4954fe3bc56487390a94fdb3321ea928cbc0","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"120,104,1,103,106,107,2,108,105,0,109,3,72,18,100,30,49,114,54,78,91,37,4,60,96,45,87,110,74,33,24,68,31,5,39,51,116,64,80,20,32,102,56,83,6,28,112,76,62,26,98,89,47,35,70,7,85,82,22,41,94,43,66,118,29,58,8,46,34,17,25,88,69,111,61,97,75,9,117,13,84,93,65,57,81,40,52,21,10,77,90,71,48,53,36,27,14,113,99,11,23,67,59,119,42,15,95,86,73,44,12,101,55,38,79,16,92,50,63,19,115","comment":null,"submitted_at":"2026-05-17 12:41:44","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/4490b18769929a280d7f44eb699f4954fe3bc56487390a94fdb3321ea928cbc0.txt"},{"canonical_hash":"873c2695e304ab27228f4348549fa7ab1dbf7f32d69d7f936466a2114b459a1d","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,43,7,26,67,49,79,95,48,69,1,82,9,23,101,11,70,54,40,55,72,103,18,102,78,115,53,30,113,74,105,80,96,47,71,97,75,33,111,21,106,119,77,118,108,84,65,99,116,27,39,100,50,86,20,45,10,92,37,85,5,46,3,73,60,68,36,112,90,91,117,110,56,87,24,89,22,38,19,25,28,35,32,41,16,44,120,31,64,104,6,13,58,57,8,29,76,66,81,107,94,109,62,15,59,114,93,42,83,98,52,17,34,12,51,88,61,4,14,63","comment":"Size-121 RC idempotent magma on F_121 = F_11² with NO size-11 sub-magmas — an \"order-8 multiplier\" construction outside the standard Phi_10 family.\n\nSize 121, fully idempotent, right-cancellative. Sub-magma count by size: only 0 (singletons) and 121 (the whole magma). Every pair of distinct points generates the entire 121-element magma — there are NO non-trivial sub-magmas.\n\nL_0 and R_0 each have cycle structure **1 + 15·8** — the multiplier in the F_121 linear operation has order **8**, not 10. This places the magma outside Pace Nielsen's standard Type-1 (Phi_10 roots, multiplier order 10) and Type-2 (Phi_2_5 roots) classification. Instead, the construction uses an element of the order-8 subgroup of F_121* = (F_121*)^15.\n\nThe additive structure is F_11² (= F_121 additively). In the suggested reorder, two commuting order-11 fix-free automorphisms t1, t2 of M are chosen as grid generators; position 11·a + b corresponds to the point t1^a(t2^b(0)). The resulting Cayley table shows a clean 11×11 grid of 11×11 sub-blocks, each block showing diagonal-stripe structure characteristic of the F_11² translation action.\n\nFamily at size 121 sharing this fingerprint (1 + 15·8 cycle): 5 RC idempotent iso classes — magma#70e5572a, magma#58669675, magma#af70b7bb, magma#fdc7e335. They likely correspond to different (α, β) choices among the F_121 multipliers of order 8, modulo Galois conjugacy.\n\nThis is one of the \"sub-11 = 0\" magmas distinct from the F_121 affine line (Phi_10 multiplier, would have sub-11 = 132 if used) and the Zassenhaus near-field (magma#5ebfbb80, multiplier order 30).\n\n[text written by Claude]","submitted_at":"2026-05-17 12:41:46","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/873c2695e304ab27228f4348549fa7ab1dbf7f32d69d7f936466a2114b459a1d.txt"},{"canonical_hash":"586696754176ae5088c76cae61112d5d95a951f7e55ddd3fb2878ab630611e4c","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,100,64,39,74,119,3,87,118,78,1,72,96,32,10,34,84,89,54,81,17,93,99,11,98,66,65,114,91,38,95,110,36,88,7,22,94,68,25,4,47,67,104,77,103,27,75,21,62,51,82,111,117,53,85,12,6,50,83,40,101,58,92,23,45,24,30,79,109,90,31,29,102,112,56,73,5,15,60,26,9,43,44,18,116,19,28,97,49,86,57,52,71,115,69,16,35,106,46,13,55,108,14,37,61,42,20,107,105,63,80,33,113,76,120,59,8,70,48,41","comment":"Size-121 RC idempotent magma on F_121 = F_11² with NO size-11 sub-magmas — an \"order-8 multiplier\" construction outside the standard Phi_10 family.\n\nSize 121, fully idempotent, right-cancellative. Sub-magma count by size: only 0 (singletons) and 121 (the whole magma). Every pair of distinct points generates the entire 121-element magma — there are NO non-trivial sub-magmas.\n\nL_0 and R_0 each have cycle structure **1 + 15·8** — the multiplier in the F_121 linear operation has order **8**, not 10. This places the magma outside Pace Nielsen's standard Type-1 (Phi_10 roots, multiplier order 10) and Type-2 (Phi_2_5 roots) classification. Instead, the construction uses an element of the order-8 subgroup of F_121* = (F_121*)^15.\n\nThe additive structure is F_11² (= F_121 additively). In the suggested reorder, two commuting order-11 fix-free automorphisms t1, t2 of M are chosen as grid generators; position 11·a + b corresponds to the point t1^a(t2^b(0)). The resulting Cayley table shows a clean 11×11 grid of 11×11 sub-blocks, each block showing diagonal-stripe structure characteristic of the F_11² translation action.\n\nFamily at size 121 sharing this fingerprint (1 + 15·8 cycle): 5 RC idempotent iso classes — magma#70e5572a, magma#873c2695, magma#af70b7bb, magma#fdc7e335. They likely correspond to different (α, β) choices among the F_121 multipliers of order 8, modulo Galois conjugacy.\n\nThis is one of the \"sub-11 = 0\" magmas distinct from the F_121 affine line (Phi_10 multiplier, would have sub-11 = 132 if used) and the Zassenhaus near-field (magma#5ebfbb80, multiplier order 30).\n\n[text written by Claude]","submitted_at":"2026-05-17 12:41:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/586696754176ae5088c76cae61112d5d95a951f7e55ddd3fb2878ab630611e4c.txt"},{"canonical_hash":"a46e856acff53b63ae60b8194f46da48c5cba2f49635e0376db9b781a6ac2d43","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"7,1,3,82,95,22,114,34,56,12,0,2,11,81,4,119,33,96,21,55,106,8,84,24,63,39,77,36,109,58,27,5,115,110,6,40,64,107,57,78,35,28,23,83,79,113,60,53,48,29,98,72,31,88,9,10,87,54,105,97,71,47,30,32,118,80,108,13,68,94,44,18,45,111,69,19,85,86,20,93,67,46,116,43,17,70,14,103,91,66,101,102,42,15,41,16,120,65,92,51,75,112,25,50,74,90,59,62,37,100,99,38,26,117,89,104,49,73,61,76,52","comment":null,"submitted_at":"2026-05-17 12:41:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/a46e856acff53b63ae60b8194f46da48c5cba2f49635e0376db9b781a6ac2d43.txt"},{"canonical_hash":"e594146c3276cf73338b03297519fc9fa0afc974624521110d07f1d949e0b20f","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"101,7,0,5,1,30,25,67,117,72,24,68,106,2,23,6,114,71,100,29,26,4,38,27,35,3,83,69,80,116,98,92,46,8,112,58,62,20,33,104,13,65,18,60,14,19,57,59,115,66,17,9,34,10,61,32,15,53,11,64,89,96,109,103,118,77,107,63,54,78,16,102,110,31,90,97,12,51,43,74,75,88,108,50,55,21,42,111,56,87,73,119,44,22,41,52,95,49,76,113,84,36,45,28,99,91,37,70,79,105,81,93,120,48,94,39,85,82,40,86,47","comment":null,"submitted_at":"2026-05-17 12:41:51","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/e594146c3276cf73338b03297519fc9fa0afc974624521110d07f1d949e0b20f.txt"},{"canonical_hash":"c9f16954aae2de0c203de4f56dff2c82cf11d4a75cfd8143605ad9b9bbc86d8f","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"99,14,113,0,1,42,8,21,86,76,31,98,2,7,13,32,85,115,75,41,22,106,3,109,81,87,58,114,64,60,56,33,62,4,88,63,107,61,55,82,34,116,59,57,54,89,20,5,35,97,79,26,30,108,117,53,6,80,90,110,29,19,93,96,25,36,12,71,74,118,69,50,104,9,47,37,40,11,111,94,72,39,48,73,38,49,10,70,77,15,92,100,24,95,28,112,43,52,65,78,101,27,16,66,44,91,51,105,119,23,120,102,18,103,84,46,17,68,45,67,83","comment":null,"submitted_at":"2026-05-17 12:41:53","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/c9f16954aae2de0c203de4f56dff2c82cf11d4a75cfd8143605ad9b9bbc86d8f.txt"},{"canonical_hash":"270b7c37e9b53dbdef1a8e5137ffe20ebeb87b2e961dcaea2048958f86ebd7f9","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"107,2,120,1,105,109,103,106,0,108,104,114,3,72,55,25,95,84,51,13,18,91,4,14,68,96,112,92,26,19,85,56,52,15,86,69,88,5,48,110,57,27,97,20,87,23,70,49,16,21,6,93,118,89,53,24,116,71,22,83,54,17,90,7,50,94,62,34,8,117,43,73,40,30,102,81,65,35,98,9,74,58,66,44,82,41,115,31,99,42,10,67,36,32,59,113,45,75,78,38,46,11,28,100,79,37,76,60,63,111,47,61,12,80,39,119,101,64,33,29,77","comment":"AG(2, 11) line magma with a 10+2 slope split across parallel classes.\n\nSize 121 = 11², fully idempotent, right-cancellative. All 132 = 12·11 lines of the AG(2, 11) affine plane appear as size-11 sub-magmas (every pair of distinct points lies in exactly one), so this is in the AG(2, 11) line family (sub-11 count = 132, \"full\" preservation).\n\nThe 12 parallel classes of AG(2, 11) carry F_11-line operations with two distinct slopes:\n- 10 parallel classes use α = α_A (each gives 11 sub-magmas iso to magma#abfd8e02)\n- 2 parallel classes use α = α_B (each gives 11 sub-magmas iso to magma#15fbff50)\n\nTotal: 110 + 22 = 132 size-11 sub-magmas. This **10+2 split** is one of the non-isomorphic ways to assign Phi_10 roots to parallel classes; other size-121 AG(2, 11)-line magmas in the DB exhibit different splits (e.g. 12+0 = pure direct product F_11 × F_11, 6+6, 8+4, etc.).\n\nL_0 cycle structure 1 + 12·10 is the standard \"translation + α-multiplication\" combination for AG(2, 11) magmas. R_0 cycle structure 1 + 20·5 + 10·2 is distinctive — the cycles of length 5 and 2 reflect the 10+2 slope distribution: 5 = order of some F_11* element, 2 from another. This R_0 fingerprint identifies the specific slope split.\n\nThe suggested reorder lays out the 121 points as an 11×11 grid using 2 of the 12 parallel classes as axes (one for rows, one for columns). Each row of the grid corresponds to one P1-block (an 11-element F_11 affine line sub-magma); each column to one P2-block. The diagonal 11×11 blocks of the Cayley table reveal the within-row F_11 line operations; off-diagonal blocks encode cross-row interactions via the affine plane's geometry.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:41:55","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/270b7c37e9b53dbdef1a8e5137ffe20ebeb87b2e961dcaea2048958f86ebd7f9.txt"},{"canonical_hash":"787061769887ffa41b70949bb5793f5663b9230a3f3185372985df9cfb003fe1","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"2,0,104,26,105,108,107,109,120,1,106,98,48,40,70,3,53,117,87,18,42,89,4,83,49,99,57,7,28,114,75,68,24,112,66,22,13,31,55,63,81,78,102,5,67,46,56,82,23,34,6,103,74,113,27,79,100,8,110,10,29,25,64,76,32,58,101,111,30,65,9,21,59,60,77,80,20,11,71,54,88,36,118,90,43,14,94,33,85,45,92,96,115,12,38,62,16,73,51,72,84,119,44,50,91,61,95,15,19,37,41,97,47,35,93,39,52,69,17,86,116","comment":null,"submitted_at":"2026-05-17 12:41:58","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/787061769887ffa41b70949bb5793f5663b9230a3f3185372985df9cfb003fe1.txt"},{"canonical_hash":"b7c6105e5e6fcefaac5907a84b12869bdc2c21de3db75bd6a0a462d63202fd05","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"109,52,107,0,120,104,108,1,106,53,105,114,81,2,15,21,102,51,78,54,10,62,74,112,55,11,17,47,3,16,60,82,103,12,75,63,83,18,4,56,7,99,110,48,8,13,100,113,19,57,61,79,49,76,5,80,9,50,77,20,59,101,111,6,14,58,93,97,22,66,69,40,119,29,42,36,86,27,89,43,32,70,117,23,67,87,98,41,68,30,88,94,71,24,44,33,37,90,115,34,64,38,91,72,45,84,95,118,28,25,96,35,116,31,73,85,39,92,26,65,46","comment":null,"submitted_at":"2026-05-17 12:42:01","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/b7c6105e5e6fcefaac5907a84b12869bdc2c21de3db75bd6a0a462d63202fd05.txt"},{"canonical_hash":"cd4269eb0dc8d73fe6a9ae3285d54d57d22f086e05292adb84623db74d1278c5","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"2,1,120,4,41,0,40,39,3,37,38,46,33,21,5,29,61,109,51,25,118,53,62,6,17,26,108,34,47,54,42,30,114,35,22,18,43,48,7,55,110,58,104,31,8,44,19,59,56,23,116,27,36,49,10,24,60,20,32,112,45,28,106,9,52,50,96,81,101,11,86,117,76,91,16,66,71,113,107,102,12,77,82,92,72,97,87,67,78,13,98,93,88,103,68,63,119,73,83,57,94,99,115,69,14,64,84,79,89,74,15,111,100,80,65,95,85,75,105,70,90","comment":null,"submitted_at":"2026-05-17 12:42:04","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/cd4269eb0dc8d73fe6a9ae3285d54d57d22f086e05292adb84623db74d1278c5.txt"},{"canonical_hash":"c867d70fe013adfa05865e368ebc100017827fbb7aff5d8eec1dbc7cd3482594","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"48,62,1,49,16,120,10,0,63,9,15,105,92,32,22,111,44,21,58,69,2,68,112,106,93,64,17,45,33,70,51,59,3,18,113,107,4,29,46,89,7,65,71,60,30,19,114,61,90,47,108,66,5,13,72,91,31,20,73,104,43,110,6,57,67,11,24,100,8,84,77,98,41,109,115,55,81,38,74,26,52,12,95,102,86,83,117,35,78,25,101,82,42,94,14,116,85,34,56,23,39,75,36,103,96,27,79,53,87,118,99,50,40,119,28,97,76,54,37,80,88","comment":null,"submitted_at":"2026-05-17 12:42:06","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/c867d70fe013adfa05865e368ebc100017827fbb7aff5d8eec1dbc7cd3482594.txt"},{"canonical_hash":"7ce9c9aa0d975569593a84542716e188a8c8aceda9d3c320067541cd263f09b4","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"80,2,81,79,1,82,4,0,3,120,83,60,22,88,114,108,90,11,5,35,50,78,110,6,61,74,12,85,31,104,23,47,91,75,105,111,92,32,62,24,13,7,49,87,93,14,76,84,25,112,8,33,106,51,63,86,34,89,59,9,77,107,21,10,48,113,15,20,43,69,119,67,99,97,26,38,58,65,102,56,41,16,72,95,29,117,39,53,70,98,109,54,100,44,27,115,17,40,68,42,30,66,46,96,57,118,18,103,36,73,55,116,71,64,28,52,19,101,94,37,45","comment":null,"submitted_at":"2026-05-17 12:42:09","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/7ce9c9aa0d975569593a84542716e188a8c8aceda9d3c320067541cd263f09b4.txt"},{"canonical_hash":"af70b7bb8ac907715809a347d0dfe8ad9ff48f6a7cd60bc12915c37a36e82d89","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,89,50,80,14,49,25,98,20,32,1,116,86,72,78,83,103,7,90,36,27,58,37,99,41,54,19,18,34,6,33,39,17,64,13,108,16,38,111,10,79,101,43,57,85,60,22,112,77,106,44,75,73,51,68,31,97,84,61,11,5,82,66,110,40,119,91,42,59,88,92,109,26,70,56,30,94,8,107,24,118,12,105,114,52,115,93,74,69,81,62,35,47,102,117,15,53,28,45,71,4,65,48,46,113,95,23,100,3,104,87,21,96,63,29,9,67,120,76,55","comment":"Size-121 RC idempotent magma on F_121 = F_11² with NO size-11 sub-magmas — an \"order-8 multiplier\" construction outside the standard Phi_10 family.\n\nSize 121, fully idempotent, right-cancellative. Sub-magma count by size: only 0 (singletons) and 121 (the whole magma). Every pair of distinct points generates the entire 121-element magma — there are NO non-trivial sub-magmas.\n\nL_0 and R_0 each have cycle structure **1 + 15·8** — the multiplier in the F_121 linear operation has order **8**, not 10. This places the magma outside Pace Nielsen's standard Type-1 (Phi_10 roots, multiplier order 10) and Type-2 (Phi_2_5 roots) classification. Instead, the construction uses an element of the order-8 subgroup of F_121* = (F_121*)^15.\n\nThe additive structure is F_11² (= F_121 additively). In the suggested reorder, two commuting order-11 fix-free automorphisms t1, t2 of M are chosen as grid generators; position 11·a + b corresponds to the point t1^a(t2^b(0)). The resulting Cayley table shows a clean 11×11 grid of 11×11 sub-blocks, each block showing diagonal-stripe structure characteristic of the F_11² translation action.\n\nFamily at size 121 sharing this fingerprint (1 + 15·8 cycle): 5 RC idempotent iso classes — magma#70e5572a, magma#873c2695, magma#58669675, magma#fdc7e335. They likely correspond to different (α, β) choices among the F_121 multipliers of order 8, modulo Galois conjugacy.\n\nThis is one of the \"sub-11 = 0\" magmas distinct from the F_121 affine line (Phi_10 multiplier, would have sub-11 = 132 if used) and the Zassenhaus near-field (magma#5ebfbb80, multiplier order 30).\n\n[text written by Claude]","submitted_at":"2026-05-17 12:42:11","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/af70b7bb8ac907715809a347d0dfe8ad9ff48f6a7cd60bc12915c37a36e82d89.txt"},{"canonical_hash":"fdc7e335a50d14fc8c3fb38551a2bc19590dd6ea767713204ed5f7e2fa2a4b96","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,3,10,76,17,105,108,69,116,97,1,98,89,5,65,14,80,55,103,87,112,101,73,64,52,6,90,51,77,34,47,12,115,20,25,70,100,13,67,19,66,84,39,104,29,120,72,49,81,85,56,96,107,118,45,27,68,63,78,9,106,23,62,24,43,36,92,21,15,46,42,102,4,114,91,50,22,35,111,58,31,75,109,48,95,117,44,113,40,33,32,30,57,79,26,86,83,60,110,82,11,54,28,99,18,53,16,37,8,71,94,41,119,88,38,7,74,93,61,59","comment":"Size-121 RC idempotent magma on F_121 = F_11² with NO size-11 sub-magmas — an \"order-8 multiplier\" construction outside the standard Phi_10 family.\n\nSize 121, fully idempotent, right-cancellative. Sub-magma count by size: only 0 (singletons) and 121 (the whole magma). Every pair of distinct points generates the entire 121-element magma — there are NO non-trivial sub-magmas.\n\nL_0 and R_0 each have cycle structure **1 + 15·8** — the multiplier in the F_121 linear operation has order **8**, not 10. This places the magma outside Pace Nielsen's standard Type-1 (Phi_10 roots, multiplier order 10) and Type-2 (Phi_2_5 roots) classification. Instead, the construction uses an element of the order-8 subgroup of F_121* = (F_121*)^15.\n\nThe additive structure is F_11² (= F_121 additively). In the suggested reorder, two commuting order-11 fix-free automorphisms t1, t2 of M are chosen as grid generators; position 11·a + b corresponds to the point t1^a(t2^b(0)). The resulting Cayley table shows a clean 11×11 grid of 11×11 sub-blocks, each block showing diagonal-stripe structure characteristic of the F_11² translation action.\n\nFamily at size 121 sharing this fingerprint (1 + 15·8 cycle): 5 RC idempotent iso classes — magma#70e5572a, magma#873c2695, magma#58669675, magma#af70b7bb. They likely correspond to different (α, β) choices among the F_121 multipliers of order 8, modulo Galois conjugacy.\n\nThis is one of the \"sub-11 = 0\" magmas distinct from the F_121 affine line (Phi_10 multiplier, would have sub-11 = 132 if used) and the Zassenhaus near-field (magma#5ebfbb80, multiplier order 30).\n\n[text written by Claude]","submitted_at":"2026-05-17 12:42:12","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/fdc7e335a50d14fc8c3fb38551a2bc19590dd6ea767713204ed5f7e2fa2a4b96.txt"},{"canonical_hash":"18db3d82204541ac3ba814fa7626af91515840082024614f8c22265359626a38","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"36,0,82,17,108,89,28,47,100,72,61,73,63,43,12,1,8,22,94,85,35,56,2,101,62,91,104,69,49,19,78,30,37,102,79,38,71,52,27,16,88,58,46,3,80,59,4,29,106,48,90,68,39,18,98,60,40,99,50,109,20,70,26,5,92,81,86,44,74,33,51,25,15,6,57,97,64,66,83,54,7,105,34,93,11,41,21,76,53,75,87,95,107,13,31,23,65,9,45,42,55,67,24,103,96,10,32,77,14,84,117,119,113,110,120,118,114,112,111,116,115","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#8edce4bd, magma#e2b4b45d, magma#ef441533, magma#0d2a7fdd, magma#6bab1ff9, magma#12644a1d, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:42:15","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/18db3d82204541ac3ba814fa7626af91515840082024614f8c22265359626a38.txt"},{"canonical_hash":"8edce4bdeb667fbd234a03c48d026ee8b99c0ee0cb04e0738466ab54a5c90f1b","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"2,7,120,35,6,36,56,57,3,1,0,25,89,4,66,78,68,42,117,30,83,105,100,47,5,50,9,97,62,13,75,114,23,112,53,37,16,22,8,96,98,61,45,74,15,111,19,44,93,58,76,52,24,102,10,49,99,103,113,59,77,20,46,11,17,94,48,14,54,101,73,21,12,110,95,51,60,84,67,18,118,107,80,70,26,39,90,32,91,119,104,27,34,109,82,85,72,63,41,64,28,55,86,43,31,106,92,79,115,69,116,87,38,88,71,40,33,65,108,29,81","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#e2b4b45d, magma#ef441533, magma#0d2a7fdd, magma#6bab1ff9, magma#12644a1d, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:42:16","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/8edce4bdeb667fbd234a03c48d026ee8b99c0ee0cb04e0738466ab54a5c90f1b.txt"},{"canonical_hash":"e2b4b45de3b19af01bdeaba80df89228892f589488a5dc61749f84aa435285ab","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"2,8,5,1,4,109,120,7,0,6,3,46,29,89,66,9,86,110,49,106,69,26,28,50,10,48,30,68,112,70,88,90,108,105,71,31,25,51,45,114,91,65,11,85,87,92,52,107,72,27,111,12,47,32,67,64,13,73,84,93,104,113,33,24,53,44,14,23,83,34,103,54,115,43,74,63,94,35,100,60,55,80,75,117,20,95,40,15,56,82,42,76,62,96,119,102,16,22,36,77,59,19,97,39,17,116,79,37,99,57,98,41,101,18,21,38,118,61,58,81,78","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#ef441533, magma#0d2a7fdd, magma#6bab1ff9, magma#12644a1d, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:42:18","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/e2b4b45de3b19af01bdeaba80df89228892f589488a5dc61749f84aa435285ab.txt"},{"canonical_hash":"ef44153348fb026d3b08934c230ce6291d91f8a3f8ff2cdaef43ae6c1e51b118","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"5,8,6,7,2,109,120,1,4,3,0,18,98,78,38,49,58,112,29,69,9,89,76,56,36,96,90,16,110,70,10,50,30,34,14,94,54,31,74,113,11,51,91,71,97,77,57,17,72,37,111,52,92,32,12,55,35,15,75,13,95,114,93,33,73,53,28,108,88,48,99,68,116,79,19,59,39,105,85,65,25,20,45,117,100,40,80,60,87,67,47,107,41,27,118,21,61,101,81,64,44,24,84,62,104,119,42,82,22,102,46,26,106,66,83,86,115,63,103,43,23","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#e2b4b45d, magma#0d2a7fdd, magma#6bab1ff9, magma#12644a1d, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:45:41","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/ef44153348fb026d3b08934c230ce6291d91f8a3f8ff2cdaef43ae6c1e51b118.txt"},{"canonical_hash":"0d2a7fdd9a9bdce3262addd77261b638f2c16f8224ff984fa3354e5e56a86e3c","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"105,103,21,71,11,93,59,23,0,107,1,16,98,2,104,106,108,54,109,66,28,6,81,79,13,63,3,95,61,25,75,73,77,14,96,48,52,44,46,62,50,64,26,4,37,35,15,65,5,97,53,27,41,39,33,87,85,17,67,7,99,55,29,91,89,83,18,100,76,80,82,74,56,78,68,30,8,43,51,19,69,9,101,57,31,47,45,49,20,102,42,36,38,40,58,34,70,32,10,22,94,92,86,88,90,60,84,72,24,12,113,111,118,112,114,116,120,110,117,115,119","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#e2b4b45d, magma#ef441533, magma#6bab1ff9, magma#12644a1d, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:45:43","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/0d2a7fdd9a9bdce3262addd77261b638f2c16f8224ff984fa3354e5e56a86e3c.txt"},{"canonical_hash":"6bab1ff90a77c9783e77f2b76ab5701c45ace0f79dfe49297cf69e297e089af4","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,2,3,120,34,47,109,35,46,108,39,95,17,45,4,41,77,43,116,37,54,90,44,40,22,5,111,42,49,36,72,38,24,89,21,30,6,26,71,28,110,32,48,94,29,25,16,7,115,27,53,31,76,33,96,84,80,18,8,117,82,55,86,68,78,79,91,23,85,9,81,73,83,112,87,50,67,97,19,63,10,59,69,61,118,65,56,92,62,58,14,11,113,60,51,64,74,66,104,93,15,100,12,106,75,98,114,102,52,88,99,105,20,13,119,107,57,101,70,103","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 7 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#e2b4b45d, magma#ef441533, magma#0d2a7fdd, magma#12644a1d, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:45:44","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/6bab1ff90a77c9783e77f2b76ab5701c45ace0f79dfe49297cf69e297e089af4.txt"},{"canonical_hash":"12644a1dda1488d9f914b42bc5c68671a4f72e89c05083a0e2fca6310de03f00","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"4,90,3,0,120,91,92,94,93,1,2,65,31,70,18,5,39,37,33,35,47,104,63,118,78,16,6,116,114,110,112,45,102,61,21,76,14,7,29,27,23,25,43,100,69,53,74,12,8,51,59,55,57,41,98,67,84,72,10,9,82,80,86,88,49,96,111,73,113,119,105,68,11,97,40,117,115,34,75,36,32,109,60,13,99,42,30,38,87,77,89,85,108,62,15,101,44,83,81,56,79,58,54,107,64,17,103,46,52,50,24,71,26,22,106,66,19,95,48,20,28","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#e2b4b45d, magma#ef441533, magma#0d2a7fdd, magma#6bab1ff9, magma#38c42b28.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:45:46","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/12644a1dda1488d9f914b42bc5c68671a4f72e89c05083a0e2fca6310de03f00.txt"},{"canonical_hash":"38c42b2858f48d28904d3748b3c685f5496c1df2e631b572a7e35d1df185694a","size":121,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"5,7,9,6,3,120,4,1,0,2,8,61,63,65,67,34,81,71,20,10,56,69,11,57,72,21,98,106,104,96,100,102,35,110,112,114,116,36,83,73,22,12,58,118,13,59,74,23,46,108,42,44,48,40,37,94,86,88,90,38,80,75,24,14,50,92,15,51,76,25,64,105,60,62,66,68,39,95,97,99,101,30,82,77,26,16,52,103,17,53,78,27,113,107,119,111,115,117,31,43,45,47,49,32,84,79,28,18,54,41,19,55,70,29,87,109,93,85,89,91,33","comment":"Twisted AG(2, 11) magma with exactly 2 of 12 parallel classes preserved as sub-magmas.\n\nSize 121 = 11², fully idempotent, right-cancellative. Exactly 22 size-11 sub-magmas in M, partitioning into 2 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; every pair of points (x, y) NOT both in some preserved-class line generates the whole 121-element magma. This is the \"2-class\" sub-family of twisted AG(2, 11) magmas — one of 8 iso classes at size 121 sharing this fingerprint.\n\nL_0 and R_0 cycle structure 1 + 12·10, matching the F_11* multiplicative scalar of the F_11 affine line operation in the preserved parallel classes.\n\nIn the suggested reorder, positions 11·r + c correspond to the unique grid point at the intersection of P1-row r and P2-column c (using the 2 preserved parallel classes as grid axes). The Cayley table then shows 11×11 blocks of 11×11: diagonal blocks reveal the row sub-magma operations (F_11 line, mostly idempotent diagonals), off-diagonal blocks encode the twisted cross-row action — chaotic in the non-preserved direction.\n\nStructurally intermediate between F_121 affine line (0 sub-magmas at all) and the full AG(2, 11) line magmas (all 132 lines preserved). The other 8 iso classes in this family: magma#18db3d82, magma#8edce4bd, magma#e2b4b45d, magma#ef441533, magma#0d2a7fdd, magma#6bab1ff9, magma#12644a1d.\n\nSee size-121 page commentary for the full taxonomy.\n\n[text written by Claude]","submitted_at":"2026-05-17 12:45:48","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/121/38c42b2858f48d28904d3748b3c685f5496c1df2e631b572a7e35d1df185694a.txt"},{"canonical_hash":"ff1349fc57922524cfb763138b8f25ce575ec74cb678c760f263766b9874cd20","size":125,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,124,2,3,4,121,12,16,8,122,9,13,5,17,19,7,15,11,120,10,18,14,123,6,20,118,82,43,61,101,92,56,68,24,89,53,65,37,108,47,75,31,105,99,78,34,115,86,50,119,62,83,21,40,72,96,28,44,106,93,25,57,102,69,35,51,112,79,87,54,109,66,90,38,42,23,81,60,117,36,88,64,111,52,85,77,114,49,33,71,100,59,27,95,104,46,30,98,74,63,41,80,116,22,48,84,113,32,76,97,107,29,73,45,110,39,67,55,91,26,70,58,94,103","comment":"Direct product of two linear magmas: F_5(2,4) × F_5(2,4) × F_5(2,4).","submitted_at":"2026-04-28 16:31:13","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/125/ff1349fc57922524cfb763138b8f25ce575ec74cb678c760f263766b9874cd20.txt"},{"canonical_hash":"9bd98b45251463ca9d54fc075d45298bcaa6f0a934390604164225b4bd18cd6d","size":125,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,3,2,124,13,14,12,15,106,86,84,87,85,101,48,50,49,51,102,64,66,65,67,113,36,37,38,39,121,93,92,94,95,109,96,99,98,97,104,56,58,57,59,117,33,32,35,34,111,60,62,63,61,112,75,74,73,72,114,23,21,22,20,120,31,29,30,28,116,71,70,68,69,107,40,41,43,42,122,11,9,10,8,105,81,82,80,83,118,46,44,47,45,103,78,79,76,77,115,25,26,27,24,108,18,19,17,16,100,4,6,5,7,110,91,88,90,89,123,53,52,55,54,119","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_5(2,4).","submitted_at":"2026-04-28 19:31:51","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/125/9bd98b45251463ca9d54fc075d45298bcaa6f0a934390604164225b4bd18cd6d.txt"},{"canonical_hash":"cf044a9b0f76e51543fb5b24f135e291b2f82ff641790055ad377dacb6ffb638","size":127,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,25,57,20,60,83,38,96,70,4,93,10,6,88,15,112,94,53,45,123,76,91,119,64,44,108,86,98,36,61,56,92,105,40,46,97,121,26,69,100,73,117,107,34,101,13,106,62,109,63,7,49,35,72,22,81,90,126,5,32,68,59,66,122,80,23,39,120,27,113,28,71,52,50,21,3,47,111,24,54,74,104,2,55,87,125,124,16,31,14,84,48,37,30,33,11,79,102,42,51,103,18,85,65,17,95,9,29,114,19,67,78,82,116,110,115,118,43,8,58,99,41,77,75,89,12","comment":"Size-127 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_127 (127 prime):\n\n  x ◇ y = x + f(y − x)    in F_127,\n  f(0) = 0,\n  f(d) = 58·d   when d is a quadratic residue mod 127,\n  f(d) = 29·d   when d is a non-residue.\n\nWhy piecewise is required: 127 is prime but |F_127*| = 126 = 2·3²·7 is not divisible by 10, so F_127 contains no primitive 10th roots of unity. The polynomial Φ_10(α) = α⁴ − α³ + α² − α + 1 — whose roots give the multipliers for the simple-linear idempotent Eq 677 magmas x ◇ y = (1 − α)x + α y — has no roots in F_127. So no single-multiplier linear construction works at this size; the piecewise pairing (α_QR, α_NQR) = (58, 29) is needed.\n\nNote: 58 = 2·29 in F_127, and 2 is a quadratic residue mod 127 (since 127 ≡ −1 (mod 8)), so the two multipliers are related by a QR scalar.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-127 fix-free magma automorphism τ (the hidden additive translation by 1 in F_127), making the cyclic F_127 translation symmetry visible: every row of the rendered Cayley table is a horizontal shift of row 0 = f.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:25:53","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/127/cf044a9b0f76e51543fb5b24f135e291b2f82ff641790055ad377dacb6ffb638.txt"},{"canonical_hash":"bc168d9812c0344b63512c07e5a3418c47a661f1f4923ccaeb5dbccee97eb3ee","size":131,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,46,63,61,26,116,74,52,64,44,70,88,23,5,109,129,117,9,51,91,126,128,111,66,65,99,124,32,121,85,94,33,89,57,73,78,105,108,49,95,110,35,101,93,7,54,48,58,10,47,115,18,81,4,82,106,127,27,14,84,12,103,107,96,67,53,25,76,3,22,15,102,125,71,21,120,39,130,104,55,86,6,60,37,80,87,68,11,90,118,2,31,42,38,77,19,79,92,62,41,17,69,16,83,50,112,75,123,113,119,72,28,36,100,45,30,114,43,40,13,8,122,24,98,29,20,56,97,59,34","comment":"Linear magma over Z/131Z (the prime field F_131): x ◇ y = 54x + 78y (mod 131).","submitted_at":"2026-04-28 16:07:19","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/131/bc168d9812c0344b63512c07e5a3418c47a661f1f4923ccaeb5dbccee97eb3ee.txt"},{"canonical_hash":"ff8cf89b7df9bc60517977b8bdcf83f4ff0ee33e12188a9de47d7e4c97c3facf","size":131,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,43,120,40,47,112,60,13,97,82,88,69,78,34,33,4,59,26,12,102,79,45,127,29,95,49,16,89,77,15,57,101,53,90,98,111,93,36,21,75,50,61,64,107,74,91,52,30,48,129,11,72,68,51,46,121,24,66,8,67,22,103,2,20,124,100,122,94,27,38,114,87,130,39,99,5,7,109,71,115,73,54,35,105,56,118,28,117,58,70,81,86,119,123,31,65,83,10,18,106,125,92,17,14,85,126,55,3,108,96,113,42,19,116,23,62,128,41,63,84,110,9,76,80,44,104,32,6,25,37","comment":"Linear magma over Z/131Z (the prime field F_131): x ◇ y = 59x + 73y (mod 131).","submitted_at":"2026-04-28 16:07:21","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/131/ff8cf89b7df9bc60517977b8bdcf83f4ff0ee33e12188a9de47d7e4c97c3facf.txt"},{"canonical_hash":"9f3b9e5aa08ce28772078ce653a8ebd59286a23b20863e67a7c8c031b40e803e","size":131,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,21,34,3,89,120,107,87,86,77,113,73,17,28,118,12,125,117,6,20,108,105,36,79,127,81,104,13,85,48,102,95,59,90,128,84,66,11,43,33,29,91,75,8,83,61,35,37,76,111,51,46,40,74,96,47,71,124,100,2,109,30,110,15,65,93,78,49,112,130,26,70,57,7,44,101,24,116,23,88,14,38,50,68,10,53,126,67,72,25,55,123,121,82,62,94,54,5,115,119,129,97,45,63,42,4,80,9,16,69,64,99,18,60,41,58,122,19,22,106,92,31,39,98,32,114,103,52,27,56","comment":"Linear magma over Z/131Z (the prime field F_131): x ◇ y = 62x + 70y (mod 131).","submitted_at":"2026-04-28 16:07:22","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/131/9f3b9e5aa08ce28772078ce653a8ebd59286a23b20863e67a7c8c031b40e803e.txt"},{"canonical_hash":"5fd22375fa1221421422cee287cb3d20085784e14c0d658686555b230cee921c","size":131,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,30,23,121,6,61,49,15,7,28,100,110,36,47,11,70,29,108,82,54,127,27,118,58,12,25,107,44,67,105,51,24,55,22,41,102,21,19,99,16,13,130,78,81,34,84,86,37,106,87,120,89,116,40,2,109,42,90,77,123,53,92,62,119,17,43,94,5,76,112,101,45,35,93,72,80,114,126,71,56,88,95,66,65,60,122,128,20,3,46,4,97,33,8,26,79,124,115,9,104,64,48,52,38,18,96,10,75,31,83,103,117,113,129,39,74,50,59,14,91,73,98,32,69,111,68,85,63,57,125","comment":"Linear magma over Z/131Z (the prime field F_131): x ◇ y = 90x + 42y (mod 131).","submitted_at":"2026-04-28 16:07:23","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/131/5fd22375fa1221421422cee287cb3d20085784e14c0d658686555b230cee921c.txt"},{"canonical_hash":"37015e639fa162d2e189297fd903e7b0458756999c9e17dab7db269725f72b78","size":133,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"132,108,120,117,113,114,110,112,124,116,125,115,121,119,123,122,109,111,118,126,95,27,106,9,30,26,28,31,2,12,11,8,97,10,29,0,101,1,127,17,81,16,74,84,80,82,85,86,77,76,73,7,75,83,78,107,79,131,92,13,88,19,5,25,14,6,4,22,21,18,96,20,15,23,102,24,128,94,67,90,60,70,66,68,71,72,63,62,59,100,61,69,64,105,65,129,91,40,87,33,43,39,41,44,3,36,35,32,98,34,42,37,103,38,130,93,53,89,46,56,52,54,57,58,49,48,45,99,47,55,50,104,51","comment":"Direct product of two linear magmas: F_7 × F_19. The operation is (x₁, x₂) ◇ (y₁, y₂) = (4x₁ + 1y₁ (mod 7), 7x₂ + 3y₂ (mod 19)).","submitted_at":"2026-04-28 16:08:13","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/133/37015e639fa162d2e189297fd903e7b0458756999c9e17dab7db269725f72b78.txt"},{"canonical_hash":"e1b46c1c197851b1f5a8a374a2f5b71e7f5748390d026e9fb5ab6785fe9950b6","size":139,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"138,0,46,31,129,122,3,125,69,99,62,88,54,89,65,47,94,37,16,41,87,50,28,67,114,103,29,82,90,98,130,136,34,71,9,106,11,134,124,72,27,115,133,48,111,4,92,121,77,86,20,105,112,19,107,2,30,109,38,79,70,43,76,7,6,1,96,93,60,135,23,91,39,42,74,63,64,137,97,13,110,127,78,119,73,53,131,81,51,132,55,108,32,61,84,80,102,21,26,116,15,35,22,68,52,66,14,123,24,18,44,59,113,118,49,25,10,117,104,56,95,128,126,40,101,8,58,85,57,5,45,12,36,83,33,17,120,100,75","comment":"Linear magma over Z/139Z (the prime field F_139): x ◇ y = 42x + 51y (mod 139).","submitted_at":"2026-04-28 16:07:24","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/139/e1b46c1c197851b1f5a8a374a2f5b71e7f5748390d026e9fb5ab6785fe9950b6.txt"},{"canonical_hash":"5068f89145914e55a3e546a894d8d8e573d65aed2eec2ef21aa12f865e703682","size":139,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"138,0,31,39,90,48,98,72,59,106,107,46,15,130,41,115,118,111,12,43,13,49,105,95,126,124,75,9,100,136,10,42,2,113,6,58,134,78,102,83,135,96,108,85,22,68,64,4,71,82,69,3,44,99,28,122,17,110,81,35,29,97,101,116,32,92,8,34,25,20,117,70,79,127,47,77,19,56,52,74,80,36,65,114,14,73,54,89,133,24,37,26,123,109,23,119,40,63,51,137,38,57,33,1,103,125,16,132,87,129,67,55,128,30,5,7,50,60,94,121,88,120,66,21,18,86,11,112,91,62,61,104,27,53,93,45,84,76,131","comment":"Linear magma over Z/139Z (the prime field F_139): x ◇ y = 42x + 130y (mod 139).","submitted_at":"2026-04-28 16:07:26","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/139/5068f89145914e55a3e546a894d8d8e573d65aed2eec2ef21aa12f865e703682.txt"},{"canonical_hash":"2029e00c101fd28b8dd131603d7a13aef4008486b74043ac0812e7fefd0c56b8","size":139,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"138,0,25,45,137,128,106,110,26,126,68,123,46,117,50,19,87,78,66,55,129,70,63,38,107,102,57,86,111,132,5,113,27,83,8,1,127,125,116,77,69,101,131,82,124,100,99,134,47,135,42,90,118,48,6,97,51,136,72,35,20,43,53,3,88,91,13,93,79,119,24,105,67,49,65,62,56,7,17,115,130,98,41,15,71,52,12,23,64,16,40,11,39,73,74,29,108,36,75,95,103,21,30,32,58,44,109,122,18,54,37,85,112,2,76,81,133,89,96,34,4,92,104,61,114,14,22,10,28,94,31,121,84,80,33,60,9,120,59","comment":"Linear magma over Z/139Z (the prime field F_139): x ◇ y = 96x + 116y (mod 139).","submitted_at":"2026-04-28 16:07:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/139/2029e00c101fd28b8dd131603d7a13aef4008486b74043ac0812e7fefd0c56b8.txt"},{"canonical_hash":"c58af111ba0846ef4023541767a122f479e52f18386f3f968f1f46b9a1f7942c","size":139,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"138,0,36,116,123,115,7,125,1,25,6,19,32,53,60,24,39,136,112,50,31,34,106,82,119,23,94,86,41,37,111,131,126,80,71,33,13,109,91,68,118,107,121,58,87,85,17,127,5,43,110,45,75,122,21,79,128,65,124,76,12,26,66,10,61,67,15,51,52,97,120,29,28,38,90,84,72,89,49,69,4,101,88,105,2,44,99,8,22,133,20,77,104,40,62,64,35,98,130,95,11,114,132,70,56,9,3,103,108,134,14,18,63,117,46,96,137,129,57,54,27,135,113,16,47,83,30,55,42,73,48,81,102,74,92,100,93,59,78","comment":"Linear magma over Z/139Z (the prime field F_139): x ◇ y = 96x + 119y (mod 139).","submitted_at":"2026-04-28 16:07:28","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/139/c58af111ba0846ef4023541767a122f479e52f18386f3f968f1f46b9a1f7942c.txt"},{"canonical_hash":"698ba0832d957692675cefaba639b682fc2329ab75d5cf7de23943da666963fb","size":143,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,5,12,15,20,25,34,39,44,49,54,59,140,1,7,10,16,21,26,33,38,43,48,53,58,142,60,65,70,76,81,86,92,97,102,107,112,117,133,63,68,73,78,83,88,93,98,103,108,113,118,135,61,66,71,75,80,85,94,99,104,109,114,119,137,2,8,13,18,23,28,31,36,41,45,50,55,138,62,67,72,77,82,87,90,95,100,106,111,116,134,120,121,122,123,124,125,126,127,128,129,130,131,132,4,6,11,17,22,27,30,35,40,46,51,56,141,64,69,74,79,84,89,91,96,101,105,110,115,136,3,9,14,19,24,29,32,37,42,47,52,57,139","comment":"F_11(10, 2) base × F_13 fiber: 11 fibers of 13 (each fiber is F_13 sub-magma). Fiber bundle: a prime-field linear base operation acts on fibers that partition the carrier.","submitted_at":"2026-04-24 11:48:48","submitted_by":null,"url":"https://eq677-magmas.icarm.cloud/magmas/143/698ba0832d957692675cefaba639b682fc2329ab75d5cf7de23943da666963fb.txt"},{"canonical_hash":"40f1f3db007d918074923e783f9c02ae2b976742541944b95c46c80af4ddb991","size":143,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"132,5,110,15,45,100,90,71,80,26,35,61,55,133,0,115,10,41,105,95,75,85,22,31,65,51,135,6,111,16,46,101,91,70,81,27,36,60,56,141,8,114,19,49,104,94,74,84,29,39,64,59,139,7,113,18,48,103,93,73,83,28,38,63,58,134,1,116,11,40,106,96,76,86,20,30,66,50,136,2,117,12,42,107,97,77,87,23,32,67,52,140,4,119,14,44,109,99,79,89,25,34,69,54,137,9,112,17,47,102,92,72,82,21,37,62,57,138,3,118,13,43,108,98,78,88,24,33,68,53,142,126,122,127,130,121,120,125,123,131,129,124,128","comment":"Direct product of two linear magmas: F_11 × F_13. The operation is (x₁, x₂) ◇ (y₁, y₂) = (10x₁ + 2y₁ (mod 11), 9x₂ + 11y₂ (mod 13)).","submitted_at":"2026-04-28 16:31:07","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/143/40f1f3db007d918074923e783f9c02ae2b976742541944b95c46c80af4ddb991.txt"},{"canonical_hash":"06f87167c641ed88bacdf1ddc56430845e75f2c4e26701d25aee82c5b89bb5ed","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,135,106,31,41,39,52,124,113,100,15,21,108,126,63,90,131,75,91,98,2,27,123,144,68,133,35,145,117,114,130,120,95,128,148,12,121,38,132,61,136,17,50,71,84,62,147,69,80,101,10,86,30,143,70,5,96,43,76,19,107,94,29,6,78,137,48,134,26,16,93,140,7,66,81,14,129,9,92,111,32,141,24,97,60,18,110,36,103,22,112,116,79,25,102,46,149,55,99,37,42,8,54,44,73,51,34,146,47,109,33,57,138,89,11,4,13,45,3,104,40,67,83,77,59,72,58,118,125,127,142,65,49,88,87,105,122,74,28,23,53,82,150,20,119,85,139,115,56,64","comment":"Linear magma over Z/151Z (the prime field F_151): x ◇ y = 9x + 143y (mod 151).","submitted_at":"2026-04-28 16:07:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/151/06f87167c641ed88bacdf1ddc56430845e75f2c4e26701d25aee82c5b89bb5ed.txt"},{"canonical_hash":"fb4e62fd0d1e70e32b2f30b122e9692347d30e79e67b1a348108bd61f4ed02d2","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,58,42,103,134,47,144,130,127,2,89,73,45,108,39,82,41,72,59,26,60,139,34,29,12,56,95,43,111,27,17,105,121,133,107,33,104,149,61,20,125,77,49,100,15,135,75,140,9,62,143,81,11,132,48,80,35,93,21,147,36,7,116,145,4,30,24,126,71,94,32,14,131,115,13,50,78,53,22,67,51,128,97,57,88,25,110,148,99,79,3,114,96,113,101,86,37,84,54,90,102,44,138,16,19,8,92,23,74,87,112,137,136,119,117,123,68,46,38,28,120,76,142,146,70,52,109,85,18,118,141,150,5,64,129,40,55,106,124,10,6,31,66,98,83,91,122,69,63,65","comment":"Linear magma over Z/151Z (the prime field F_151): x ◇ y = 20x + 132y (mod 151).","submitted_at":"2026-04-28 16:07:31","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/151/fb4e62fd0d1e70e32b2f30b122e9692347d30e79e67b1a348108bd61f4ed02d2.txt"},{"canonical_hash":"4bb5d326ebede88980fbf421b623b61c2468f2aed93f4aa7f61f0ae47a514e63","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"150,0,110,33,145,101,68,11,105,126,136,137,28,13,46,59,140,134,86,120,96,104,97,65,63,127,48,9,6,147,19,119,100,20,94,37,121,143,80,106,131,18,139,109,132,149,25,148,23,82,87,17,8,12,44,88,41,3,107,90,54,7,79,62,135,39,55,69,129,83,72,61,81,36,103,10,115,73,141,51,91,102,53,24,99,85,144,30,92,49,112,84,60,77,108,146,58,1,117,113,122,57,52,128,43,130,47,27,4,34,123,26,76,50,38,16,142,64,125,70,14,124,42,111,114,78,22,93,95,67,74,66,15,56,29,35,89,2,118,133,32,31,21,75,116,98,71,40,138,5,45","comment":"Linear magma over Z/151Z (the prime field F_151): x ◇ y = 32x + 68y (mod 151).","submitted_at":"2026-04-28 16:07:36","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/151/4bb5d326ebede88980fbf421b623b61c2468f2aed93f4aa7f61f0ae47a514e63.txt"},{"canonical_hash":"17c2495e0cbe8bead1aee64d636a386ef2cac83bd503e7d270e4a61308d5bf4d","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"150,0,41,111,21,29,91,115,63,66,71,64,146,101,95,79,5,23,4,46,51,70,2,112,126,59,81,129,75,69,134,9,36,127,65,83,39,35,26,56,44,141,50,48,37,47,92,62,106,12,8,148,136,108,109,45,130,96,149,31,114,143,33,133,16,144,107,84,3,67,138,140,19,90,15,122,68,131,49,135,24,22,121,99,43,53,28,132,17,74,27,60,147,103,11,14,86,55,54,20,32,93,128,52,116,7,88,78,89,104,25,85,110,142,76,80,42,119,73,77,94,18,123,34,13,40,113,72,58,98,124,105,87,100,139,97,38,10,1,30,118,125,120,117,61,6,145,137,57,82,102","comment":"Linear magma over Z/151Z (the prime field F_151): x ◇ y = 32x + 115y (mod 151).","submitted_at":"2026-04-28 16:07:38","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/151/17c2495e0cbe8bead1aee64d636a386ef2cac83bd503e7d270e4a61308d5bf4d.txt"},{"canonical_hash":"4f3364bd5b92000d2295c0d4214b139f1595449ab2d92ee93602880e41303a5f","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,122,115,80,30,41,114,11,6,69,23,138,14,29,111,134,109,136,4,39,113,48,94,31,36,139,16,5,55,140,147,26,25,90,22,71,126,83,8,89,75,13,102,99,116,119,70,43,110,130,32,86,148,82,84,108,117,100,87,124,88,145,3,34,46,2,132,12,67,112,78,49,45,56,98,72,93,103,121,131,60,118,19,35,51,79,66,104,42,52,15,150,40,77,17,129,91,54,76,10,44,143,85,106,146,128,68,97,73,81,20,24,53,137,92,37,107,27,21,9,28,120,63,149,62,125,142,133,59,57,123,61,7,105,135,18,95,144,141,74,127,38,50,64,33,58,101,96,47,65","comment":"Linear magma over Z/151Z (the prime field F_151): x ◇ y = 60x + 92y (mod 151).","submitted_at":"2026-04-28 16:07:39","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/151/4f3364bd5b92000d2295c0d4214b139f1595449ab2d92ee93602880e41303a5f.txt"},{"canonical_hash":"cf3f61b297ddda40a4eaddca8243f0a0eaba0a7be77fec362fbaaf4033d52130","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,109,21,16,82,13,143,44,9,136,129,104,111,34,19,118,38,57,41,46,134,26,25,58,125,112,36,45,93,22,64,101,56,48,52,78,3,117,62,141,114,73,33,145,115,32,79,103,65,97,113,132,135,70,119,61,130,43,14,6,2,147,12,50,127,51,29,15,99,71,55,66,108,146,106,63,123,49,5,94,92,59,149,42,85,35,150,10,60,17,124,84,67,69,30,24,148,88,131,121,133,91,80,96,74,40,4,76,102,75,37,122,27,31,39,18,105,86,144,95,110,107,138,72,90,128,54,7,140,120,8,98,139,116,87,142,28,53,77,23,81,126,89,47,68,20,11,137,100,83","comment":"Linear magma over Z/151Z (the prime field F_151): x ◇ y = 65x + 87y (mod 151).","submitted_at":"2026-04-28 16:07:41","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/151/cf3f61b297ddda40a4eaddca8243f0a0eaba0a7be77fec362fbaaf4033d52130.txt"},{"canonical_hash":"5f38e8c86c1d8abb817aa26d5a43287b0cd0c02764b35067b6bfef5c5c2f0221","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,14,25,50,138,62,142,7,108,81,69,37,29,16,56,95,20,109,150,59,26,145,106,47,23,6,119,131,58,38,92,112,88,19,31,45,32,99,71,40,148,5,105,110,125,117,101,143,144,30,66,10,134,140,78,49,46,98,27,65,74,114,63,28,76,122,3,70,123,17,13,133,4,102,11,85,33,139,57,80,54,12,79,77,136,137,147,39,53,68,91,61,82,96,146,132,111,141,118,103,8,97,87,86,127,129,43,104,130,107,89,2,135,42,52,35,83,44,48,73,120,34,72,126,22,113,64,124,115,21,149,15,18,128,90,84,41,116,24,94,93,51,67,75,60,55,36,100,9,121","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 122 (count 50, order 50 in F_151*, NOT in H)\n  • ratio δ(d)/d = 143 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:10","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/5f38e8c86c1d8abb817aa26d5a43287b0cd0c02764b35067b6bfef5c5c2f0221.txt"},{"canonical_hash":"7a7b8be778b52fd8aaacdf3f022475849c532699c2cba1d450f1993e67b2a656","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,141,122,125,17,67,36,18,100,74,137,31,3,56,8,50,139,11,88,27,25,102,116,66,52,37,15,138,48,89,13,45,106,40,19,87,124,148,30,24,117,29,75,72,91,38,99,147,21,140,79,92,146,57,16,84,144,44,145,68,73,109,149,110,104,63,136,81,114,6,32,35,49,80,39,103,120,101,5,4,105,61,93,71,58,82,62,77,128,10,14,115,119,85,76,34,133,9,150,46,83,22,126,135,69,65,26,47,78,127,112,132,108,121,143,111,55,41,42,51,70,53,2,130,12,23,20,43,64,131,86,113,54,60,98,59,123,118,95,7,94,134,28,107,96,142,129,90,33,97","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 132 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 94 (count 50, order 25 in F_151*, NOT in H)\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:12","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/7a7b8be778b52fd8aaacdf3f022475849c532699c2cba1d450f1993e67b2a656.txt"},{"canonical_hash":"3055ca0b5f60b3a77f44796f0c97dd54a4623b3605e3294faba27e2d3012eca8","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,94,120,93,28,140,38,49,46,2,123,54,112,63,128,125,106,90,58,146,72,33,108,138,12,66,107,134,55,110,17,71,95,27,99,144,57,43,86,20,44,105,118,51,15,29,127,34,9,50,37,111,11,26,104,147,122,129,21,41,136,7,75,39,4,102,24,45,76,143,130,14,25,61,13,82,119,74,22,70,96,47,135,80,109,132,91,42,113,133,3,97,121,83,65,131,100,103,88,137,79,148,32,16,19,8,115,23,68,145,69,31,30,67,89,73,84,126,114,124,81,141,36,40,62,60,77,117,18,53,35,150,5,78,48,142,52,85,87,10,6,116,56,149,139,101,59,98,64,92","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 10×δ=87 / 5×δ=132.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:87, coset2:87, coset3:132, coset4:87, coset5:87, coset6:132, coset7:87, coset8:87, coset9:132, coset10:87, coset11:87, coset12:132, coset13:87, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:14","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/3055ca0b5f60b3a77f44796f0c97dd54a4623b3605e3294faba27e2d3012eca8.txt"},{"canonical_hash":"c54ddefc1977344bc8f23b978cdbf01d51e805eed34dbcd28941945adbb8a57b","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,146,86,129,119,131,89,78,94,72,15,21,74,100,73,43,120,28,44,26,2,103,84,142,93,108,105,136,70,88,126,52,48,138,118,12,96,137,114,85,140,17,51,75,37,79,124,87,33,66,10,39,135,148,81,5,49,107,29,19,80,47,141,6,31,134,127,102,109,16,46,116,7,55,34,14,132,9,45,56,123,110,24,25,91,18,62,149,54,22,50,76,32,115,60,139,112,71,27,143,113,8,77,101,63,95,111,130,133,68,117,59,128,42,11,4,13,145,3,98,125,99,36,30,97,69,53,64,106,144,104,61,121,41,40,92,90,57,147,23,83,35,150,20,58,38,122,82,65,67","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 10×δ=87 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:87, coset2:87, coset3:143, coset4:87, coset5:87, coset6:143, coset7:87, coset8:87, coset9:143, coset10:87, coset11:87, coset12:143, coset13:87, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:15","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/c54ddefc1977344bc8f23b978cdbf01d51e805eed34dbcd28941945adbb8a57b.txt"},{"canonical_hash":"092d754976d1c4fbe2475cda272f54b9939960a13562220693b73fa971fd0852","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,64,39,49,47,58,80,149,92,117,89,88,17,90,123,22,143,135,119,61,35,68,10,148,24,43,11,96,60,21,132,83,19,14,81,144,46,23,66,2,141,134,86,51,78,13,62,103,104,57,75,38,9,74,97,95,26,55,65,76,71,37,109,79,3,31,25,34,129,59,6,121,126,115,105,20,145,147,124,40,7,125,107,54,53,112,44,128,101,136,84,91,33,116,29,15,94,131,45,50,133,82,27,110,146,42,12,30,100,41,118,4,111,69,85,93,28,73,140,48,138,139,67,142,98,130,108,16,18,8,114,32,99,87,52,56,122,36,113,70,127,150,77,120,63,5,72,106,102,137","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 94 (count 50, order 25 in F_151*, NOT in H)\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 143 (count 50, order 10 in F_151*, IN H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:17","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/092d754976d1c4fbe2475cda272f54b9939960a13562220693b73fa971fd0852.txt"},{"canonical_hash":"a0f77a001aaf65edc65b6347fbc9a65c905074733b1db38dc364c6712915b765","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,81,135,80,32,105,42,28,25,2,118,91,147,50,123,140,131,77,95,121,59,37,103,133,12,53,142,139,92,125,17,58,82,31,86,149,94,47,73,20,48,120,113,88,15,33,112,38,9,87,41,136,11,30,109,132,107,134,21,45,111,7,62,43,4,137,24,49,63,138,145,14,29,98,13,69,124,61,22,57,83,26,100,67,114,117,78,46,108,128,3,84,146,70,52,106,115,148,75,122,66,143,36,16,19,8,130,23,55,110,56,35,34,54,76,60,71,101,119,129,68,116,40,44,99,97,64,102,18,90,39,150,5,65,27,127,89,72,74,10,6,141,93,104,144,126,96,85,51,79","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 5×δ=92 / 5×δ=132.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:87, coset2:92, coset3:132, coset4:87, coset5:92, coset6:132, coset7:87, coset8:92, coset9:132, coset10:87, coset11:92, coset12:132, coset13:87, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:20","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/a0f77a001aaf65edc65b6347fbc9a65c905074733b1db38dc364c6712915b765.txt"},{"canonical_hash":"d131ee90fbd290fd4d4f294cdbf10b59403dde4b2946212b2265bd49a4817deb","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,135,97,148,138,120,50,89,55,83,15,21,85,129,84,38,149,48,39,46,2,112,95,141,54,117,134,125,81,99,115,63,43,147,127,12,57,136,133,96,119,17,62,86,32,90,143,98,28,77,10,34,114,107,92,5,44,106,49,19,91,42,130,6,26,103,126,101,128,16,41,105,7,66,29,14,131,9,40,67,132,139,24,45,52,18,73,118,65,22,61,87,27,144,71,108,111,82,47,102,122,8,88,140,74,56,100,109,142,79,116,70,137,37,11,4,13,124,3,59,104,60,31,25,58,80,64,75,145,113,123,72,110,36,35,53,51,68,146,23,94,30,150,20,69,33,121,93,76,78","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 5×δ=92 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:87, coset2:92, coset3:143, coset4:87, coset5:92, coset6:143, coset7:87, coset8:92, coset9:143, coset10:87, coset11:92, coset12:143, coset13:87, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:24","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/d131ee90fbd290fd4d4f294cdbf10b59403dde4b2946212b2265bd49a4817deb.txt"},{"canonical_hash":"e1e19e6c4151ef01c6916d649437a48946ecac9dc8dca89b4826d61b228f08d4","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,93,141,45,66,111,51,62,59,2,144,83,133,25,149,146,127,82,94,117,95,71,129,109,12,91,128,105,28,131,17,47,38,65,49,115,46,56,96,20,57,126,139,42,15,67,148,72,9,97,50,132,11,64,125,118,143,100,21,54,107,7,33,52,4,123,24,58,81,114,101,14,63,32,13,85,140,88,22,77,86,60,106,92,130,103,27,55,134,104,3,31,142,30,43,102,121,124,89,108,44,119,70,16,19,8,136,23,84,116,29,69,68,36,34,40,78,147,135,145,37,112,74,53,80,87,26,138,18,35,73,150,5,99,61,113,90,48,41,10,6,137,76,120,110,122,39,79,98,75","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 10×δ=132.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:132, coset2:87, coset3:132, coset4:132, coset5:87, coset6:132, coset7:132, coset8:87, coset9:132, coset10:132, coset11:87, coset12:132, coset13:132, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:26","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/e1e19e6c4151ef01c6916d649437a48946ecac9dc8dca89b4826d61b228f08d4.txt"},{"canonical_hash":"643d39f249b3bf8048e24f51ce348eaa004e2a428195be65bd1caf120d51ee5d","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,54,148,87,48,118,33,44,41,2,101,69,140,92,106,103,134,63,60,124,66,28,136,116,12,67,135,112,85,138,17,99,95,47,86,122,93,38,72,20,39,133,146,94,15,49,105,29,9,53,32,139,11,46,132,125,100,107,21,36,114,7,90,34,4,130,24,40,57,121,108,14,45,84,13,56,147,74,22,58,62,42,113,73,137,110,79,37,141,111,3,78,149,97,75,109,128,131,55,115,81,126,27,16,19,8,143,23,50,123,91,26,25,83,96,82,64,104,142,102,89,119,31,35,51,68,98,145,18,77,30,150,5,65,43,120,61,80,88,10,6,144,52,127,117,129,76,70,59,71","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 5×δ=132 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:143, coset2:87, coset3:132, coset4:143, coset5:87, coset6:132, coset7:143, coset8:87, coset9:132, coset10:143, coset11:87, coset12:132, coset13:143, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:28","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/643d39f249b3bf8048e24f51ce348eaa004e2a428195be65bd1caf120d51ee5d.txt"},{"canonical_hash":"ce9bc37e4e16a028ca976028a09f3f8129fc33bfc7d98784808cd262d056da25","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,140,48,123,113,125,80,26,45,47,15,21,40,144,86,66,114,51,67,74,2,147,30,136,91,102,149,130,29,41,120,42,71,132,112,12,38,131,108,94,134,17,88,79,60,90,118,87,56,43,10,62,129,142,83,5,72,101,52,19,44,70,135,6,54,128,121,146,103,16,69,110,7,99,57,14,126,9,68,28,117,104,24,73,98,18,32,143,35,22,49,33,55,109,39,133,106,93,50,137,107,8,97,145,96,84,105,124,127,36,111,85,122,65,11,4,13,139,3,31,119,95,59,53,77,75,81,25,100,138,148,78,115,64,63,27,34,92,141,23,76,58,150,20,46,61,116,37,89,82","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 5×δ=132 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:132, coset2:87, coset3:143, coset4:132, coset5:87, coset6:143, coset7:132, coset8:87, coset9:143, coset10:132, coset11:87, coset12:143, coset13:132, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:30","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/ce9bc37e4e16a028ca976028a09f3f8129fc33bfc7d98784808cd262d056da25.txt"},{"canonical_hash":"a7daa0c95fac0ab7c64fece2b69b369b68153d1c0f187b12b9978ea1dd50551f","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,142,69,125,115,127,93,62,51,63,15,21,71,146,79,35,116,45,36,43,2,149,61,138,84,104,101,132,55,52,122,58,40,134,114,12,59,133,110,77,136,17,91,87,29,78,120,85,25,64,10,31,131,144,86,5,41,103,46,19,70,39,137,6,48,130,123,148,105,16,38,112,7,82,26,14,128,9,37,74,119,106,24,42,76,18,73,145,66,22,50,54,49,111,65,135,108,96,44,139,109,8,95,147,89,92,107,126,129,72,113,98,124,34,11,4,13,141,3,67,121,83,28,47,75,88,99,56,102,140,100,81,117,33,32,68,60,90,143,23,94,27,150,20,57,30,118,53,97,80","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 10×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:143, coset2:87, coset3:143, coset4:143, coset5:87, coset6:143, coset7:143, coset8:87, coset9:143, coset10:143, coset11:87, coset12:143, coset13:143, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:33","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/a7daa0c95fac0ab7c64fece2b69b369b68153d1c0f187b12b9978ea1dd50551f.txt"},{"canonical_hash":"57bd0b3c651522438e756116d241d0ddc8b548ff21c6f069877888a71673325c","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,77,123,66,47,143,32,43,40,2,126,87,115,86,131,128,109,83,81,149,85,27,111,141,12,69,110,137,98,113,17,74,88,46,82,147,70,37,89,20,38,108,121,54,15,48,130,28,9,93,31,114,11,45,107,100,125,132,21,35,139,7,68,33,4,105,24,39,79,146,133,14,44,64,13,95,122,57,22,63,99,41,138,73,112,135,94,36,116,136,3,60,124,56,58,134,103,106,61,140,62,101,26,16,19,8,118,23,91,148,52,25,49,80,72,96,67,129,117,127,84,144,30,34,75,53,90,120,18,76,29,150,5,51,42,145,65,78,50,10,6,119,59,102,142,104,92,71,97,55","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 5×δ=92 / 5×δ=132.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:92, coset2:87, coset3:132, coset4:92, coset5:87, coset6:132, coset7:92, coset8:87, coset9:132, coset10:92, coset11:87, coset12:132, coset13:92, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:35","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/57bd0b3c651522438e756116d241d0ddc8b548ff21c6f069877888a71673325c.txt"},{"canonical_hash":"9e89b287f720f5e9ce5112cc541186808b02e734b2df7b7278b0c8284e189d40","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,109,99,142,132,144,82,61,87,95,15,21,67,113,56,45,133,30,46,28,2,116,77,105,76,121,118,149,73,71,139,75,25,101,131,12,59,100,127,88,103,17,64,78,39,72,137,60,35,79,10,41,148,111,94,5,26,120,31,19,83,49,104,6,33,147,140,115,122,16,48,129,7,58,36,14,145,9,47,69,136,123,24,27,54,18,85,112,97,22,53,89,34,128,63,102,125,84,29,106,126,8,50,114,96,98,124,143,146,51,130,52,141,44,11,4,13,108,3,81,138,92,38,32,70,62,86,57,119,107,117,74,134,43,42,65,93,80,110,23,66,37,150,20,91,40,135,55,68,90","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 5×δ=92 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:92, coset2:87, coset3:143, coset4:92, coset5:87, coset6:143, coset7:92, coset8:87, coset9:143, coset10:92, coset11:87, coset12:143, coset13:92, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:37","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/9e89b287f720f5e9ce5112cc541186808b02e734b2df7b7278b0c8284e189d40.txt"},{"canonical_hash":"89ce585f4851edbba74ee862aed5914477d4af552a8cdf78c19a94aa37f95027","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,65,149,54,49,119,34,45,42,2,132,75,111,74,137,104,145,71,69,135,73,29,117,147,12,57,106,103,86,139,17,62,76,48,70,113,58,39,77,20,40,134,127,92,15,25,126,30,9,81,33,100,11,47,123,146,121,148,21,37,125,7,56,35,4,101,24,41,67,102,109,14,46,52,13,83,138,95,22,51,87,43,114,61,128,131,82,38,122,142,3,98,110,94,96,120,129,112,99,136,50,107,28,16,19,8,144,23,79,124,90,27,26,68,60,84,55,115,133,143,72,130,32,36,63,91,78,116,18,64,31,150,5,89,44,141,53,66,88,10,6,105,97,118,108,140,80,59,85,93","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 10×δ=92 / 5×δ=132.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:92, coset2:92, coset3:132, coset4:92, coset5:92, coset6:132, coset7:92, coset8:92, coset9:132, coset10:92, coset11:92, coset12:132, coset13:92, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:39","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/89ce585f4851edbba74ee862aed5914477d4af552a8cdf78c19a94aa37f95027.txt"},{"canonical_hash":"65d226b60c187fdeb96c074e4fdf40681ed1ca7eeabd9e7e2c27f3cce170f627","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,109,51,122,112,144,84,63,89,97,15,21,69,103,58,30,123,40,31,38,2,136,79,115,78,141,108,149,75,73,139,77,35,121,101,12,61,110,107,90,143,17,66,80,49,74,117,62,45,81,10,26,138,131,96,5,36,130,41,19,85,34,104,6,43,127,100,125,102,16,33,129,7,60,46,14,105,9,32,71,106,113,24,37,56,18,87,142,99,22,55,91,44,118,65,132,135,86,39,126,146,8,52,114,98,50,124,133,116,53,140,54,111,29,11,4,13,148,3,83,128,94,48,42,72,64,88,59,119,137,147,76,134,28,27,67,95,82,120,23,68,47,150,20,93,25,145,57,70,92","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 10×δ=92 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:92, coset2:92, coset3:143, coset4:92, coset5:92, coset6:143, coset7:92, coset8:92, coset9:143, coset10:92, coset11:92, coset12:143, coset13:92, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:41","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/65d226b60c187fdeb96c074e4fdf40681ed1ca7eeabd9e7e2c27f3cce170f627.txt"},{"canonical_hash":"3c0f9b5a025d3dff58619436926e158f1399ef9ef1a93fec5343177f91041d22","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,76,141,27,64,111,74,60,57,2,124,91,103,32,129,146,137,90,77,127,78,69,109,139,12,99,148,145,35,131,17,29,45,63,31,105,28,54,79,20,55,126,119,49,15,65,118,70,9,80,73,142,11,62,115,138,113,140,21,52,117,7,40,50,4,143,24,56,89,144,101,14,61,39,13,93,130,96,22,85,94,58,106,75,120,123,34,53,114,134,3,38,102,37,25,112,121,104,97,128,26,149,68,16,19,8,136,23,92,116,36,67,66,43,41,47,86,107,125,135,44,122,72,51,88,95,33,108,18,42,71,150,5,82,59,133,98,30,48,10,6,147,84,110,100,132,46,87,81,83","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=92 / 10×δ=132.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:132, coset2:92, coset3:132, coset4:132, coset5:92, coset6:132, coset7:132, coset8:92, coset9:132, coset10:132, coset11:92, coset12:132, coset13:132, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:43","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/3c0f9b5a025d3dff58619436926e158f1399ef9ef1a93fec5343177f91041d22.txt"},{"canonical_hash":"25f178bfb833e40b92923cd0968b304569de2ed66e33be7f8277c71ac459c7f6","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,59,146,77,48,116,33,44,41,2,129,74,108,82,134,101,142,68,65,132,71,28,114,144,12,72,103,100,75,136,17,89,85,47,76,110,83,38,52,20,39,131,124,84,15,49,123,29,9,58,32,147,11,46,120,143,118,145,21,36,122,7,80,34,4,148,24,40,62,149,106,14,45,99,13,61,135,54,22,63,67,42,111,53,125,128,94,37,119,139,3,93,107,87,90,117,126,109,60,133,96,104,27,16,19,8,141,23,55,121,81,26,25,98,86,97,69,112,130,140,79,127,31,35,56,73,88,113,18,92,30,150,5,70,43,138,66,95,78,10,6,102,57,115,105,137,91,50,64,51","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=92 / 5×δ=132 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:132, coset1:143, coset2:92, coset3:132, coset4:143, coset5:92, coset6:132, coset7:143, coset8:92, coset9:132, coset10:143, coset11:92, coset12:132, coset13:143, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:44","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/25f178bfb833e40b92923cd0968b304569de2ed66e33be7f8277c71ac459c7f6.txt"},{"canonical_hash":"bf1122ec21ac438c26a9c934c8aef72c3f1b1072cd44bdc1ce5af4eddb206d1d","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,138,21,16,81,13,122,44,9,115,108,133,140,34,19,147,38,56,41,46,113,26,25,67,104,141,36,45,52,22,83,130,95,48,51,87,3,146,61,120,143,82,33,124,144,32,98,132,94,96,142,111,114,99,148,50,109,43,14,6,2,126,12,79,106,90,29,15,68,60,84,55,137,125,135,72,102,49,5,63,91,78,128,42,64,35,150,10,89,17,103,53,66,88,30,24,127,97,110,100,112,80,59,85,93,40,4,65,131,54,37,101,27,31,39,18,134,75,123,74,139,136,117,71,69,107,73,7,119,149,8,57,118,145,86,121,28,62,76,23,70,105,58,47,77,20,11,116,129,92","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 10×δ=87 / 5×δ=92.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:87, coset1:92, coset2:87, coset3:87, coset4:92, coset5:87, coset6:87, coset7:92, coset8:87, coset9:87, coset10:92, coset11:87, coset12:87, coset13:92, coset14:87.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/bf1122ec21ac438c26a9c934c8aef72c3f1b1072cd44bdc1ce5af4eddb206d1d.txt"},{"canonical_hash":"a7cf489ff1cd5329e443981919bdf38d390de5392706d37c2fc7febe182937d8","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,142,40,105,145,127,91,43,37,39,15,21,32,136,97,50,106,60,51,58,2,119,47,148,77,124,141,132,46,33,122,34,55,104,134,12,30,143,140,80,126,17,99,90,69,76,100,98,65,35,10,71,121,114,94,5,56,113,61,19,36,54,137,6,63,110,133,108,135,16,53,112,7,85,66,14,138,9,52,45,139,146,24,57,84,18,49,125,27,22,41,25,64,101,31,115,118,79,59,109,129,8,83,147,82,95,107,116,149,28,123,96,144,74,11,4,13,131,3,48,111,81,68,62,88,86,92,42,102,120,130,89,117,73,72,44,26,78,103,23,87,67,150,20,38,70,128,29,75,93","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=92 / 5×δ=132 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:132, coset2:92, coset3:143, coset4:132, coset5:92, coset6:143, coset7:132, coset8:92, coset9:143, coset10:132, coset11:92, coset12:143, coset13:132, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:48","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/a7cf489ff1cd5329e443981919bdf38d390de5392706d37c2fc7febe182937d8.txt"},{"canonical_hash":"94e87e20bb87109b08412f42b75a866a5d54bb9c021a9d88f5102d66726b15ed","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,32,102,65,50,73,135,114,140,148,15,21,120,48,109,84,28,94,85,92,2,61,130,41,129,30,69,42,126,124,27,128,89,25,45,12,112,72,29,141,33,17,117,131,78,125,44,113,99,132,10,80,64,40,147,5,90,52,95,19,136,88,63,6,97,34,57,31,60,16,87,37,7,111,75,14,26,9,86,122,66,38,24,91,107,18,138,70,100,22,106,142,98,59,116,55,46,137,93,71,51,8,103,53,149,101,68,43,56,104,67,105,35,83,11,4,13,54,3,134,74,145,77,96,123,115,139,110,47,49,39,127,58,82,81,118,146,133,62,23,119,76,150,20,144,79,36,108,121,143","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=92 / 10×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:92, coset2:143, coset3:143, coset4:92, coset5:143, coset6:143, coset7:92, coset8:143, coset9:143, coset10:92, coset11:143, coset12:143, coset13:92, coset14:143.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/94e87e20bb87109b08412f42b75a866a5d54bb9c021a9d88f5102d66726b15ed.txt"},{"canonical_hash":"03c3924e8ad8b561896de944db551208be55f827c655a0a9a8e95915239191d4","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,126,119,84,30,41,118,11,6,83,23,142,14,29,115,138,113,140,4,39,117,48,58,31,36,143,16,5,59,144,101,26,25,94,22,65,130,57,8,53,79,13,106,63,120,123,74,43,114,134,32,80,102,66,98,112,121,104,71,128,62,149,3,34,46,2,136,12,51,116,52,49,45,50,72,56,67,107,125,135,64,122,19,35,95,93,60,108,42,86,15,150,40,61,17,133,85,68,70,10,44,147,89,110,100,132,92,81,97,75,20,24,77,141,76,37,111,27,21,9,28,124,87,103,96,129,146,137,73,91,127,55,7,109,139,18,99,148,145,88,131,38,54,78,33,82,105,90,47,69","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=87 / 10×δ=92.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:92, coset1:87, coset2:92, coset3:92, coset4:87, coset5:92, coset6:92, coset7:87, coset8:92, coset9:92, coset10:87, coset11:92, coset12:92, coset13:87, coset14:92.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:53","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/03c3924e8ad8b561896de944db551208be55f827c655a0a9a8e95915239191d4.txt"},{"canonical_hash":"644c60e3104bb9b63985595a7b7e60e0694e1d289303945ed868366e298562e0","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,149,113,56,52,93,75,109,146,61,144,119,49,17,13,11,145,16,86,85,64,42,35,108,124,76,134,103,67,147,100,73,27,30,118,62,88,101,6,116,45,150,15,66,36,51,138,112,68,25,22,123,148,97,117,53,84,126,74,58,5,12,114,135,136,46,95,41,43,47,19,69,94,111,96,59,125,143,102,106,63,98,31,99,139,14,130,121,127,72,55,24,120,92,39,104,107,128,26,90,20,33,65,79,60,10,28,81,38,18,82,34,133,7,32,87,141,91,137,2,37,83,4,132,48,8,131,23,40,110,129,115,3,50,140,21,78,57,54,9,142,70,29,105,122,77,71,80,44,89","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 129 (count 50, order 150 in F_151*, NOT in H)\n  • ratio δ(d)/d = 92 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 145 (count 50, order 75 in F_151*, NOT in H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:55","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/644c60e3104bb9b63985595a7b7e60e0694e1d289303945ed868366e298562e0.txt"},{"canonical_hash":"d77de3cfff63599fbfb60416319c8526f1ad978fa92c6f892914712770d77ed5","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,61,27,122,107,115,136,30,49,26,15,21,44,72,142,89,52,99,90,97,2,113,34,50,147,69,106,71,33,45,56,46,94,64,59,12,42,119,73,125,57,17,144,135,83,146,63,143,79,47,10,85,101,54,139,5,95,124,75,19,48,93,105,6,77,53,104,65,117,16,92,66,7,130,80,14,60,9,91,32,118,62,24,96,129,18,36,102,39,22,28,37,78,121,43,112,55,149,98,123,103,8,128,120,127,140,110,67,108,40,114,141,74,88,11,4,13,116,3,35,111,126,82,76,133,131,137,29,51,68,58,134,100,87,86,31,38,148,109,23,132,81,150,20,25,84,70,41,145,138","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 10×δ=132 / 5×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:132, coset2:132, coset3:143, coset4:132, coset5:132, coset6:143, coset7:132, coset8:132, coset9:143, coset10:132, coset11:132, coset12:143, coset13:132, coset14:132.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:57","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/d77de3cfff63599fbfb60416319c8526f1ad978fa92c6f892914712770d77ed5.txt"},{"canonical_hash":"459ccbc5610b41cb9c641b20654c23863b85242e74902239ae3f6a70fc0c27e0","size":151,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,39,58,127,137,135,108,61,55,57,15,21,50,30,114,86,35,96,87,94,2,148,65,48,119,37,131,49,64,51,34,52,91,32,27,12,73,134,36,122,40,17,116,107,80,118,26,115,76,53,10,82,126,47,111,5,92,139,97,19,54,90,125,6,99,41,144,38,147,16,89,44,7,102,77,14,33,9,88,63,128,45,24,93,101,18,67,132,70,22,59,68,75,146,74,142,28,121,95,133,138,8,100,140,124,112,130,25,143,71,129,113,42,85,11,4,13,141,3,66,136,123,79,98,105,103,109,60,29,31,46,106,145,84,83,62,69,120,149,23,104,78,150,20,56,81,43,72,117,110","comment":"Size-151 idempotent right-cancellative translation-invariant magma on F_151 (= Z/151 additively). The operation has the form x ◇ y = x + δ_i · (y - x) where δ_i depends on which coset of the order-10 subgroup H ⊂ F_151* the difference (y - x) lies in (15 cosets total).\n\nδ-distribution across the 15 cosets: 5×δ=132 / 10×δ=143.\n\nPer-coset δ values (in the F_151*/H ordering induced by a primitive root): coset0:143, coset1:132, coset2:143, coset3:143, coset4:132, coset5:143, coset6:143, coset7:132, coset8:143, coset9:143, coset10:132, coset11:143, coset12:143, coset13:132, coset14:143.\n\nEach δ_i is one of the 4 primitive 10th roots of unity in F_151* — namely {87, 92, 132, 143} — exactly the roots of the 10th cyclotomic polynomial Φ_10(x) = x⁴ - x³ + x² - x + 1 mod 151. eq677 follows from the per-coset identity α⁴ - α³ + α² - α + 1 ≡ 0. The magma is globally NOT medial.\n\nDisplay reorder relabels points by the cyclic translation group: original index 0 stays at 0, and successive indices follow a fixed magma automorphism of order 151. Under this reorder the Cayley table is Z/151-translation-invariant: T[i+1][j+1] ≡ T[i][j] + 1 (mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:10:59","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/459ccbc5610b41cb9c641b20654c23863b85242e74902239ae3f6a70fc0c27e0.txt"},{"canonical_hash":"451073c43b1c876d7477767f7e07e183be67d5ac7111dbe3e155ee01949fed04","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,27,3,115,21,106,12,5,69,129,111,83,147,85,70,97,52,103,16,9,114,80,96,149,124,44,120,91,112,50,133,87,59,11,48,118,94,63,20,26,30,119,72,57,18,88,60,73,84,51,89,39,22,46,144,17,79,43,81,77,143,76,61,45,14,108,35,137,90,145,58,148,123,56,53,139,86,40,128,92,33,54,6,122,41,136,104,93,7,23,131,55,140,82,95,29,71,49,68,10,101,28,100,99,78,102,130,146,135,38,67,47,138,34,13,15,107,109,142,4,19,116,75,150,74,141,66,65,117,134,132,24,8,32,113,36,98,25,110,121,105,127,42,62,125,2,126,64,31,37","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 94 (count 50, order 25 in F_151*, NOT in H)\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 122 (count 50, order 50 in F_151*, NOT in H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:11:01","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/451073c43b1c876d7477767f7e07e183be67d5ac7111dbe3e155ee01949fed04.txt"},{"canonical_hash":"3528ae88c6aa0234425d74b1bda84ea875a7e11fa0c1d6187f1353c039865213","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,45,62,111,96,116,92,105,127,95,139,11,25,135,54,137,8,114,48,2,10,39,149,115,70,97,138,144,82,143,107,102,79,28,78,118,29,91,80,126,113,74,49,81,133,44,125,106,109,18,51,41,32,84,58,121,21,22,140,42,37,123,34,72,15,30,86,100,148,136,5,40,122,9,73,12,17,90,47,46,71,108,134,7,16,101,43,59,56,75,19,83,131,24,124,63,76,130,141,4,68,128,3,129,52,57,93,132,94,88,147,120,65,98,14,35,27,23,64,33,87,104,85,50,36,89,145,77,55,142,66,146,61,112,20,26,99,103,69,60,13,117,6,150,31,67,38,110,119,53","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 87 (count 100, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 94 (count 50, order 25 in F_151*, NOT in H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:11:02","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/3528ae88c6aa0234425d74b1bda84ea875a7e11fa0c1d6187f1353c039865213.txt"},{"canonical_hash":"eaa05df65d2f4266ab664c14fc02d4c74ee0f1da722d9464b8a41f3400041da0","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,62,108,40,56,109,6,30,119,34,88,42,71,21,125,143,66,140,36,65,63,122,123,133,35,139,54,77,147,68,82,132,118,97,127,104,89,10,83,73,72,113,115,11,90,116,93,75,46,121,17,138,9,69,5,31,59,106,15,58,112,26,99,148,110,101,32,134,18,50,114,76,70,23,102,14,80,79,137,53,61,146,141,3,86,4,107,135,2,24,8,19,124,149,128,16,94,67,55,47,45,12,142,81,38,95,150,145,13,131,92,37,20,22,105,117,144,41,78,98,74,44,33,49,27,85,57,29,136,28,91,96,111,103,87,129,130,39,52,48,120,126,64,25,43,84,7,51,60,100","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 87 (count 100, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 122 (count 50, order 50 in F_151*, NOT in H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:11:05","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/eaa05df65d2f4266ab664c14fc02d4c74ee0f1da722d9464b8a41f3400041da0.txt"},{"canonical_hash":"18ebb6890d340ba51ebafe8b15d861c7fc126833335b5435067ee5064a1d6ea1","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,146,125,65,144,35,127,73,14,121,104,40,4,114,48,53,36,66,5,120,138,131,105,20,60,58,87,118,128,9,134,119,72,142,133,147,97,83,92,122,69,84,34,78,68,137,108,110,45,55,81,88,70,30,116,11,103,23,64,29,15,54,71,39,123,77,10,94,115,75,96,26,99,22,24,79,141,135,27,67,28,145,74,132,149,56,111,136,7,51,18,102,130,46,38,12,33,89,113,93,50,59,62,148,41,19,6,107,76,42,90,150,140,17,126,57,31,44,16,100,112,109,25,143,63,139,8,37,13,21,80,52,43,101,32,86,61,106,98,82,124,95,3,117,2,85,91,129,49,47","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 92 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 94 (count 50, order 25 in F_151*, NOT in H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:11:07","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/18ebb6890d340ba51ebafe8b15d861c7fc126833335b5435067ee5064a1d6ea1.txt"},{"canonical_hash":"899541e178dbb118d421602f497292ec3dd55b9bf722168d47ba86fbfac37f0a","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,4,127,94,45,15,96,115,33,143,79,43,2,35,133,9,51,30,74,132,149,56,17,136,73,47,71,102,130,75,131,63,141,38,6,16,147,3,62,148,85,89,55,39,76,103,90,150,140,53,126,14,105,139,135,100,112,28,97,41,31,13,91,113,81,125,80,52,121,22,123,86,42,106,98,82,124,5,101,34,83,10,27,18,129,93,8,65,146,40,20,144,77,29,26,99,12,104,67,119,114,111,36,95,66,137,120,138,7,50,107,60,58,49,118,128,109,134,23,72,142,46,19,44,21,92,122,48,84,59,78,68,24,108,110,57,25,32,88,70,87,116,145,11,61,64,69,117,54,37","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 122 (count 50, order 50 in F_151*, NOT in H)\n  • ratio δ(d)/d = 92 (count 50, order 10 in F_151*, IN H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:11:09","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/899541e178dbb118d421602f497292ec3dd55b9bf722168d47ba86fbfac37f0a.txt"},{"canonical_hash":"8d2ec49a8b9a696a1d636d8cf85d71f9b883e25534abeb2bfa66546cfda4f317","size":151,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,44,3,95,59,13,131,112,21,16,110,143,32,5,65,14,70,133,85,80,77,20,61,132,103,86,104,39,11,73,126,124,37,84,94,75,100,43,138,108,10,42,22,30,58,88,23,148,125,144,134,17,74,76,123,31,19,54,136,53,82,111,40,127,130,135,83,120,34,115,50,12,93,60,36,41,62,81,33,109,145,48,24,46,99,27,117,6,140,98,114,122,29,102,139,49,137,68,96,141,97,129,107,8,25,15,113,38,128,116,51,55,121,47,142,69,56,150,106,119,92,2,71,105,101,66,78,18,63,35,45,28,57,79,147,91,146,118,87,4,89,52,9,72,64,149,90,26,67,7","comment":"Size-151 non-right-cancellative idempotent translation-invariant magma on F_151 (= Z/151 additively). Operation x ◇ y = x + δ(y - x) for a function δ : F_151 → F_151 with δ(0) = 0. δ IS a permutation (so the magma is left-cancellative), but the column-map x ↦ x + δ(y - x) is NOT injective in x for some y, so the magma is non-right-cancellative.\n\nPer-element ratio distribution (δ(d)/d for d ≠ 0, in F_151* multiplicatively):\n  • ratio δ(d)/d = 87 (count 50, order 10 in F_151*, IN H)\n  • ratio δ(d)/d = 122 (count 50, order 50 in F_151*, NOT in H)\n  • ratio δ(d)/d = 132 (count 50, order 10 in F_151*, IN H)\n\nCompared with the RC variants of this family (all ratios in H = order-10 subgroup of F_151* = {1, 8, 19, 59, 64, 87, 92, 132, 143, 150}), the nRC variants include ratios OUTSIDE H — specifically of orders 25 or 50 — which cause δ to shift the multiplicative coset of (y-x) within F_151*. This shift is what breaks right-cancellativity. The 4 primitive 10th roots of F_151 (= roots of Φ_10 = x⁴-x³+x²-x+1 mod 151) are {87, 92, 132, 143}; ratios outside H are extensions to higher-order roots.\n\nDisplay reorder: relabel points so that the magma's order-151 translation auto acts as i ↦ i+1, making Z/151-translation-invariance visible (T[i+1][j+1] ≡ T[i][j] + 1 mod 151).\n\n[text written by Claude]","submitted_at":"2026-05-13 08:11:11","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/151/8d2ec49a8b9a696a1d636d8cf85d71f9b883e25534abeb2bfa66546cfda4f317.txt"},{"canonical_hash":"1c1647c9850e1bdc2db455abd845ddb5aa4b93fca899fc03f8d5179521b89d97","size":155,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,2,3,147,4,5,6,7,146,116,117,118,119,127,56,57,58,59,149,84,85,86,87,145,76,77,78,79,124,12,13,14,15,136,120,121,122,123,126,108,109,110,111,140,60,61,62,63,143,52,53,54,55,148,100,101,102,103,150,8,9,10,11,137,88,89,90,91,144,92,93,94,95,138,40,41,42,43,154,28,29,30,31,151,68,69,70,71,129,24,25,26,27,152,48,49,50,51,135,36,37,38,39,133,72,73,74,75,128,80,81,82,83,125,112,113,114,115,141,104,105,106,107,153,96,97,98,99,139,20,21,22,23,130,44,45,46,47,134,64,65,66,67,142,16,17,18,19,131,32,33,34,35,132","comment":"F_31(17, 15) base × F_5 fiber: 31 fibers of 5 (each = F_5 sub-magma). Clean fiber bundle: the magma is a (base linear magma) × (fiber linear magma) bundle in which each fiber is itself a sub-magma isomorphic to the fiber factor.","submitted_at":"2026-04-24 11:49:33","submitted_by":null,"url":"https://eq677-magmas.icarm.cloud/magmas/155/1c1647c9850e1bdc2db455abd845ddb5aa4b93fca899fc03f8d5179521b89d97.txt"},{"canonical_hash":"82a1fe8aa6ac4a12c0bb060b1b5f84bf5f7348e4a1237f233ebd314f1eeb8635","size":157,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"156,0,117,52,71,92,45,37,25,131,85,129,150,81,142,20,130,8,124,135,39,116,122,46,104,60,35,59,96,126,2,54,123,57,113,5,78,128,89,9,144,90,70,112,76,99,151,146,58,62,14,87,140,38,13,97,50,63,80,111,118,107,47,44,77,49,11,148,67,125,110,10,32,119,121,139,82,42,114,19,98,138,83,26,24,127,66,15,30,1,53,106,105,133,100,103,12,23,16,136,7,145,41,108,94,84,143,109,6,153,51,56,43,132,17,3,34,88,65,33,72,134,61,18,152,28,149,69,31,40,154,91,4,48,102,27,21,95,79,29,64,74,115,86,137,55,73,141,75,120,93,101,36,155,147,22,68","comment":"Linear magma over Z/157Z (the prime field F_157): x ◇ y = 12x + 32y (mod 157).","submitted_at":"2026-04-28 16:07:42","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/157/82a1fe8aa6ac4a12c0bb060b1b5f84bf5f7348e4a1237f233ebd314f1eeb8635.txt"},{"canonical_hash":"8780cbd77badd70dfbc098e9718ef5b2a6f2dadfceace7824e8f4d7bb07689dd","size":157,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"156,0,134,101,5,90,72,4,128,39,61,111,95,53,127,28,151,103,10,99,84,94,82,155,66,17,24,129,150,142,51,29,122,49,74,83,33,19,70,143,107,1,65,34,105,118,135,35,89,149,40,41,47,44,152,38,121,37,113,146,22,86,52,32,145,132,20,115,97,102,106,31,56,62,42,7,93,104,114,140,78,67,133,16,88,30,57,80,76,71,141,46,6,119,58,26,112,48,120,139,11,147,12,126,18,21,15,14,123,63,9,2,144,79,60,91,136,81,117,96,45,59,109,100,23,148,55,25,116,124,3,50,43,92,138,108,68,110,73,36,77,125,54,153,27,69,85,87,13,154,130,98,64,131,75,8,137","comment":"Linear magma over Z/157Z (the prime field F_157): x ◇ y = 12x + 137y (mod 157).","submitted_at":"2026-04-28 16:07:43","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/157/8780cbd77badd70dfbc098e9718ef5b2a6f2dadfceace7824e8f4d7bb07689dd.txt"},{"canonical_hash":"62ead366753577f5b93971646b772976536cc0c743de29c5a1183d87c9e5f6ca","size":157,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"156,0,37,123,83,65,10,67,43,48,111,44,129,103,113,8,89,31,94,56,71,2,90,128,16,139,63,21,73,98,36,127,49,17,150,141,54,85,102,149,117,61,38,32,50,122,15,121,135,143,26,115,109,112,140,118,119,29,58,146,82,138,14,124,95,18,136,125,7,53,28,5,100,41,45,64,62,120,6,152,77,105,107,88,84,57,151,144,96,153,9,20,134,52,81,130,22,39,30,101,145,76,75,24,69,66,72,142,27,19,78,131,79,93,148,155,104,74,33,59,42,97,25,4,133,92,11,3,55,116,137,106,23,132,12,47,35,114,99,51,147,46,154,70,60,13,87,68,91,86,110,126,108,40,80,1,34","comment":"Linear magma over Z/157Z (the prime field F_157): x ◇ y = 144x + 39y (mod 157).","submitted_at":"2026-04-28 16:07:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/157/62ead366753577f5b93971646b772976536cc0c743de29c5a1183d87c9e5f6ca.txt"},{"canonical_hash":"4cb07e83ec0331e38301bc75f54d12615093a38908c441fb55e92923ec012461","size":157,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"156,0,124,55,141,22,20,138,1,108,39,33,37,98,4,75,123,9,73,49,56,34,50,110,54,94,63,109,120,148,92,78,140,86,26,53,90,100,14,151,21,3,51,93,15,128,127,96,19,117,59,62,80,71,126,105,137,102,113,155,57,10,95,87,2,118,103,119,43,6,18,84,107,42,65,147,31,12,116,142,38,5,121,91,16,81,58,44,32,17,145,77,144,131,61,69,36,83,134,139,76,111,79,152,97,106,88,85,143,45,70,153,154,41,67,25,130,47,125,40,74,64,27,52,60,114,104,66,122,146,135,89,68,28,136,24,8,30,23,99,35,149,101,129,72,11,7,13,82,132,112,46,48,115,29,150,133","comment":"Linear magma over Z/157Z (the prime field F_157): x ◇ y = 144x + 105y (mod 157).","submitted_at":"2026-04-28 16:07:46","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/157/4cb07e83ec0331e38301bc75f54d12615093a38908c441fb55e92923ec012461.txt"},{"canonical_hash":"d022eeee690573c9f55652da5688d8c6bd0fb66a8a89206aaeb22e63f01ec638","size":163,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"162,0,96,157,42,158,22,114,128,8,23,103,108,86,60,7,74,101,88,136,109,40,49,143,54,6,32,149,146,91,89,131,160,29,47,41,34,122,9,12,55,59,126,51,135,150,2,53,140,78,90,27,118,46,14,30,161,62,37,134,35,43,77,106,25,13,115,156,133,69,127,24,120,85,68,151,87,67,98,142,141,75,145,71,72,28,137,17,10,138,15,50,94,57,139,63,5,45,83,95,36,147,113,105,64,107,132,81,100,84,116,48,97,20,148,70,123,159,11,65,121,56,129,125,82,152,52,104,111,117,99,1,61,19,21,76,79,102,155,124,73,119,110,39,66,18,31,144,154,130,16,38,33,93,153,58,44,92,3,112,4,26,80","comment":"Linear magma over Z/163Z (the prime field F_163): x ◇ y = 58x + 64y (mod 163).","submitted_at":"2026-04-28 16:07:47","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/163/d022eeee690573c9f55652da5688d8c6bd0fb66a8a89206aaeb22e63f01ec638.txt"},{"canonical_hash":"cb21ee5a4beab35b0b7aa97443e0a894e35811c4f6c09b9bbef1eb5256fa92d9","size":163,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"162,0,48,6,156,50,71,121,119,29,124,111,145,125,84,150,82,14,60,141,87,110,74,8,108,92,88,18,30,159,113,107,28,100,45,35,134,143,104,114,33,142,161,120,20,139,73,55,4,63,38,37,34,86,160,25,61,130,122,95,76,98,3,99,59,39,12,115,153,31,66,15,97,72,106,81,1,53,77,117,64,41,105,94,19,158,83,148,51,42,102,67,147,96,129,5,17,144,137,89,69,151,68,157,65,24,32,91,123,79,56,132,135,136,93,152,85,103,7,118,22,154,10,131,16,40,11,36,133,109,70,126,43,49,78,128,116,58,62,44,140,155,46,57,9,90,146,52,2,54,27,13,47,26,127,21,23,101,80,75,138,112,149","comment":"Linear magma over Z/163Z (the prime field F_163): x ◇ y = 58x + 157y (mod 163).","submitted_at":"2026-04-28 16:07:49","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/163/cb21ee5a4beab35b0b7aa97443e0a894e35811c4f6c09b9bbef1eb5256fa92d9.txt"},{"canonical_hash":"6fc5dd6ffbf2c04ab7c23187d56a8f6df1b94cd35defe2e9938ab5871b202c80","size":166,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"4,45,39,18,12,131,49,43,22,16,8,53,35,26,0,14,30,51,33,24,132,10,55,37,28,3,1,47,41,20,40,19,13,29,50,133,23,17,9,54,36,27,2,5,46,159,163,149,154,157,161,148,151,153,156,160,155,150,152,158,25,6,7,44,38,134,11,32,48,42,21,15,31,52,34,59,57,60,65,62,165,58,56,63,70,64,67,68,66,61,92,113,119,103,82,130,109,115,78,77,96,105,123,102,86,147,143,140,138,135,164,144,141,136,162,146,145,139,137,142,107,125,80,88,94,129,121,100,84,90,111,117,76,73,98,74,99,108,126,81,128,95,104,122,101,85,91,112,118,71,79,87,93,114,120,127,83,89,110,116,75,72,97,106,124,69","comment":"Size-166 sporadic magma originally constructed and posted by user 3121 in the Zulip discussion of equation 677 [1]. Decomposes as 11 fibers of 15 plus 1 adjoined right-identity element.\r\n\r\n[1] https://leanprover.zulipchat.com/#narrow/channel/458659-Equational/topic/FINITE.3A.20677.20-.3E.20255/near/565902285","submitted_at":"2026-04-28 21:28:15","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/166/6fc5dd6ffbf2c04ab7c23187d56a8f6df1b94cd35defe2e9938ab5871b202c80.txt"},{"canonical_hash":"8c3fe321fb1bea776c24e11aa4d08db38962ad6164328e462e0d219a2ce93b5e","size":167,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"164,111,165,46,62,16,61,146,85,6,140,88,135,34,126,160,158,152,133,154,115,22,91,0,153,58,4,98,116,151,78,7,103,119,43,76,23,49,129,87,156,93,40,97,166,70,161,27,52,3,20,94,101,139,138,37,24,124,147,69,29,35,150,118,55,137,65,117,5,9,2,30,57,39,31,128,72,63,68,148,53,14,155,36,143,82,13,106,80,77,51,17,64,73,132,127,92,67,125,99,79,15,84,113,95,114,86,28,41,104,131,42,100,136,142,10,33,18,1,59,11,123,8,26,163,44,112,102,71,121,56,32,89,134,66,21,75,109,141,145,38,157,45,122,12,149,108,60,83,74,120,48,110,107,159,47,25,19,105,144,81,54,96,50,162,90,130","comment":null,"submitted_at":"2026-05-13 08:26:30","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/167/8c3fe321fb1bea776c24e11aa4d08db38962ad6164328e462e0d219a2ce93b5e.txt"},{"canonical_hash":"999b9730db8f3dee2ce8851a81a496e24a00bf66c938615ac9380b4589d69850","size":169,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"168,0,4,2,7,3,5,9,10,1,6,11,8,12,57,64,141,107,30,108,89,43,160,154,125,72,15,92,49,46,67,163,133,146,96,128,33,75,111,13,156,31,58,152,109,65,123,87,142,73,44,105,18,144,95,99,52,131,38,25,70,78,166,114,136,17,45,132,127,113,48,162,98,77,91,66,145,35,16,126,161,90,34,134,50,76,147,47,112,97,68,23,61,104,119,40,151,83,54,138,27,86,157,122,21,28,149,62,84,81,102,158,55,117,120,139,41,14,143,110,167,74,63,32,42,124,59,106,88,153,20,101,37,80,135,94,130,69,116,148,51,24,165,22,118,82,29,121,103,150,140,159,60,39,56,85,19,79,129,155,164,36,93,115,26,100,137,71,53","comment":"Direct product of two linear magmas: F_13 × F_13. The operation is (x₁, x₂) ◇ (y₁, y₂) = (9x₁ + 11y₁ (mod 13), 9x₂ + 11y₂ (mod 13)).","submitted_at":"2026-04-28 16:08:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/169/999b9730db8f3dee2ce8851a81a496e24a00bf66c938615ac9380b4589d69850.txt"},{"canonical_hash":"dba976f1b1267cc455f832b2c24df0db38c6e9de3f93160fff3ca0b2db488fb4","size":169,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"168,0,129,12,40,26,73,157,101,115,87,54,143,19,14,124,15,107,22,158,86,58,95,126,148,113,80,156,75,119,35,165,76,37,18,59,83,24,2,122,48,125,117,70,102,68,92,39,118,4,161,60,150,98,5,79,145,120,30,153,96,85,67,130,146,136,16,132,106,116,131,62,65,71,53,82,84,139,33,162,109,100,36,29,28,127,140,63,13,121,138,108,6,46,88,147,3,52,103,104,111,25,34,78,61,7,9,166,128,155,149,137,56,41,31,57,91,66,167,55,151,10,21,69,105,45,1,163,142,23,47,135,77,141,43,114,17,152,27,154,42,50,123,164,144,99,8,134,93,112,160,81,110,44,159,72,94,38,64,51,20,133,11,74,97,32,90,49,89","comment":"Linear magma over the extension field F_169 = F_13[α]/⟨α² - 2⟩.\n\nOperation: x ◇ y = a·x + b·y in F_169 with (a, b) = (3, 8 + α). Here β = 8 + α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_169, and α_coef = -β³ - β - 1 = 3 (in F_169). This is Pace Nielsen's Type-2 non-fully-idempotent linear 677 magma family.\n\nF_169 is the proper degree-2 extension of F_13; do NOT confuse with the ring Z/169Z (which has zero divisors and is NOT a field).\n\nSize 169, not fully idempotent, right-cancellative.\n\n[text written by Claude]","submitted_at":"2026-04-28 18:08:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/169/dba976f1b1267cc455f832b2c24df0db38c6e9de3f93160fff3ca0b2db488fb4.txt"},{"canonical_hash":"9ba2c3252a9217772b22e8d7a201f43492237b78e5f5e4a2d2cf32684f5a192d","size":171,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"170,144,156,153,149,150,146,148,160,152,161,151,157,155,159,158,145,147,154,162,85,123,39,53,117,77,61,13,101,47,109,6,131,21,29,93,69,139,165,121,9,33,89,81,113,97,127,65,1,73,43,17,135,35,57,105,25,164,112,42,24,80,72,104,88,2,56,32,64,142,50,126,134,120,96,16,166,58,18,0,98,90,122,106,136,74,128,82,10,26,36,44,66,114,34,163,103,141,15,71,63,95,79,31,119,23,55,133,41,3,125,111,87,49,168,76,5,138,116,108,68,52,46,92,38,100,28,143,12,20,84,60,130,167,67,27,129,107,99,59,115,37,83,137,91,19,4,45,11,75,51,8,169,94,132,48,62,54,86,70,22,110,14,118,124,140,30,7,102,78,40","comment":"Direct product of two linear magmas: F_9 × F_19(7,3).","submitted_at":"2026-04-28 16:31:04","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/171/9ba2c3252a9217772b22e8d7a201f43492237b78e5f5e4a2d2cf32684f5a192d.txt"},{"canonical_hash":"ed855124232b703748d5095d0c94bbf1766e8923a90571cf2bd41cc2010079cd","size":175,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"150,18,67,98,43,121,72,151,17,66,99,42,123,74,152,2,51,111,27,135,86,174,148,147,149,146,144,145,153,1,50,110,26,134,85,154,12,61,104,37,128,79,162,13,62,103,38,127,78,166,6,55,115,31,139,90,170,23,70,117,46,142,93,158,7,56,106,32,130,81,161,16,65,100,41,124,75,169,9,58,96,34,122,91,157,0,48,109,24,133,84,173,20,68,118,44,140,95,165,3,52,112,28,136,87,168,10,59,97,35,120,73,160,15,64,101,40,125,76,164,4,53,113,29,137,88,172,21,69,119,45,143,94,156,19,49,108,25,132,83,163,14,63,102,39,126,77,155,11,60,105,36,129,80,159,8,57,107,33,131,82,171,22,71,116,47,141,92,167,5,54,114,30,138,89","comment":"Direct product of two linear magmas: F_5(2,4) × F_5(2,4) × F_7(4,1).","submitted_at":"2026-04-28 16:31:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/175/ed855124232b703748d5095d0c94bbf1766e8923a90571cf2bd41cc2010079cd.txt"},{"canonical_hash":"b9de522453e3fa122a64cff43bfc0df3d92e544d29dc14c1457437ec5f7fa4d2","size":175,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"150,0,24,48,12,60,36,151,11,25,49,13,61,37,167,122,113,97,132,72,84,165,121,109,98,134,74,86,159,9,33,57,21,69,45,153,3,27,51,15,63,39,154,4,28,52,16,64,40,158,8,32,56,20,68,44,173,130,116,105,142,81,93,168,129,115,106,141,82,94,157,7,31,55,19,67,43,174,149,145,147,144,148,146,155,5,29,53,17,65,41,163,127,117,102,138,79,91,171,120,108,99,135,75,87,162,124,112,100,136,76,88,170,126,110,103,139,78,90,166,123,119,96,133,73,85,172,131,118,104,143,80,92,152,2,26,50,14,62,38,161,1,35,59,23,71,47,169,128,114,107,140,83,95,160,10,34,58,22,70,46,156,6,30,54,18,66,42,164,125,111,101,137,77,89","comment":"Direct product of two linear magmas: d732efd1 × F_7(4,1).","submitted_at":"2026-04-28 19:31:53","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/175/b9de522453e3fa122a64cff43bfc0df3d92e544d29dc14c1457437ec5f7fa4d2.txt"},{"canonical_hash":"1d93b59bf84639434b5500fba18daa567b76c24b559b5d4f85b24c96818ebd06","size":175,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"150,0,98,122,50,26,74,151,10,107,131,59,35,83,166,15,111,135,63,39,87,165,13,109,133,61,37,85,159,7,104,128,56,32,80,153,1,97,120,49,24,73,154,2,99,123,51,27,75,158,6,103,127,55,31,79,173,17,113,137,65,41,89,169,18,114,138,66,42,90,157,5,102,126,54,30,78,174,149,148,144,146,145,147,155,3,100,124,52,28,76,163,23,119,143,71,47,95,171,14,110,134,62,38,86,162,21,117,141,69,45,93,170,22,118,142,70,46,94,167,12,108,132,60,36,84,172,19,115,139,67,43,91,152,11,96,121,48,25,72,161,9,106,130,58,34,82,168,16,112,136,64,40,88,160,8,105,129,57,33,81,156,4,101,125,53,29,77,164,20,116,140,68,44,92","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_7(4,3).","submitted_at":"2026-04-28 19:31:54","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/175/1d93b59bf84639434b5500fba18daa567b76c24b559b5d4f85b24c96818ebd06.txt"},{"canonical_hash":"8c2e93f24bfb71860ff9bac35b6807b78e0274fa1dc0003cf7809e6dc47f7199","size":176,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,11,170,8,6,5,7,2,13,3,10,12,4,14,9,32,44,33,166,34,43,30,39,38,41,36,35,42,37,40,31,27,24,28,169,16,15,26,22,19,17,18,20,25,29,23,21,138,146,149,168,139,145,147,144,140,135,137,136,143,148,141,142,123,121,124,175,129,134,122,131,126,133,128,127,120,125,132,130,71,72,65,173,74,61,63,60,70,67,62,69,66,64,73,68,80,77,81,172,86,75,79,88,83,76,85,84,78,82,89,87,101,98,102,171,94,90,96,100,99,92,93,104,95,103,97,91,45,50,54,165,59,47,49,48,52,55,46,58,53,56,51,57,153,163,155,167,161,164,152,159,160,154,150,157,156,158,151,162,106,116,109,174,119,112,111,113,107,105,115,108,114,110,117,118","comment":"Tao(F_11,β=9) × F_16(ζ=8,ω=6). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-24 11:50:47","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/176/8c2e93f24bfb71860ff9bac35b6807b78e0274fa1dc0003cf7809e6dc47f7199.txt"},{"canonical_hash":"43f0cc11902a00070180e5a8c5b6305d82e2ae790f42e30a6705254aea583d00","size":176,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,7,56,46,20,32,40,17,24,28,36,13,142,11,52,42,57,9,50,48,22,5,34,19,26,30,38,15,141,3,54,44,58,2,53,43,25,29,37,14,21,4,33,18,140,8,49,47,126,81,134,91,75,114,116,98,120,102,85,110,135,87,130,106,143,145,155,153,149,172,151,146,148,150,152,147,174,144,156,154,71,73,66,62,68,69,74,67,72,63,61,70,175,65,60,64,170,164,157,160,159,165,168,162,167,163,158,166,171,161,169,173,59,1,55,45,27,31,39,16,23,6,35,12,139,10,51,41,124,79,133,89,77,112,122,96,118,100,83,108,136,93,128,104,129,105,132,94,84,109,119,101,123,97,78,113,137,90,125,80,127,103,76,92,82,115,117,99,121,95,86,111,138,88,131,107","comment":"Tao(F_11,β=5) × F_16(ζ=8,ω=6). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 16:53:33","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/176/43f0cc11902a00070180e5a8c5b6305d82e2ae790f42e30a6705254aea583d00.txt"},{"canonical_hash":"ac3b427a70ae8b4f3a46f409b0ea386180860e4baab22a69883d08db58aa46d2","size":176,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,3,14,35,10,39,8,28,45,18,139,55,59,51,41,22,5,32,15,36,11,40,9,29,46,19,142,56,4,52,42,23,145,150,146,152,147,151,144,172,153,149,174,155,143,156,154,148,108,112,95,99,118,122,91,87,81,77,136,133,124,128,105,101,7,27,17,38,13,34,1,31,48,21,141,50,57,54,44,25,65,73,74,61,72,68,62,64,67,70,175,71,66,60,63,69,113,109,100,96,123,119,88,92,75,82,137,132,129,125,102,106,2,30,12,33,16,37,6,26,43,24,140,53,58,49,47,20,166,165,162,163,167,168,161,160,158,159,171,157,170,169,164,173,111,115,98,94,121,117,86,90,84,80,138,79,127,131,107,104,110,114,97,93,120,116,85,89,83,76,135,134,126,130,78,103","comment":"Tao(F_11,β=5) × F_16(ζ=8,ω=7). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:54:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/176/ac3b427a70ae8b4f3a46f409b0ea386180860e4baab22a69883d08db58aa46d2.txt"},{"canonical_hash":"5386346c2f0edc0868b4bd6c8fd13b79862d0713128148c706f1ff4dde0edb7b","size":176,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,170,10,6,14,7,5,12,8,9,3,4,11,13,2,30,42,166,36,31,38,33,44,35,32,40,41,37,43,39,34,20,23,169,24,29,22,16,17,18,26,27,28,25,15,19,21,139,138,168,143,149,140,147,145,142,148,136,135,144,146,137,141,125,128,175,129,124,134,120,127,123,131,132,133,130,126,121,122,70,73,173,64,68,72,69,67,63,74,61,65,66,62,60,71,80,83,172,84,79,89,75,82,78,86,87,88,85,81,76,77,90,95,171,100,92,94,102,96,97,103,99,93,98,104,101,91,45,59,165,48,52,58,55,50,46,56,51,53,49,57,47,54,154,151,167,164,157,159,163,158,152,161,160,155,156,162,153,150,111,105,174,106,114,107,118,115,113,119,109,110,116,117,108,112","comment":"Tao(F_11,β=9) × F_16(ζ=8,ω=7). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:55:05","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/176/5386346c2f0edc0868b4bd6c8fd13b79862d0713128148c706f1ff4dde0edb7b.txt"},{"canonical_hash":"355635ab8bef1e5d48451d25a96d293ccb3daad8e2a14bc0338f09e8e99d788e","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,14,17,142,73,21,139,88,134,171,61,70,170,160,114,55,18,177,57,41,91,136,16,105,148,56,85,5,50,112,31,131,22,81,51,69,168,26,4,24,64,58,94,59,34,72,67,75,90,127,132,167,119,79,118,124,157,137,159,35,129,111,96,155,71,164,52,110,138,100,116,15,45,149,3,76,174,117,44,151,115,54,27,37,130,121,38,74,103,6,154,133,9,150,147,179,178,63,65,144,156,13,39,89,176,32,102,80,98,175,126,145,92,163,60,108,53,84,7,62,93,82,162,158,141,152,2,40,106,153,68,47,101,166,10,161,109,169,180,36,49,28,143,33,86,107,128,20,46,173,135,19,8,25,29,97,78,122,140,99,113,48,120,30,77,12,66,42,83,95,87,165,43,104,172,146,23,11,125,123","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 43x + 139y (mod 181).","submitted_at":"2026-04-28 16:07:50","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/355635ab8bef1e5d48451d25a96d293ccb3daad8e2a14bc0338f09e8e99d788e.txt"},{"canonical_hash":"5c97e821f6fe61aaee832bc2bfc74754529cbb7d25901b7fd5f1bbca46659af5","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"180,0,84,160,169,150,118,115,37,9,108,14,18,142,15,125,27,45,62,85,8,59,67,32,71,174,100,138,68,168,52,31,80,143,5,49,147,145,170,176,61,47,144,11,152,3,22,72,156,141,42,79,126,78,96,133,153,119,36,121,137,50,21,93,165,166,101,159,88,66,134,46,105,136,103,23,38,98,44,24,146,172,132,54,102,69,64,17,110,30,86,41,75,65,157,109,114,57,99,177,2,6,164,89,53,83,163,58,122,60,91,120,111,43,19,56,26,25,48,161,95,123,135,81,74,13,178,51,33,140,34,87,127,16,117,162,173,12,151,130,92,106,179,1,131,7,94,175,129,35,76,97,28,113,124,55,4,116,77,112,104,148,40,107,90,167,139,155,128,158,154,63,149,82,70,73,10,29,20,39,171","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 48x + 15y (mod 181).","submitted_at":"2026-04-28 16:07:52","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/5c97e821f6fe61aaee832bc2bfc74754529cbb7d25901b7fd5f1bbca46659af5.txt"},{"canonical_hash":"6960b95b8bdb2bb74f12ce487743199e69f00fa7231c7f044059a05122fc1b0b","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"180,0,132,115,39,107,58,25,145,41,50,63,164,104,111,69,88,9,147,5,156,130,169,159,71,61,15,166,54,154,175,75,31,152,127,122,90,121,123,30,99,153,37,14,76,158,102,155,18,8,167,110,117,62,73,144,160,142,97,131,82,27,6,56,137,10,95,67,70,85,65,105,33,34,64,150,66,42,136,35,26,92,96,108,143,138,116,80,7,2,101,83,29,21,98,134,120,161,126,78,74,12,53,118,60,48,168,46,4,3,87,47,103,52,49,77,24,119,38,20,13,100,113,79,124,178,162,91,44,135,128,149,22,32,173,84,176,94,1,55,171,81,16,141,139,72,140,109,170,17,93,157,172,36,148,179,43,89,177,151,112,174,19,165,23,106,51,129,86,146,45,68,59,163,11,40,125,57,133,114,28","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 48x + 33y (mod 181).","submitted_at":"2026-04-28 16:07:53","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/6960b95b8bdb2bb74f12ce487743199e69f00fa7231c7f044059a05122fc1b0b.txt"},{"canonical_hash":"e8378e6065d355d973f5d5311fbf599a750d905373650dac193ec2e17cc43eba","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,90,58,179,15,38,93,57,154,98,22,178,95,68,139,14,174,114,132,37,28,86,66,92,116,167,142,56,120,170,108,153,125,165,11,97,122,161,137,21,41,73,82,177,159,129,59,94,23,140,133,67,143,109,12,138,83,60,134,13,135,46,45,173,102,54,44,113,149,70,172,131,48,33,101,36,19,31,53,27,156,118,43,85,50,6,112,65,4,105,148,91,39,99,69,115,87,168,171,166,162,74,130,141,110,61,47,55,71,34,32,119,7,106,100,169,75,62,35,107,63,180,18,152,80,17,30,124,145,151,52,164,77,79,26,10,2,16,155,96,175,29,117,121,126,123,42,160,24,144,84,136,103,150,49,20,157,51,5,40,88,163,111,72,8,76,64,81,146,78,3,176,127,25,104,158,89,9,147,128","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 60x + 122y (mod 181).","submitted_at":"2026-04-28 16:07:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/e8378e6065d355d973f5d5311fbf599a750d905373650dac193ec2e17cc43eba.txt"},{"canonical_hash":"5c9529786213dc57186719a72af778adf5fb0b06f7c92b2d685a9e8666f30763","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,175,75,116,148,71,9,163,65,156,45,27,170,41,121,135,162,26,109,159,145,19,5,86,141,66,52,80,49,85,44,139,67,120,149,7,90,70,92,33,39,20,32,2,134,78,43,117,93,73,18,131,22,57,169,180,12,150,115,42,111,100,82,69,132,105,36,48,157,113,128,158,81,118,88,53,56,63,124,174,133,96,3,107,6,123,176,97,51,112,61,34,25,110,14,179,64,130,13,161,8,31,122,15,166,119,55,23,102,140,47,46,62,143,114,30,94,17,72,24,10,177,38,106,137,126,138,87,16,76,4,104,101,152,40,11,160,153,147,125,60,151,154,91,95,136,171,84,89,29,58,144,68,54,28,35,168,129,59,74,77,50,103,164,98,173,37,172,79,127,142,167,108,99,165,83,155,21,178,146","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 126x + 56y (mod 181).","submitted_at":"2026-04-28 16:07:56","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/5c9529786213dc57186719a72af778adf5fb0b06f7c92b2d685a9e8666f30763.txt"},{"canonical_hash":"df073ec93cbe5c1ac9bb708444453f984c4b6037f14c9da6afd8bae2ee8cb71d","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"180,0,165,140,122,160,97,103,79,72,117,62,54,176,60,92,36,63,179,163,74,35,14,89,6,112,133,25,12,124,49,91,173,174,15,55,166,170,120,108,31,59,172,68,156,19,46,4,148,178,69,175,90,177,141,9,154,95,81,100,27,53,48,147,130,128,131,142,157,16,7,61,123,29,127,44,77,137,65,42,168,116,11,45,129,10,3,56,113,93,161,71,24,18,146,115,105,39,135,106,2,78,132,155,47,167,134,37,98,33,151,102,111,67,52,41,38,40,57,138,143,96,5,171,26,64,104,51,87,21,85,159,88,58,99,136,114,66,158,82,149,121,13,30,80,76,145,110,84,83,22,139,34,107,94,43,17,101,20,109,125,164,73,119,153,126,23,150,86,144,152,1,162,169,8,28,70,32,50,75,118","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 132x + 54y (mod 181).","submitted_at":"2026-04-28 16:07:58","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/df073ec93cbe5c1ac9bb708444453f984c4b6037f14c9da6afd8bae2ee8cb71d.txt"},{"canonical_hash":"45b4632cc18d253095da62e522b21780d8c2c66d682cae136e74c6a15b2b3980","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"180,0,23,18,163,41,158,44,140,153,10,43,135,175,13,30,117,144,130,164,37,8,12,70,112,53,6,125,40,22,32,92,94,7,121,56,107,151,141,26,152,100,35,109,39,165,47,90,89,59,179,116,33,138,102,55,155,136,162,101,147,172,69,168,71,49,34,15,98,42,171,122,84,31,128,3,118,58,166,20,129,97,77,126,150,156,86,157,154,114,142,52,2,64,67,38,66,60,174,167,24,177,93,76,148,1,115,176,79,36,170,123,132,25,113,82,139,161,78,159,124,57,28,72,46,65,145,29,48,81,4,120,149,16,17,137,75,87,11,83,27,62,99,51,61,9,146,169,105,21,19,80,95,88,173,104,143,14,160,110,106,85,74,178,54,5,103,111,127,45,133,108,63,50,134,68,131,73,91,96,119","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 132x + 78y (mod 181).","submitted_at":"2026-04-28 16:07:59","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/45b4632cc18d253095da62e522b21780d8c2c66d682cae136e74c6a15b2b3980.txt"},{"canonical_hash":"d836a20987955de00b875cadcfdc5f124490d6b0c467c38554841e4ac99ea574","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,85,89,27,134,168,79,13,68,60,126,83,76,137,108,159,21,95,51,147,87,128,149,144,176,56,162,119,142,25,47,73,35,16,32,115,7,174,132,165,3,62,53,121,9,180,54,166,8,17,48,120,177,129,52,160,77,61,80,28,2,70,97,164,117,11,131,99,104,173,42,102,6,140,66,114,153,92,31,38,171,15,23,58,34,123,179,72,44,40,46,45,124,24,39,154,141,43,100,118,71,81,161,178,18,55,122,4,175,33,74,143,57,150,148,22,138,127,14,135,86,170,110,146,37,64,50,30,106,94,91,156,20,152,112,158,113,157,107,65,111,136,139,151,75,5,19,82,101,155,125,41,90,59,172,93,67,103,105,12,98,29,78,130,49,167,10,63,133,116,36,26,163,145,88,96,109,84,69,169","comment":"Linear magma over Z/181Z (the prime field F_181): x ◇ y = 136x + 46y (mod 181).","submitted_at":"2026-04-28 16:08:01","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/181/d836a20987955de00b875cadcfdc5f124490d6b0c467c38554841e4ac99ea574.txt"},{"canonical_hash":"2c0a619ddc1b123a88bf06021406aa6195ec1abb3f4373825c7df4f9324856fd","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,155,58,118,15,38,176,57,93,91,22,171,160,68,168,14,113,143,179,37,28,86,66,139,127,124,99,56,95,145,101,146,100,140,11,144,169,172,94,21,41,73,82,134,98,158,59,123,23,115,126,67,136,138,12,131,83,60,163,13,110,46,45,166,149,54,44,106,178,70,129,142,48,33,112,36,19,31,53,27,167,111,43,85,50,6,159,65,4,170,141,102,39,128,69,90,87,161,92,177,119,74,105,152,175,61,47,55,71,34,32,148,7,117,165,108,75,62,35,154,63,180,18,109,80,17,30,153,120,162,52,103,77,79,26,10,2,16,130,107,150,29,164,132,137,116,42,135,24,173,84,147,96,125,49,20,114,51,5,40,88,156,122,72,8,76,64,81,157,78,3,97,174,25,133,151,89,9,104,121","comment":"Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 122·d when d is a quadratic residue mod 181, and f(d) = 46·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:32","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/2c0a619ddc1b123a88bf06021406aa6195ec1abb3f4373825c7df4f9324856fd.txt"},{"canonical_hash":"7580f29f9f1b81ce8cffad189b0e4037b0ea5d85764cbbe1e6876ffe003b584a","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,14,17,78,138,21,75,168,119,62,96,150,61,51,139,120,18,68,172,41,171,72,16,175,84,146,90,5,170,177,31,131,22,166,106,124,59,26,4,24,174,108,159,134,34,112,162,100,145,117,157,58,179,114,153,129,48,73,50,35,169,151,121,46,176,55,132,125,74,135,101,15,130,85,3,126,65,127,44,87,165,94,27,37,105,141,38,164,123,6,45,93,9,86,83,70,69,148,110,80,47,13,39,104,67,32,97,140,173,66,91,81,107,54,160,163,158,154,7,122,133,102,53,49,77,88,2,40,111,89,98,92,161,57,10,52,99,60,180,36,144,28,79,33,116,137,143,20,156,64,71,19,8,25,29,147,178,167,76,109,113,118,115,30,152,12,136,42,128,95,142,56,43,149,63,82,23,11,155,103","comment":"Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 139·d when d is a quadratic residue mod 181, and f(d) = 122·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:34","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/7580f29f9f1b81ce8cffad189b0e4037b0ea5d85764cbbe1e6876ffe003b584a.txt"},{"canonical_hash":"8c3de954cbb4dda8ba3c3bc092489f3cdba76d02b158e6348d849ae74f6721e0","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,148,139,27,94,166,40,106,151,14,108,25,104,48,83,85,105,127,29,17,64,129,5,165,55,161,115,144,112,155,51,80,171,73,59,7,82,156,57,22,46,130,21,2,119,169,50,88,67,164,128,125,132,172,103,180,43,69,35,49,31,61,170,146,117,66,52,111,15,33,122,16,160,98,140,116,162,176,68,138,118,97,3,86,6,58,158,62,114,32,167,23,126,30,36,143,141,124,44,10,8,20,93,37,100,63,152,133,81,90,110,109,177,75,34,19,77,39,154,134,41,168,45,76,60,120,70,175,38,149,4,56,71,89,47,42,9,11,84,78,157,79,12,92,87,95,153,145,150,18,137,54,136,142,26,24,102,123,147,174,159,113,91,107,72,173,53,163,179,121,65,101,28,96,99,135,13,131,178,74","comment":"Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 56·d when d is a quadratic residue mod 181, and f(d) = 139·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:36","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/8c3de954cbb4dda8ba3c3bc092489f3cdba76d02b158e6348d849ae74f6721e0.txt"},{"canonical_hash":"2f9657895c93273cfaf7753200a41d127846a5b515e97517c07bf79b308a99c1","size":181,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,70,121,9,143,46,109,57,101,124,44,39,110,162,84,11,4,26,40,38,20,28,170,129,89,176,99,69,112,153,135,114,134,12,165,29,100,161,48,65,92,23,37,158,163,105,90,175,2,68,75,87,113,173,137,118,78,32,82,147,159,59,157,62,131,141,125,67,83,73,120,17,117,19,24,140,178,136,60,79,7,55,144,133,126,171,86,179,47,8,18,95,156,34,123,106,3,42,152,10,167,76,56,77,22,54,127,41,88,146,71,15,154,160,96,98,149,145,166,142,21,52,97,102,66,43,115,51,104,85,164,63,128,155,31,169,107,6,151,61,111,130,138,172,150,36,50,35,148,139,91,45,122,13,132,5,116,180,58,177,74,168,64,103,33,81,25,93,108,94,27,16,80,72,53,119,30,174,49,14","comment":"Size-181 idempotent non-right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 139·d when d is a quadratic residue mod 181, and f(d) = 176·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:38","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/2f9657895c93273cfaf7753200a41d127846a5b515e97517c07bf79b308a99c1.txt"},{"canonical_hash":"f14f808fdebadfb339ee419f3efd5fd9dc0bee42c6261f7a0c5328024e0a6c86","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,14,17,50,107,21,47,137,124,79,173,101,78,68,144,161,18,85,105,41,158,89,16,126,56,133,131,5,121,110,31,118,22,153,93,129,76,26,4,24,179,167,164,139,34,135,95,141,96,140,90,75,94,119,122,134,65,45,67,35,174,138,108,63,163,72,155,166,46,176,178,15,171,57,3,113,82,150,44,59,116,99,27,37,146,128,38,169,92,6,62,152,9,58,55,87,86,117,151,52,64,13,39,109,84,32,120,91,142,83,168,53,130,71,111,132,127,159,7,145,102,125,70,66,49,60,2,40,98,61,157,115,148,74,10,69,104,77,180,36,149,28,51,33,103,160,112,20,143,81,88,19,8,25,29,170,147,100,48,114,172,177,156,30,175,12,123,42,97,136,165,73,43,154,80,54,23,11,106,162","comment":"Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 139·d when d is a quadratic residue mod 181, and f(d) = 46·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:45","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/f14f808fdebadfb339ee419f3efd5fd9dc0bee42c6261f7a0c5328024e0a6c86.txt"},{"canonical_hash":"70249bf6f30b97f16867a295f6d738e462498dbbdac33235e7d483a37e89e6ad","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,105,141,38,164,123,72,10,93,51,25,34,17,87,148,110,9,61,40,45,104,54,5,97,140,173,23,91,20,107,81,160,163,158,154,7,122,133,102,31,85,55,30,2,63,111,89,98,92,161,62,69,57,99,16,180,75,144,37,88,42,116,137,143,70,156,82,19,52,44,66,53,147,178,167,24,109,113,118,115,71,152,3,136,6,128,95,142,22,43,149,32,60,41,77,155,103,68,76,47,8,29,138,78,13,168,119,58,96,150,18,26,139,120,36,28,172,80,171,59,73,175,84,146,90,64,170,177,79,131,4,166,106,124,86,74,46,48,174,108,159,134,49,112,162,100,145,117,157,27,179,114,153,129,35,33,15,67,169,151,121,21,176,11,132,125,83,135,101,65,130,14,39,126,12,127,50,56,165,94","comment":"Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 56·d when d is a quadratic residue mod 181, and f(d) = 122·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/70249bf6f30b97f16867a295f6d738e462498dbbdac33235e7d483a37e89e6ad.txt"},{"canonical_hash":"3beeddeed1cde1c1424a9062aa9dd6ab2a12b2c89b1b1f58fabb13ec511eb9fb","size":181,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,103,33,32,109,80,168,135,44,39,137,157,118,56,40,123,52,69,164,115,6,136,91,54,89,51,66,122,12,174,30,17,64,38,141,22,53,26,88,50,158,48,85,35,4,29,166,92,172,143,108,21,110,98,163,113,159,82,179,124,154,167,37,149,62,126,111,146,114,3,76,9,55,27,129,112,63,175,116,58,20,77,176,104,75,31,140,49,169,170,43,177,93,119,121,90,84,99,165,81,73,78,125,10,142,19,150,127,94,97,162,151,46,130,60,11,47,42,160,15,153,161,105,173,57,71,134,171,5,72,144,145,41,155,128,139,180,79,68,18,101,7,87,132,178,34,74,131,117,36,45,24,16,152,23,102,107,148,120,70,106,14,25,86,2,67,13,156,83,147,65,138,133,95,28,8,96,100,61,59","comment":"Size-181 idempotent non-right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 48·d when d is a quadratic residue mod 181, and f(d) = 139·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:49","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/3beeddeed1cde1c1424a9062aa9dd6ab2a12b2c89b1b1f58fabb13ec511eb9fb.txt"},{"canonical_hash":"ddf8aaa4de5b63c69b5e463ffef52f398538147a138758661538cddcf5aacec7","size":181,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,164,146,68,97,110,34,40,170,61,86,12,38,46,135,169,39,18,70,55,127,20,5,138,109,160,84,96,81,148,49,129,150,145,177,7,163,120,143,9,53,21,17,2,73,116,48,175,133,166,19,79,23,122,37,180,28,167,67,47,63,121,178,130,80,161,50,89,62,65,76,54,98,165,118,85,132,100,105,174,72,103,3,141,6,115,154,93,83,64,172,10,26,71,30,124,90,78,29,57,8,16,125,31,43,155,142,24,101,119,88,87,162,179,66,15,123,33,176,25,35,144,52,151,149,74,139,128,32,136,4,171,111,147,45,27,56,58,107,95,92,157,59,153,113,159,114,158,108,14,112,137,140,152,13,11,36,77,102,156,126,82,91,41,173,94,51,104,106,75,99,44,69,131,42,168,60,22,134,117","comment":"Size-181 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. Tao Type II piecewise-linear construction on F_181 (181 prime): x ◇ y = x + f(y − x) in F_181, where f(0) = 0, f(d) = 56·d when d is a quadratic residue mod 181, and f(d) = 46·d when d is a non-residue. So the multiplier on the difference y − x depends only on its QR/NQR class.\n\nThe display reorder presents elements as the orbit 0, τ(0), τ²(0), … of an order-181 magma automorphism τ (the hidden additive translation by 1 in F_181), making the magma fully translation-invariant in the rendered table: every row is a horizontal shift of row 0.\n\n[text written by Claude]","submitted_at":"2026-05-13 08:26:51","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/181/ddf8aaa4de5b63c69b5e463ffef52f398538147a138758661538cddcf5aacec7.txt"},{"canonical_hash":"ced83f3810c0d102d87573bb023c72e53a0f7df2b5a8f93afeefae34c98752ca","size":185,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"180,0,127,82,74,62,29,78,45,119,8,4,111,70,25,143,103,123,66,54,135,115,131,37,58,99,18,22,107,33,90,41,50,86,94,139,12,181,2,124,80,72,61,31,76,47,117,11,7,109,69,27,140,101,120,65,53,132,113,128,39,57,97,19,23,105,35,88,43,49,84,92,136,15,182,3,126,81,73,60,28,77,44,118,9,5,110,68,24,142,102,122,64,52,134,114,130,36,56,98,17,20,106,32,89,40,48,85,93,138,13,184,157,144,177,175,172,164,176,162,153,159,158,151,168,163,148,155,149,167,170,146,152,145,166,171,154,179,156,150,165,173,161,169,178,174,147,160,183,1,125,83,75,63,30,79,46,116,10,6,108,71,26,141,100,121,67,55,133,112,129,38,59,96,16,21,104,34,91,42,51,87,95,137,14","comment":"Direct product F_5 × F_37 of linear eq677 magmas: on F_5, x◇y = 2x + 4y; on F_37, x◇y = 26x + 2y. Element (i,j) ∈ F_5 × F_37 is indexed as 37·i + j; the displayed ordering shows the 5×5 outer block structure with 37×37 inner blocks.","submitted_at":"2026-05-12 14:47:33","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/185/ced83f3810c0d102d87573bb023c72e53a0f7df2b5a8f93afeefae34c98752ca.txt"},{"canonical_hash":"d66759dc65bc2ec5d1ae130953ffed6cc3aff72f6a7adf5eb8db1f1240be31fd","size":191,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,105,184,75,142,36,30,172,11,76,39,54,13,96,46,180,102,168,173,9,49,164,141,137,24,51,95,55,67,78,140,162,59,122,161,87,181,82,61,16,62,94,166,159,150,10,41,126,108,167,2,152,91,189,138,124,72,86,42,143,5,149,20,56,74,188,157,3,12,19,146,114,163,113,134,34,139,14,70,111,15,88,130,119,107,43,103,171,85,89,17,101,156,26,21,50,33,98,44,160,106,186,128,158,25,177,183,90,127,37,53,148,147,68,48,145,27,153,77,110,28,135,60,84,132,99,125,97,116,29,71,182,7,179,187,144,169,23,133,131,63,121,118,178,57,165,155,117,104,151,185,190,38,4,52,65,8,18,109,31,66,69,115,79,81,170,22,92,40,32,154,35,123,176,64,45,73,47,80,136,112,83,175,58,129,6,174,93,100,120","comment":"Linear magma over Z/191Z (the prime field F_191): x ◇ y = 40x + 152y (mod 191).","submitted_at":"2026-04-28 16:08:02","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/191/d66759dc65bc2ec5d1ae130953ffed6cc3aff72f6a7adf5eb8db1f1240be31fd.txt"},{"canonical_hash":"c455742dc1c80f1295117c7af80a67b625e28b10e3a7dd11fcf606739e743d18","size":191,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,16,89,142,65,150,129,176,181,66,11,153,187,164,81,70,160,93,67,59,110,189,21,149,112,87,132,82,80,35,62,56,117,148,120,48,60,172,116,99,2,179,15,178,146,113,72,10,42,151,43,138,58,75,36,101,184,79,12,76,97,103,171,121,123,91,128,71,13,157,53,69,100,108,134,24,111,122,28,51,17,147,107,45,40,88,14,106,6,130,152,137,136,166,63,109,96,33,154,37,34,156,174,49,29,115,27,161,77,175,9,105,3,46,159,183,95,124,162,86,90,114,7,168,119,133,158,4,141,177,44,167,126,186,57,135,125,144,188,102,155,190,19,61,52,8,84,94,98,50,85,31,180,41,5,140,22,92,78,32,143,73,131,127,26,83,54,47,23,182,139,64,145,39,118,25,163,74,165,185,38,20,170,173,18,169,55,68,104,30","comment":"Linear magma over Z/191Z (the prime field F_191): x ◇ y = 50x + 142y (mod 191).","submitted_at":"2026-04-28 16:08:04","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/191/c455742dc1c80f1295117c7af80a67b625e28b10e3a7dd11fcf606739e743d18.txt"},{"canonical_hash":"4694589622340c6b99aba64883fb8d560d758a62e7b3190aeadbfd0228e3420c","size":191,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,89,57,69,107,4,83,24,165,17,163,115,144,103,180,141,41,33,169,6,96,27,29,66,52,185,151,65,32,114,3,37,73,43,153,186,75,183,160,76,131,53,178,135,117,148,86,67,112,126,137,120,175,30,174,85,130,152,31,28,40,162,106,81,176,97,91,123,49,35,121,7,45,61,94,128,138,170,99,15,146,190,127,34,80,189,119,147,113,42,64,26,140,16,68,142,110,78,157,100,87,181,59,9,12,171,149,104,155,11,156,139,118,145,93,48,105,129,136,116,159,72,150,95,179,164,56,167,172,62,54,18,22,133,13,46,132,166,71,47,10,8,77,25,188,14,60,122,161,84,125,134,182,36,184,5,102,23,88,50,38,108,20,19,101,124,187,70,21,55,158,92,154,58,109,63,79,98,44,90,39,173,111,177,74,2,51,168,143,82","comment":"Linear magma over Z/191Z (the prime field F_191): x ◇ y = 110x + 82y (mod 191).","submitted_at":"2026-04-28 16:08:05","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/191/4694589622340c6b99aba64883fb8d560d758a62e7b3190aeadbfd0228e3420c.txt"},{"canonical_hash":"887eebb7df8eed1d8d385fc60cfbcdda3e717d90c1d520ab667f6373d8955a31","size":191,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,11,163,5,167,171,190,76,72,100,68,106,96,95,64,124,102,51,92,14,91,130,60,188,120,145,98,119,47,12,88,136,10,148,87,73,126,181,56,75,184,125,116,161,141,38,94,61,115,58,43,154,8,13,84,114,132,22,6,127,144,81,83,169,69,162,122,135,177,143,52,44,71,78,180,36,121,23,112,63,157,160,137,70,34,174,90,172,57,45,111,28,54,97,39,113,150,33,4,15,9,175,80,104,110,99,128,55,18,134,2,149,123,16,140,152,77,185,79,129,165,42,65,62,158,17,118,26,131,85,173,166,139,147,48,82,40,27,67,164,74,178,176,49,32,101,117,37,19,179,108,103,59,138,153,20,156,189,133,46,66,21,30,89,170,151,86,31,168,182,53,105,41,183,107,142,24,3,50,25,93,155,35,186,109,187,146,7,29,159","comment":"Linear magma over Z/191Z (the prime field F_191): x ◇ y = 185x + 7y (mod 191).","submitted_at":"2026-04-28 16:08:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/191/887eebb7df8eed1d8d385fc60cfbcdda3e717d90c1d520ab667f6373d8955a31.txt"},{"canonical_hash":"1fb86f75942bfb9a6e93a1d7bbf7162be410559c146e8cb6cf31459b3da0e51c","size":193,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"192,0,98,42,58,185,4,124,20,162,43,87,178,135,84,25,92,47,122,131,5,142,161,60,138,130,31,66,158,159,163,152,52,105,9,69,82,181,27,153,179,19,102,2,121,107,22,157,34,10,26,167,169,33,140,146,118,149,119,182,123,133,112,46,14,80,65,114,183,180,143,99,156,89,39,148,165,187,113,3,139,186,91,36,62,30,176,63,81,23,67,21,94,56,117,76,172,64,184,11,164,88,127,175,129,189,171,68,100,170,106,85,78,145,109,7,79,57,40,147,83,48,29,137,72,75,8,173,188,120,154,6,191,17,74,13,41,12,38,134,103,61,59,96,116,104,49,128,37,15,108,32,125,71,45,97,73,190,177,115,35,160,44,55,51,50,174,101,24,144,168,53,136,111,1,16,155,86,95,90,141,70,93,151,54,126,18,110,77,166,150,28,132","comment":"Linear magma over Z/193Z (the prime field F_193): x ◇ y = 108x + 123y (mod 193).","submitted_at":"2026-04-28 16:08:08","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/193/1fb86f75942bfb9a6e93a1d7bbf7162be410559c146e8cb6cf31459b3da0e51c.txt"},{"canonical_hash":"05ddef7bf14ce5689c0d591edb56fdad056e56ec989ee7eaf410f8d3b90c110c","size":193,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"192,0,111,76,78,36,19,155,21,4,190,90,6,148,122,131,151,85,114,42,133,63,33,119,116,115,91,55,65,179,98,105,118,185,52,47,57,141,172,32,100,94,30,165,187,39,62,138,59,166,58,180,34,132,22,2,8,137,146,68,41,83,72,158,61,16,128,113,182,27,177,38,24,183,84,23,139,101,186,92,43,191,37,124,160,164,108,87,130,176,169,135,29,13,81,121,26,14,109,93,25,17,147,181,188,142,99,120,152,5,112,49,162,31,80,174,89,127,11,96,171,12,50,189,15,170,125,140,28,73,3,60,95,53,56,134,149,20,157,10,144,46,168,70,154,71,150,74,51,175,153,18,82,88,44,184,129,69,35,40,173,106,117,86,167,77,67,79,103,104,107,45,75,145,54,126,97,163,143,110,136,161,102,178,159,9,1,7,48,66,64,123,156","comment":"Linear magma over Z/193Z (the prime field F_193): x ◇ y = 108x + 178y (mod 193).","submitted_at":"2026-04-28 16:08:10","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/193/05ddef7bf14ce5689c0d591edb56fdad056e56ec989ee7eaf410f8d3b90c110c.txt"},{"canonical_hash":"b856989647daf5fe09421b7f2545a3c1bd76fc4c5a2e362ce8fde6e08a7fc8e4","size":205,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"202,203,195,173,184,193,164,197,176,167,170,166,171,172,201,168,189,180,177,191,199,198,187,200,165,175,192,194,182,178,185,204,181,174,186,190,188,179,169,196,183,136,52,128,60,120,68,112,76,104,84,96,92,88,100,80,108,72,116,64,124,56,132,48,140,40,148,32,156,24,17,6,9,2,13,20,160,28,152,36,144,44,81,137,157,101,45,33,89,145,149,93,37,41,97,153,141,85,29,49,105,161,133,77,21,57,113,14,125,69,3,65,121,10,117,61,7,73,129,18,109,53,25,51,143,163,12,5,155,39,131,63,107,87,83,111,59,135,35,159,0,16,31,139,55,115,79,91,103,67,127,43,151,27,8,23,147,47,123,71,99,95,75,119,142,82,70,154,26,126,98,54,15,42,110,114,38,19,58,94,130,22,150,74,78,146,1,134,90,62,162,34,118,106,46,11,50,102,122,30,158,66,86,138,4","comment":"Direct product F_5 × F_41 of linear eq677 magmas: on F_5, x◇y = 2x + 4y; on F_41, x◇y = 11x + 31y. Element (i,j) ∈ F_5 × F_41 indexed as 41·i + j; the natural submission ordering shows the 5×5 outer block structure with 41×41 inner blocks.","submitted_at":"2026-05-12 14:51:10","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/205/b856989647daf5fe09421b7f2545a3c1bd76fc4c5a2e362ce8fde6e08a7fc8e4.txt"},{"canonical_hash":"8689a785bcf371719ed6f7ab843180687c1d527e6fed7f04127481bf67ca7800","size":209,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"198,0,101,161,40,50,10,30,140,70,150,60,110,91,130,120,80,20,171,199,1,100,160,41,51,11,31,141,71,151,61,111,90,131,121,81,21,170,201,3,103,163,43,53,13,33,143,73,153,63,113,93,133,123,83,23,173,207,9,109,169,49,59,19,39,149,79,159,69,119,99,139,129,89,29,179,205,7,107,167,47,57,17,37,147,77,157,67,117,97,137,127,87,27,177,200,2,102,162,42,52,12,32,142,72,152,62,112,92,132,122,82,22,172,202,4,104,164,44,54,14,34,144,74,154,64,114,94,134,124,84,24,174,206,8,108,168,48,58,18,38,148,78,158,68,118,98,138,128,88,28,178,203,5,105,165,45,55,15,35,145,75,155,65,115,95,135,125,85,25,175,204,6,106,166,46,56,16,36,146,76,156,66,116,96,136,126,86,26,176,208,191,185,182,194,195,197,193,180,189,181,196,186,184,188,187,190,192,183","comment":"Direct product of two linear magmas: F_11 × F_19. The operation is (x₁, x₂) ◇ (y₁, y₂) = (10x₁ + 2y₁ (mod 11), 7x₂ + 3y₂ (mod 19)).","submitted_at":"2026-04-28 16:08:17","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/209/8689a785bcf371719ed6f7ab843180687c1d527e6fed7f04127481bf67ca7800.txt"},{"canonical_hash":"f8e863f33e3bac9850c5f1243a1a42bb895f81bdc298398560f3e60e3743aec1","size":211,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,195,171,146,33,19,176,7,174,106,12,115,91,147,96,94,126,205,105,46,25,139,210,42,122,143,8,3,29,191,193,50,188,18,109,9,77,209,79,116,130,49,74,98,203,202,100,69,194,151,157,141,95,179,159,119,2,152,16,31,129,110,154,165,178,47,89,11,88,34,180,41,149,23,80,76,37,84,43,150,27,103,175,153,65,199,45,75,5,184,187,4,38,21,201,92,111,170,15,167,101,93,40,58,51,28,64,182,127,48,169,136,196,158,168,86,114,10,66,133,121,26,35,67,208,20,160,59,156,63,117,6,164,132,123,24,36,163,107,17,183,71,61,99,39,72,145,30,85,161,125,148,155,137,190,198,70,112,73,14,189,104,118,135,206,90,87,207,172,142,102,162,56,78,200,124,53,140,181,134,173,177,120,52,138,83,131,185,108,186,144,81,68,57,13,32,128,113,55,204,22,62,82,192,44,60,54,97,166,197","comment":"Linear magma over Z/211Z (the prime field F_211): x ◇ y = 189x + 23y (mod 211).","submitted_at":"2026-04-28 16:21:25","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/211/f8e863f33e3bac9850c5f1243a1a42bb895f81bdc298398560f3e60e3743aec1.txt"},{"canonical_hash":"b3100b007b985d0c6682937d8454a5951a0e5a90cd32f0216342b6a3e39c8eac","size":211,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,204,17,91,79,18,174,39,11,172,19,34,44,48,108,12,15,96,146,83,35,159,5,191,75,109,56,111,200,28,97,148,189,25,143,36,102,121,51,81,192,61,154,90,65,57,10,125,63,47,29,151,145,32,169,190,113,185,199,163,37,24,100,132,50,52,179,89,176,187,62,22,2,31,208,66,198,92,183,131,126,104,175,73,203,30,128,173,182,7,33,72,45,14,181,114,158,13,165,55,164,206,147,210,42,101,59,160,60,118,53,9,76,119,150,177,138,112,77,68,23,135,98,178,70,209,21,26,78,197,93,171,103,136,107,127,167,82,71,194,74,157,155,27,205,129,142,58,94,80,8,85,64,137,40,46,134,152,168,20,115,162,170,195,49,166,87,186,156,16,207,141,38,130,84,43,202,133,95,6,161,4,180,86,110,54,140,188,41,201,120,117,3,153,149,139,124,67,116,144,69,123,184,196,122,99,106,105,88,193","comment":"Linear magma over Z/211Z (the prime field F_211): x ◇ y = 108x + 104y (mod 211).","submitted_at":"2026-04-28 16:21:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/211/b3100b007b985d0c6682937d8454a5951a0e5a90cd32f0216342b6a3e39c8eac.txt"},{"canonical_hash":"d1af8bee6afc9f4fa56f4fcf6d22b3259569f2b6b1bfa38e50a4b43ed2b67961","size":211,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,202,91,179,48,203,130,54,128,194,180,14,146,83,33,204,117,171,111,65,55,40,67,158,60,195,81,100,28,122,15,148,189,46,151,84,43,120,17,133,205,186,90,165,53,172,145,160,170,6,66,12,99,138,188,41,119,75,89,23,159,25,98,153,74,196,97,106,105,109,101,78,102,163,93,123,192,103,70,174,149,57,94,209,21,47,155,193,19,32,85,64,71,59,115,121,37,150,184,132,134,52,95,5,8,187,62,22,2,73,166,108,156,92,141,173,168,20,49,31,161,114,86,131,182,7,201,72,129,140,13,30,116,181,39,139,80,38,147,210,42,143,185,34,144,76,11,135,118,35,24,177,96,112,77,26,191,9,56,136,154,125,63,68,36,197,51,3,61,178,107,127,167,82,113,110,200,157,29,27,79,45,142,16,10,164,176,169,190,137,124,88,50,152,126,104,199,162,44,69,175,208,87,18,198,58,207,183,206,4","comment":"Linear magma over Z/211Z (the prime field F_211): x ◇ y = 72x + 140y (mod 211).","submitted_at":"2026-04-28 16:21:28","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/211/d1af8bee6afc9f4fa56f4fcf6d22b3259569f2b6b1bfa38e50a4b43ed2b67961.txt"},{"canonical_hash":"99f4af57a89b75eaaed4f890772fe3e147bf96a2601f56c60c3fce281f6778c3","size":211,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,126,27,61,151,108,44,112,24,54,89,202,184,25,101,63,135,92,150,146,99,164,38,51,19,16,93,91,85,179,124,6,187,175,130,113,123,23,132,94,3,193,160,68,14,67,163,104,136,80,195,21,114,48,182,129,183,45,78,118,209,17,138,8,103,15,60,72,121,9,64,200,206,208,131,134,166,153,49,109,31,35,207,20,178,111,140,69,87,204,169,139,102,159,98,36,176,142,11,116,115,152,128,174,201,52,198,41,170,161,168,120,162,18,26,57,76,32,188,173,34,117,22,62,82,189,65,39,75,97,205,194,84,43,171,105,185,96,40,110,7,192,145,12,196,28,144,33,10,165,181,186,88,4,157,210,42,119,203,71,66,50,125,148,29,143,81,127,30,77,122,100,155,106,70,95,56,158,199,79,90,107,190,154,180,74,197,177,137,2,149,58,73,147,191,172,141,133,47,5,53,46,55,156,83,167,86,59,13,37","comment":"Linear magma over Z/211Z (the prime field F_211): x ◇ y = 56x + 156y (mod 211).","submitted_at":"2026-04-28 16:21:29","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/211/99f4af57a89b75eaaed4f890772fe3e147bf96a2601f56c60c3fce281f6778c3.txt"},{"canonical_hash":"d948db335f369c549857fd6778f932b5ada0c2bc5373fe748113c45b79319acd","size":223,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"222,0,19,140,37,208,158,135,57,55,2,8,176,162,153,123,75,195,73,33,20,48,26,134,194,191,180,192,171,53,141,137,93,147,213,118,91,181,221,77,38,201,68,185,44,36,152,193,212,43,209,110,198,85,210,215,189,172,17,126,159,12,155,187,111,145,165,1,7,47,136,200,109,11,199,106,71,142,95,14,58,107,219,41,86,178,203,138,64,131,56,72,170,50,211,16,6,94,63,62,3,143,128,66,216,31,103,148,4,79,9,96,207,122,190,117,35,214,144,105,177,15,30,116,173,174,205,119,129,100,163,59,183,167,18,175,25,92,67,197,154,108,218,169,127,206,29,182,217,88,124,220,89,23,160,120,113,54,32,52,76,42,125,46,13,130,61,78,104,99,196,87,51,98,156,101,82,39,149,157,74,179,90,151,188,164,70,202,5,102,34,204,24,28,112,60,81,69,80,83,21,139,161,133,146,184,84,186,10,40,49,65,121,115,166,168,22,45,97,150,27,132,114","comment":"Linear magma over Z/223Z (the prime field F_223): x ◇ y = 39x + 64y (mod 223).","submitted_at":"2026-04-28 16:21:31","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/223/d948db335f369c549857fd6778f932b5ada0c2bc5373fe748113c45b79319acd.txt"},{"canonical_hash":"0ba1852406347f0406d0b9ee6f54ed6f4c3fd035e0c5d68c9cc17baafe49785a","size":223,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"222,0,53,54,83,118,84,95,113,85,148,14,114,140,125,149,143,47,115,27,178,126,40,192,144,213,170,116,155,217,179,123,173,41,77,190,145,73,57,171,208,131,156,129,70,180,20,6,174,167,8,78,200,61,146,105,185,58,221,80,209,66,153,157,203,17,71,120,107,21,220,10,175,163,103,9,87,82,201,94,3,147,161,139,186,142,159,26,100,39,210,212,30,154,49,122,204,76,197,72,51,207,108,128,12,19,91,166,176,199,135,104,215,1,88,65,55,202,110,119,4,219,96,162,183,86,187,93,15,160,43,141,101,99,150,211,137,48,31,75,28,50,36,127,205,90,193,198,133,214,52,64,117,109,112,218,13,182,124,92,46,42,177,98,191,136,169,74,216,35,172,89,189,132,56,63,130,111,69,181,5,45,7,97,60,168,184,34,79,188,152,62,16,68,106,44,25,59,102,33,81,151,2,67,138,24,158,32,38,18,29,23,121,37,196,22,206,195,11,194,165,164,134","comment":"Linear magma over Z/223Z (the prime field F_223): x ◇ y = 39x + 198y (mod 223).","submitted_at":"2026-04-28 16:21:36","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/223/0ba1852406347f0406d0b9ee6f54ed6f4c3fd035e0c5d68c9cc17baafe49785a.txt"},{"canonical_hash":"c200891c3d995360babe07a06780685757ab7d526dbfe8aad0e400e4b76d0cc1","size":225,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"200,0,98,74,122,50,170,146,24,201,11,96,72,120,49,169,144,25,219,22,118,94,142,70,190,166,46,223,23,119,95,143,71,191,167,47,210,8,105,81,129,57,177,153,33,204,2,99,75,123,51,171,147,27,205,3,100,76,124,52,172,148,28,209,7,104,80,128,56,176,152,32,220,14,110,84,134,61,182,158,36,212,12,109,85,133,60,181,157,42,208,6,103,79,127,55,175,151,31,224,193,196,195,197,199,192,198,194,206,4,101,77,125,53,173,149,29,216,17,113,89,137,65,185,161,40,222,21,117,93,141,69,189,165,45,215,19,115,91,139,67,187,163,43,221,16,112,88,136,64,184,160,39,218,20,116,92,140,68,188,164,44,213,13,108,86,132,62,180,156,37,203,1,97,73,121,48,168,145,26,202,10,107,83,131,59,179,155,35,214,15,111,87,135,63,183,159,38,211,9,106,82,130,58,178,154,34,207,5,102,78,126,54,174,150,30,217,18,114,90,138,66,186,162,41","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_9.","submitted_at":"2026-04-28 19:31:58","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/225/c200891c3d995360babe07a06780685757ab7d526dbfe8aad0e400e4b76d0cc1.txt"},{"canonical_hash":"c736a4f80930ae25b80e13f9135650f25368cde546e8281ec394ad544db38a7e","size":229,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"228,0,149,7,99,29,139,192,170,74,198,61,89,197,44,19,22,108,129,26,50,182,116,193,160,78,49,64,213,211,188,153,191,51,179,127,227,13,195,187,219,168,34,52,5,107,45,204,110,10,133,98,218,46,119,94,65,16,63,171,40,96,103,172,43,132,220,166,31,183,1,12,150,151,145,68,47,159,39,180,71,54,20,60,203,59,221,201,137,205,178,2,214,143,56,75,181,15,142,41,83,155,169,4,70,117,215,224,8,152,165,3,120,175,185,128,118,177,23,222,209,28,167,158,174,111,24,226,212,42,82,199,72,124,18,97,200,157,35,121,148,194,144,164,100,146,101,77,95,112,123,80,216,88,109,202,208,207,32,36,126,11,223,163,189,84,115,62,55,81,114,104,73,106,53,176,87,161,57,190,30,69,147,86,66,25,93,14,225,162,130,138,33,38,184,122,92,134,210,131,154,156,105,90,21,217,136,173,125,91,6,186,67,79,76,85,140,48,102,141,17,113,135,196,9,58,27,206,37","comment":"Linear magma over Z/229Z (the prime field F_229): x ◇ y = 134x + 10y (mod 229).","submitted_at":"2026-04-28 16:21:37","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/229/c736a4f80930ae25b80e13f9135650f25368cde546e8281ec394ad544db38a7e.txt"},{"canonical_hash":"0a70f64d61cd32800269b4cf04652b6023808191a688caa9edfb5a242795e05d","size":229,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"228,0,21,58,42,20,81,35,95,213,47,163,60,208,50,80,74,98,192,14,94,71,142,140,206,46,187,157,85,104,226,144,220,107,77,55,171,90,41,152,73,114,217,181,121,191,119,59,185,96,93,209,166,193,136,141,64,86,16,108,205,36,123,182,199,186,13,194,223,17,84,183,150,224,69,225,56,132,131,11,219,101,2,10,196,76,160,53,100,116,170,177,1,9,82,40,164,179,75,44,72,33,188,52,145,216,172,154,115,27,120,201,210,176,65,118,37,5,8,67,184,62,57,39,102,92,161,25,178,125,165,128,34,49,173,135,202,212,32,43,63,214,162,51,129,15,203,207,215,105,204,78,79,153,111,122,110,97,26,137,198,109,19,200,29,12,31,70,175,6,222,197,139,117,88,83,18,45,4,146,149,28,156,66,22,68,30,103,61,126,99,174,143,38,158,130,221,106,91,112,218,138,54,24,167,7,87,89,124,147,195,23,151,127,133,159,3,113,48,168,227,148,180,134,189,169,155,190,211","comment":"Linear magma over Z/229Z (the prime field F_229): x ◇ y = 134x + 124y (mod 229).","submitted_at":"2026-04-28 16:21:39","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/229/0a70f64d61cd32800269b4cf04652b6023808191a688caa9edfb5a242795e05d.txt"},{"canonical_hash":"e4c98b9705a5c8544e6373bb79bc290a0595983179d139ecedcef9afa801a1bf","size":241,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"240,0,239,221,172,127,222,105,173,169,128,82,223,14,106,178,174,122,170,76,129,29,83,9,224,211,15,196,107,154,179,102,175,6,123,62,171,36,77,65,130,202,30,70,84,229,10,150,225,215,212,46,16,164,197,39,108,24,155,137,180,219,103,80,176,98,7,194,100,60,63,68,148,44,37,135,78,192,66,133,131,144,203,146,31,55,71,205,85,91,230,124,11,50,151,33,226,161,216,57,213,52,47,73,17,113,165,207,198,20,40,87,109,189,25,93,156,116,138,232,181,1,220,126,104,168,81,13,177,121,99,28,8,210,195,153,101,5,61,35,64,201,69,228,149,238,45,163,38,23,136,218,79,97,193,59,67,43,134,191,132,143,145,54,204,90,147,49,32,160,56,75,72,112,206,19,86,188,92,115,231,2,125,167,12,120,51,209,152,4,34,200,227,237,162,22,217,96,58,42,214,142,53,89,48,159,74,111,18,187,114,3,166,119,208,27,199,236,21,95,41,141,88,158,110,186,190,118,26,235,94,140,157,185,117,234,139,184,233,183,182","comment":"Linear magma over Z/241Z (the prime field F_241): x ◇ y = 225x + 9y (mod 241).","submitted_at":"2026-04-28 16:21:41","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/241/e4c98b9705a5c8544e6373bb79bc290a0595983179d139ecedcef9afa801a1bf.txt"},{"canonical_hash":"88d579a423933c760f2ff419bf11ad5783ca82b9e3d65792423cc5fc312dd325","size":241,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,193,67,107,223,99,22,225,216,61,222,78,49,134,153,158,112,38,231,97,137,215,51,68,124,148,28,135,205,58,186,125,48,115,105,240,129,139,72,101,162,82,229,111,4,172,100,92,75,239,113,121,207,14,136,182,177,110,73,54,198,85,192,201,46,123,199,131,91,217,25,24,151,98,7,144,204,187,9,120,56,83,6,64,60,208,155,95,2,202,181,211,79,8,166,133,52,209,128,141,116,53,220,227,5,35,37,34,183,161,146,108,200,17,174,154,188,214,160,149,3,19,234,130,142,66,180,93,147,16,169,74,20,70,23,218,21,165,39,57,213,12,206,212,87,191,102,221,127,89,114,18,195,176,86,143,119,62,152,219,42,138,65,103,197,126,167,63,236,230,36,237,81,15,189,45,194,47,94,44,50,145,40,171,69,156,90,118,106,210,43,27,173,184,238,164,178,150,41,224,132,170,185,159,10,13,11,29,203,196,77,140,117,104,233,76,109,190,32,55,235,157,226,26,71,179,232,84,88,30,59,80,96,33,163,228,168,31,122,175","comment":"Linear magma over Z/241Z (the prime field F_241): x ◇ y = 206x + 36y (mod 241).","submitted_at":"2026-04-28 16:21:43","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/241/88d579a423933c760f2ff419bf11ad5783ca82b9e3d65792423cc5fc312dd325.txt"},{"canonical_hash":"1173b6b3ee2ba21701dc8bc2bb7b39558e2fa03deb0775e9a6f093c294405749","size":241,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,112,51,183,81,85,237,36,172,22,55,13,99,37,194,5,39,126,207,148,80,34,154,200,28,87,6,159,125,74,157,219,133,175,142,52,156,117,205,201,63,171,232,121,120,196,20,203,56,33,25,168,220,179,239,72,221,141,223,188,92,208,98,78,31,202,69,58,163,93,86,11,61,91,7,182,65,109,204,49,217,90,164,38,16,135,167,143,152,166,215,73,2,130,30,66,35,230,9,231,233,102,108,41,79,173,96,71,17,75,214,227,174,26,177,162,225,12,40,45,19,3,118,89,106,27,224,184,187,235,50,29,128,116,234,197,60,138,4,70,14,24,240,144,134,190,124,18,180,77,114,236,8,149,170,115,67,64,104,147,226,209,238,123,139,165,160,132,105,42,57,146,54,107,94,195,137,191,216,53,199,161,228,222,113,111,129,110,155,186,150,10,122,193,95,46,32,23,47,15,136,158,44,210,97,169,84,229,185,62,127,211,181,131,206,213,43,178,189,82,151,198,218,88,212,68,103,21,101,192,119,59,100,48,145,153,176,83,140,76","comment":"Linear magma over Z/241Z (the prime field F_241): x ◇ y = 99x + 143y (mod 241).","submitted_at":"2026-04-28 16:21:44","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/241/1173b6b3ee2ba21701dc8bc2bb7b39558e2fa03deb0775e9a6f093c294405749.txt"},{"canonical_hash":"64782d5f3e730b7a7259102d11d1d61be4c7955ac355db2907f36d05ce15ce62","size":241,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,105,224,35,236,124,96,49,112,99,135,129,181,237,84,172,22,151,205,3,37,98,101,183,174,207,100,176,178,58,56,220,87,54,63,221,218,157,123,85,31,142,52,204,117,61,9,15,219,232,169,216,4,116,155,104,225,121,120,76,83,143,72,29,189,175,140,92,160,50,30,79,202,213,10,115,45,134,59,109,139,7,182,161,13,108,193,217,186,68,230,64,231,167,95,152,214,71,25,2,226,126,114,131,86,153,39,185,102,60,89,223,125,144,119,17,171,118,227,78,74,177,162,81,12,136,141,163,195,70,233,154,27,128,88,187,91,146,173,80,164,138,197,156,90,148,166,158,168,240,48,38,46,28,210,36,77,18,44,200,53,26,211,67,208,8,147,34,113,190,75,43,21,16,132,201,42,57,194,198,107,238,51,137,239,24,5,103,209,180,222,65,159,33,206,11,234,6,106,122,145,191,94,32,215,47,111,184,110,188,66,97,73,228,133,41,62,127,19,229,179,14,165,235,130,93,82,199,150,170,40,212,20,55,69,149,192,23,203,196","comment":"Linear magma over Z/241Z (the prime field F_241): x ◇ y = 92x + 150y (mod 241).","submitted_at":"2026-04-28 16:21:46","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/241/64782d5f3e730b7a7259102d11d1d61be4c7955ac355db2907f36d05ce15ce62.txt"},{"canonical_hash":"e92b913c2d5cd9f7cb11a4d337c081834dd1214c82b6e4b8aab052156cf02f81","size":241,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,61,44,48,119,63,112,133,4,212,144,167,80,117,33,87,179,75,12,20,170,209,203,21,35,46,19,81,162,105,188,64,206,86,184,68,225,42,201,139,166,155,141,83,89,50,140,132,195,59,207,153,237,200,47,24,92,124,13,232,183,239,168,164,181,121,120,187,27,233,148,100,128,238,18,137,230,51,38,53,123,202,157,107,77,65,10,199,11,36,71,95,54,76,58,32,129,145,73,40,122,49,143,190,14,114,222,229,154,111,177,223,90,228,127,41,43,192,97,55,189,26,85,66,22,135,30,39,180,104,219,101,213,218,31,182,45,16,56,125,29,94,91,208,172,6,115,84,198,236,74,226,216,240,96,106,194,116,78,204,235,126,52,88,211,214,149,5,176,136,165,62,151,98,93,221,99,224,60,159,150,15,142,186,205,146,69,175,217,72,163,161,7,108,210,103,57,231,34,109,102,234,134,70,23,169,2,160,193,25,9,152,178,196,174,215,191,156,131,79,130,185,197,227,37,82,3,173,158,171,110,17,138,118,8,220,28,113,147,67","comment":"Linear magma over Z/241Z (the prime field F_241): x ◇ y = 88x + 154y (mod 241).","submitted_at":"2026-04-28 16:21:48","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/241/e92b913c2d5cd9f7cb11a4d337c081834dd1214c82b6e4b8aab052156cf02f81.txt"},{"canonical_hash":"b1f90994bda5274ee2b6faf3993e238319a81fb92e38f13d45f86fdb9a6f57dd","size":241,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"240,0,74,32,84,190,42,25,94,212,200,179,52,213,35,144,104,181,222,119,210,205,189,163,62,76,223,166,45,2,154,221,114,133,191,137,232,49,129,167,220,226,215,217,199,98,173,36,6,198,86,135,233,162,176,239,55,73,72,64,164,238,231,159,124,99,143,146,201,117,147,197,16,115,59,44,139,126,177,24,230,120,236,140,225,67,227,30,209,43,108,160,183,175,46,19,68,132,208,87,96,51,145,21,17,91,172,50,186,47,75,229,65,28,83,63,82,121,4,128,174,11,22,180,15,202,169,203,134,171,109,195,153,66,156,9,211,123,127,39,157,216,207,88,26,188,125,152,12,1,54,228,149,89,136,107,187,105,34,116,14,110,130,7,20,33,150,165,235,122,77,41,237,81,40,37,219,18,53,111,118,58,170,192,193,161,185,8,56,113,29,206,78,178,142,10,218,79,97,95,106,100,61,23,155,112,31,71,27,234,101,48,182,151,60,103,196,168,57,69,85,90,13,102,3,224,38,141,93,158,5,80,92,214,131,148,70,204,138,194,184","comment":"Linear magma over Z/241Z (the prime field F_241): x ◇ y = 225x + 216y (mod 241).","submitted_at":"2026-04-28 16:21:50","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/241/b1f90994bda5274ee2b6faf3993e238319a81fb92e38f13d45f86fdb9a6f57dd.txt"},{"canonical_hash":"0ab755831eebe1a3420a0d6d1a38ac8f329df43bac54fba6191ee4c1a4c72250","size":245,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"3,4,2,25,1,171,174,172,209,173,29,27,28,30,26,20,18,19,21,17,8,6,7,22,5,12,10,11,23,9,16,14,15,24,13,176,177,178,200,175,180,181,182,201,179,184,185,186,202,183,188,189,190,203,187,192,193,194,204,191,196,197,198,199,195,97,96,98,112,95,101,100,102,113,99,105,104,106,114,103,93,92,94,115,91,119,118,120,116,117,109,108,110,111,107,121,122,123,145,124,147,148,149,146,150,137,138,139,141,140,125,126,127,142,128,129,130,131,143,132,133,134,135,144,136,67,66,68,82,65,71,70,72,83,69,75,74,76,84,73,63,62,64,85,61,89,88,90,86,87,79,78,80,81,77,44,41,42,31,43,48,45,46,32,47,52,49,50,33,51,56,53,54,34,55,60,57,58,35,59,40,37,38,36,39,155,158,156,206,157,159,162,160,207,161,163,166,164,208,165,167,170,168,0,169,151,154,152,205,153,218,217,215,219,216,212,213,211,214,210,220,221,222,224,223,228,227,225,229,226,232,233,230,234,231,239,238,237,235,236,240,241,242,244,243","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_5(2,4).","submitted_at":"2026-04-28 19:33:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/245/0ab755831eebe1a3420a0d6d1a38ac8f329df43bac54fba6191ee4c1a4c72250.txt"},{"canonical_hash":"729e669b71c305a1f5857f58c43908a9116c88e5a6c4ffa52f5431385065f096","size":245,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"3,0,2,24,1,160,158,159,168,157,26,25,28,29,27,17,16,19,20,18,5,4,7,21,6,9,10,11,22,8,12,14,15,23,13,196,197,195,199,198,176,177,175,200,178,180,181,179,201,182,184,185,183,202,186,188,189,187,203,190,192,193,191,204,194,121,119,122,136,120,125,123,126,137,124,129,127,130,138,128,117,115,118,139,116,143,141,144,140,142,133,131,134,135,132,99,97,100,108,98,87,85,88,109,86,113,111,114,110,112,103,101,104,105,102,91,89,92,106,90,95,93,96,107,94,82,83,81,207,84,62,63,61,208,64,66,67,65,30,68,70,71,69,209,72,74,75,73,205,76,78,79,77,206,80,53,55,54,34,56,57,59,58,35,60,37,39,38,36,40,41,43,42,31,44,45,47,46,32,48,49,51,50,33,52,174,172,173,170,171,164,162,163,165,161,152,150,151,166,149,156,154,155,167,153,148,146,147,169,145,215,216,217,219,218,210,211,212,214,213,220,221,222,224,223,225,226,227,229,228,230,231,232,234,233,236,237,238,235,239,243,242,240,244,241","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 d50b3565) × F_5(2,4).","submitted_at":"2026-04-28 19:39:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/245/729e669b71c305a1f5857f58c43908a9116c88e5a6c4ffa52f5431385065f096.txt"},{"canonical_hash":"98645e18cc75be280b175da1b057a539aa5187ace0e0ae7009f590a3adf2570d","size":247,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"246,0,12,9,5,6,2,4,16,8,17,7,13,11,15,14,1,3,10,18,186,137,143,154,218,30,189,105,33,70,183,102,64,140,67,221,224,99,21,108,233,230,76,41,73,111,192,79,157,114,198,160,227,163,44,38,195,19,222,65,71,190,35,187,225,141,184,106,219,138,100,68,103,32,245,135,24,204,47,53,172,236,169,207,123,166,88,201,120,82,50,85,239,242,117,23,72,197,194,40,113,37,75,156,43,229,78,162,232,191,235,116,110,159,22,36,161,158,112,77,109,39,228,115,193,42,234,196,155,199,80,74,231,29,90,215,212,58,131,55,93,174,61,148,96,180,151,209,145,134,128,177,27,126,152,149,94,59,91,129,210,97,175,132,216,178,146,181,62,56,213,20,31,101,107,226,182,223,153,69,220,142,34,66,136,104,139,185,188,63,26,168,119,125,244,200,241,171,87,238,52,165,84,46,122,49,203,206,81,28,54,179,176,130,95,127,57,147,133,211,60,144,214,173,217,98,92,150,25,240,83,89,208,164,205,243,51,202,124,237,48,118,86,121,167,170,45","comment":"Direct product of two linear magmas: F_13 × F_19. The operation is (x₁, x₂) ◇ (y₁, y₂) = (9x₁ + 11y₁ (mod 13), 7x₂ + 3y₂ (mod 19)).","submitted_at":"2026-04-28 16:08:20","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/247/98645e18cc75be280b175da1b057a539aa5187ace0e0ae7009f590a3adf2570d.txt"},{"canonical_hash":"ae5a66f37780a81ac2ecf5a3a32e35e0716562db71c8a214e7c1ae9cc728e98a","size":249,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"243,245,244,241,242,240,247,246,234,239,160,236,237,238,233,235,170,172,171,174,175,176,169,173,149,151,150,145,146,147,148,144,187,189,188,191,192,185,186,190,0,3,2,5,6,7,1,4,85,87,86,81,82,83,84,80,153,155,154,157,158,159,152,156,201,203,202,205,206,207,208,204,53,55,54,49,50,51,52,48,21,23,22,17,18,19,20,16,72,74,73,76,77,78,79,75,101,103,102,97,98,99,100,96,26,28,27,30,31,24,25,29,89,91,90,93,94,95,88,92,180,182,181,184,177,178,179,183,223,217,224,219,220,221,222,218,133,135,134,129,130,131,132,128,65,67,66,69,70,71,64,68,137,139,138,141,142,143,136,140,33,35,34,37,38,39,32,36,58,60,59,62,63,56,57,61,8,10,9,12,13,14,15,11,168,162,161,164,165,166,167,163,117,119,118,113,114,115,116,112,121,123,122,125,126,127,120,124,40,42,41,44,45,46,47,43,232,226,225,228,229,230,231,227,105,107,106,109,110,111,104,108,213,215,214,209,210,211,212,216,198,200,199,194,195,196,197,193,248","comment":null,"submitted_at":"2026-05-17 17:30:46","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/249/ae5a66f37780a81ac2ecf5a3a32e35e0716562db71c8a214e7c1ae9cc728e98a.txt"},{"canonical_hash":"cbf572d35bb5091b3492a7590a795fef9f1b9a94773e844f6e37c5bb2a715014","size":251,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,246,128,163,193,22,235,186,9,161,99,175,158,122,59,115,111,28,137,51,26,40,237,230,143,166,155,95,31,210,75,250,200,85,156,220,30,41,18,105,112,165,151,176,12,153,236,240,184,247,33,50,224,36,134,61,110,147,68,38,3,121,126,125,107,69,98,132,37,168,218,185,64,109,177,171,192,19,35,196,86,245,140,32,73,203,231,173,239,138,91,6,123,11,180,10,92,242,164,204,90,233,87,17,44,172,66,53,219,103,72,70,24,199,4,244,14,62,209,56,34,77,80,154,82,170,113,81,229,221,63,130,76,25,182,167,54,208,27,88,97,116,243,58,100,124,214,23,174,226,2,141,102,8,20,146,190,65,21,145,133,227,16,127,101,49,148,89,249,225,183,118,241,222,213,152,83,179,42,57,150,201,5,188,96,104,206,238,45,207,29,205,202,159,181,84,187,139,119,129,74,149,195,197,228,94,178,191,47,169,142,212,108,215,79,39,117,217,135,55,136,248,131,216,13,114,48,106,78,198,157,15,120,211,71,160,144,67,46,52,234,189,60,93,43,162,7,223,194,232","comment":"Linear magma over Z/251Z (the prime field F_251): x ◇ y = 220x + 32y (mod 251).","submitted_at":"2026-04-28 16:21:51","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/251/cbf572d35bb5091b3492a7590a795fef9f1b9a94773e844f6e37c5bb2a715014.txt"},{"canonical_hash":"d6d9663c21752c8167dd57c70a6d577fc084b2e89031167c30dfc33f5cff270d","size":251,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,105,138,146,4,6,188,145,207,179,55,202,59,231,234,187,39,19,29,224,49,45,197,178,244,128,241,47,69,142,212,58,65,229,189,117,217,235,155,186,198,181,16,213,14,248,156,28,148,157,115,220,11,121,10,44,67,96,52,134,89,160,43,243,162,7,173,94,232,100,51,46,78,113,143,22,85,236,159,211,249,25,108,122,209,215,161,228,137,101,76,140,237,80,93,216,5,195,81,60,175,250,50,185,206,70,130,91,218,205,112,15,201,226,12,103,36,90,84,247,233,150,124,86,34,111,210,147,18,238,203,171,176,225,107,219,48,132,37,118,168,35,214,9,177,221,192,169,135,246,136,95,240,32,23,153,31,123,139,88,141,56,73,61,30,110,92,242,64,104,190,183,87,17,194,172,116,3,119,53,72,170,174,99,154,144,164,62,109,106,184,77,180,54,82,20,63,131,129,21,13,230,126,125,182,167,204,158,27,38,97,166,193,8,200,24,114,223,74,26,2,191,102,208,120,196,40,165,71,245,83,227,66,127,151,199,98,239,149,75,133,68,41,222,163,152,33,79,42,57","comment":"Linear magma over Z/251Z (the prime field F_251): x ◇ y = 150x + 102y (mod 251).","submitted_at":"2026-04-28 16:21:53","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/251/d6d9663c21752c8167dd57c70a6d577fc084b2e89031167c30dfc33f5cff270d.txt"},{"canonical_hash":"5cc46bf7537b9e8a24bd65f75d4ed801566b2f1bccf1e3b7eaa39981989cfae1","size":251,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,36,161,76,99,48,218,73,17,80,54,35,194,213,239,176,232,59,207,133,235,2,195,160,159,126,32,243,78,221,23,226,230,8,152,75,158,129,87,104,21,119,37,214,127,130,179,98,125,178,41,147,145,165,155,51,135,189,137,47,31,97,168,162,240,33,88,42,169,205,245,217,242,249,204,64,27,228,109,171,11,102,94,72,77,177,244,105,148,163,65,106,142,29,123,16,220,40,216,141,13,202,211,56,68,100,233,79,22,146,241,28,149,14,150,198,185,209,117,53,225,144,248,122,197,183,49,60,222,120,166,34,229,164,203,15,184,250,25,174,44,5,70,193,7,154,63,219,208,24,38,156,89,110,66,212,151,50,26,39,116,173,115,187,82,112,181,238,74,134,227,215,52,43,172,107,57,199,61,175,157,188,108,140,224,4,114,139,85,18,236,231,128,136,170,12,143,69,186,223,45,90,83,58,86,46,10,201,247,192,81,3,9,131,190,206,103,30,101,210,121,6,111,113,200,19,91,132,20,96,93,55,196,153,180,138,246,95,124,234,118,167,71,67,182,62,237,84,191,92","comment":"Linear magma over Z/251Z (the prime field F_251): x ◇ y = 114x + 138y (mod 251).","submitted_at":"2026-04-28 16:21:54","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/251/5cc46bf7537b9e8a24bd65f75d4ed801566b2f1bccf1e3b7eaa39981989cfae1.txt"},{"canonical_hash":"c1a3ba0d39150a2abb0c4764794524c3e087e533ef5310d356399c8bce31be10","size":251,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,89,91,198,65,187,82,112,156,138,124,184,227,165,52,68,172,107,57,249,36,125,157,213,8,215,149,54,39,189,35,43,211,206,153,236,245,12,168,119,161,248,120,40,108,83,61,21,85,176,247,192,56,28,59,231,140,181,3,105,76,160,96,106,86,13,150,69,66,132,95,71,118,5,171,178,130,163,221,45,49,159,18,167,46,67,182,62,237,9,166,92,75,101,11,136,51,24,73,243,98,17,30,104,110,244,238,164,151,232,109,207,158,185,2,145,235,209,226,32,143,103,196,48,201,180,33,152,25,183,179,87,29,121,44,37,139,127,205,229,123,200,203,16,147,220,240,230,26,210,239,137,47,6,97,193,162,190,58,113,42,219,155,195,217,242,174,129,114,27,128,34,146,111,102,19,72,77,177,169,55,173,188,15,81,142,79,23,116,170,115,191,241,38,202,186,31,93,50,133,4,22,246,216,53,199,64,225,223,135,134,117,78,175,194,148,122,197,208,99,10,222,70,141,84,154,214,228,90,234,250,100,224,94,80,20,218,7,204,88,144,233,74,63,131,14,60,41,212,126","comment":"Linear magma over Z/251Z (the prime field F_251): x ◇ y = 21x + 231y (mod 251).","submitted_at":"2026-04-28 16:21:56","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/251/c1a3ba0d39150a2abb0c4764794524c3e087e533ef5310d356399c8bce31be10.txt"},{"canonical_hash":"b2fd4f5470da8730900ebc57f92f199b0444ff57d28ec0a1533dc9dd4bf98d8e","size":271,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,160,111,78,209,121,181,36,226,173,202,2,212,48,23,256,228,138,249,259,70,140,161,117,208,255,270,108,61,264,14,128,217,112,102,126,81,109,170,195,65,149,55,26,79,183,34,268,62,225,258,13,148,147,18,210,237,84,8,265,114,132,32,19,136,57,122,51,221,233,15,11,178,159,211,116,101,182,236,50,235,129,106,45,163,238,190,94,37,130,96,215,218,76,67,87,85,154,120,227,107,169,224,113,10,105,75,9,4,53,174,46,186,72,103,5,99,199,266,240,247,203,164,172,69,127,54,146,135,115,189,153,3,239,188,244,82,175,59,205,133,245,251,213,191,30,143,110,47,207,125,33,83,220,49,95,168,185,171,187,29,167,20,176,40,24,38,21,242,196,73,230,180,137,60,194,257,131,177,44,66,104,98,145,58,206,28,229,97,41,92,150,6,42,262,123,134,201,139,216,25,17,56,100,93,119,52,246,152,250,219,39,193,27,200,151,156,222,252,157,260,77,22,254,80,267,7,232,234,214,223,71,68,243,142,184,241,43,91,16,192,253,141,88,197,89,35,248,263,64,12,31,158,162,86,74,198,269,204,124,166,179,144,261,118,155,231,90,63,165","comment":"Linear magma over Z/271Z (the prime field F_271): x ◇ y = 245x + 27y (mod 271).","submitted_at":"2026-04-28 16:21:57","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/271/b2fd4f5470da8730900ebc57f92f199b0444ff57d28ec0a1533dc9dd4bf98d8e.txt"},{"canonical_hash":"b36f8ad4c6cab8cf78e085901ad669313d2bbece718723763061cdd76f422f01","size":271,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,77,207,33,3,233,211,220,140,55,28,123,20,23,75,95,59,64,256,39,113,125,257,146,44,254,63,29,87,236,193,262,208,169,19,152,150,104,259,93,184,142,219,175,105,92,197,265,165,237,206,181,267,18,126,171,108,134,41,24,246,235,14,47,234,137,109,53,160,43,6,166,107,189,9,195,185,38,61,67,180,209,81,270,216,74,45,202,196,173,50,60,144,54,242,31,141,178,25,188,244,2,99,182,149,100,111,159,176,269,243,36,261,153,132,46,71,102,30,130,62,227,240,40,84,7,49,228,124,239,15,17,154,34,73,127,58,101,222,164,198,119,179,11,122,260,248,174,121,199,194,230,210,158,155,258,163,190,5,85,76,98,138,168,72,212,136,135,224,177,90,86,238,252,245,97,231,143,79,145,83,12,170,162,217,201,128,255,129,186,205,229,65,80,161,22,131,56,91,247,69,37,78,139,268,250,183,118,156,106,251,32,148,249,151,57,203,52,223,88,187,68,192,16,114,13,167,116,241,21,253,48,115,133,4,213,172,204,112,226,191,266,157,26,215,200,94,70,51,264,120,263,66,82,27,35,147,218,10,214,8,96,232,110,117,103,221,225,42,89","comment":"Linear magma over Z/271Z (the prime field F_271): x ◇ y = 188x + 84y (mod 271).","submitted_at":"2026-04-28 16:21:59","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/271/b36f8ad4c6cab8cf78e085901ad669313d2bbece718723763061cdd76f422f01.txt"},{"canonical_hash":"404c1c497b9c4610c4064d19f5919c62cfd482e711a3650985b6eef4a4616754","size":271,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"270,0,29,190,93,13,254,2,157,145,127,113,48,76,27,180,221,87,209,82,83,188,69,250,112,3,140,100,91,28,244,247,177,18,151,11,165,131,146,31,147,223,252,246,133,135,44,94,68,19,117,42,204,75,56,103,155,37,92,122,38,53,41,143,241,66,24,251,215,205,125,6,17,60,195,170,210,111,95,115,211,5,179,33,46,77,40,253,197,7,199,74,108,202,158,72,132,236,25,185,73,10,106,191,268,178,139,54,228,200,59,86,219,260,101,240,156,256,78,85,102,153,225,70,105,43,207,212,35,201,130,162,88,80,45,90,171,234,161,169,81,49,120,224,23,126,232,186,259,36,1,183,166,267,67,237,159,182,71,30,167,248,119,39,243,8,97,79,110,187,141,262,104,214,47,51,261,239,121,189,263,118,138,116,64,229,266,235,222,98,136,22,196,176,192,21,89,114,249,148,137,206,124,26,62,213,255,160,12,230,242,227,203,173,226,269,184,245,264,123,231,198,150,257,175,233,4,52,57,63,34,16,220,15,50,84,142,20,149,96,58,55,217,172,181,9,134,193,61,258,107,164,163,128,168,32,99,216,265,129,194,208,14,238,152,65,144,174,109,218,154","comment":"Linear magma over Z/271Z (the prime field F_271): x ◇ y = 28x + 137y (mod 271).","submitted_at":"2026-04-28 16:22:01","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/271/404c1c497b9c4610c4064d19f5919c62cfd482e711a3650985b6eef4a4616754.txt"},{"canonical_hash":"8a78d2702e35cf02791391c656a7fa4d9df6e4f1dce56a6039f1e54feae45be7","size":271,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"270,0,38,189,61,130,137,89,21,93,15,23,220,150,112,214,92,103,116,243,86,248,94,255,168,80,233,252,45,135,162,81,115,170,126,39,49,101,191,129,109,108,196,238,117,43,203,159,251,25,2,262,181,127,200,111,68,24,218,143,245,4,1,29,48,175,253,98,11,6,62,254,72,217,124,239,139,70,14,87,42,10,41,55,144,53,186,114,50,97,66,209,151,240,242,268,199,182,96,74,36,136,210,107,264,138,12,259,148,164,44,260,28,230,95,145,166,213,226,3,193,52,34,192,37,105,100,215,71,19,258,205,201,167,121,142,82,241,32,18,22,63,202,266,9,160,165,172,57,169,187,58,222,269,30,106,85,155,110,211,65,179,104,88,64,195,78,69,227,27,76,171,134,156,47,16,73,122,120,91,26,261,157,185,234,51,188,84,190,176,216,177,147,197,265,79,119,244,8,267,59,257,219,194,158,133,40,183,212,224,221,125,83,7,207,263,231,17,247,46,67,223,208,131,99,20,178,237,118,13,228,229,249,56,161,184,174,246,35,235,141,102,75,180,132,113,140,33,60,154,128,146,123,236,163,152,31,232,90,5,206,198,153,204,149,77,250,256,54,173,225","comment":"Linear magma over Z/271Z (the prime field F_271): x ◇ y = 28x + 162y (mod 271).","submitted_at":"2026-04-28 16:22:04","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/271/8a78d2702e35cf02791391c656a7fa4d9df6e4f1dce56a6039f1e54feae45be7.txt"},{"canonical_hash":"7ec4872ebe6c93feebc2db8cf253945099a0c89b0d1b43e65a00f4d7aa116d62","size":271,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,225,143,187,57,264,191,103,213,174,239,22,263,242,223,31,105,37,147,67,121,182,144,133,234,238,221,32,109,69,229,3,110,52,130,157,25,137,30,256,96,136,5,248,265,261,160,117,209,148,94,120,10,78,4,250,269,236,49,266,201,186,76,164,237,84,214,116,252,28,27,183,39,125,212,88,131,228,16,204,9,118,245,211,42,71,202,241,23,45,156,126,140,235,206,180,203,151,138,168,146,169,189,95,100,226,75,128,165,41,224,80,74,132,65,33,260,154,46,115,97,55,44,190,86,79,108,58,34,93,215,199,38,35,197,205,21,230,259,51,141,258,249,123,62,227,60,216,167,104,47,54,29,91,122,200,112,246,244,53,63,99,181,171,161,247,13,166,83,267,270,240,56,193,40,220,134,198,208,72,90,26,217,219,139,173,149,64,2,81,20,77,194,243,87,254,89,150,222,231,114,24,232,257,48,178,170,8,11,172,188,66,7,85,135,106,59,163,17,82,70,142,19,127,233,6,92,159,101,107,251,14,192,155,102,253,73,68,162,196,119,195,111,124,176,207,179,262,113,153,129,18,50,268,175,98,15,184,218,145,36,177,43,255,158,61,185,152,12,210","comment":"Linear magma over Z/271Z (the prime field F_271): x ◇ y = 101x + 171y (mod 271).","submitted_at":"2026-04-28 16:22:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/271/7ec4872ebe6c93feebc2db8cf253945099a0c89b0d1b43e65a00f4d7aa116d62.txt"},{"canonical_hash":"a27d3c0090d02179a0ecebd9eabc9b148971f279511bff3f22947bdaec01d9c9","size":271,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,207,232,38,240,28,80,106,193,61,143,62,262,268,94,158,211,99,247,166,111,89,167,6,132,32,46,254,57,122,105,204,243,123,65,188,250,194,35,20,246,219,23,137,21,25,18,173,248,227,121,37,103,15,252,228,130,67,87,58,245,93,156,107,260,180,59,118,78,48,36,31,134,265,100,169,72,49,113,126,155,249,142,176,213,255,236,96,127,81,264,172,88,145,163,84,195,198,200,82,212,86,242,79,147,234,223,174,3,153,83,47,136,98,114,29,257,76,68,178,222,154,251,56,231,128,159,13,51,119,75,171,179,19,267,217,201,33,150,186,50,241,71,120,131,44,182,4,189,109,185,97,95,92,187,60,42,191,69,26,184,230,199,133,17,110,73,39,11,52,229,216,152,175,66,203,27,237,269,139,151,181,221,162,77,22,210,53,196,7,161,190,170,233,125,14,253,206,140,224,124,10,70,256,263,259,34,261,116,8,258,138,91,12,85,168,226,5,101,208,225,160,16,149,135,235,244,64,192,214,63,9,202,108,55,197,30,24,165,40,164,90,209,183,266,2,141,129,104,239,238,148,205,215,43,177,144,117,218,157,270,54,115,220,41,74,146,112,102,45","comment":"Linear magma over Z/271Z (the prime field F_271): x ◇ y = 11x + 261y (mod 271).","submitted_at":"2026-04-28 16:22:08","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/271/a27d3c0090d02179a0ecebd9eabc9b148971f279511bff3f22947bdaec01d9c9.txt"},{"canonical_hash":"1d208a46a9b9ad13521d1ad8ca97ab290a864d18a5dbee60403232e8bc63c1ee","size":275,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,5,2,3,274,8,7,9,6,4,35,39,32,30,34,256,33,38,36,31,37,217,210,212,216,218,251,215,219,211,213,214,125,127,120,128,129,252,124,123,126,122,121,160,167,169,161,163,263,168,165,164,162,166,91,95,96,98,93,271,97,94,92,99,90,235,238,239,231,236,259,230,232,233,234,237,246,241,242,244,247,254,243,240,248,245,249,144,149,142,146,140,267,143,147,141,148,145,80,86,88,89,82,261,87,84,83,81,85,159,155,158,156,152,262,153,150,157,154,151,186,180,185,182,187,264,184,183,188,181,189,56,52,54,55,58,270,53,51,59,57,50,77,73,75,76,79,266,74,71,70,78,72,174,177,178,170,172,257,171,173,179,175,176,107,104,103,100,109,272,108,102,101,105,106,23,26,27,29,22,255,28,20,24,21,25,201,202,205,209,206,268,207,208,204,200,203,112,118,116,114,110,253,115,117,111,113,119,194,190,192,193,196,265,191,198,197,195,199,66,68,62,69,61,258,65,64,67,63,60,46,42,44,43,47,250,45,40,49,48,41,13,19,10,12,15,260,11,17,16,14,18,228,222,226,224,221,273,220,225,227,223,229,139,135,137,138,131,269,136,133,132,130,134","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_11(10,2).","submitted_at":"2026-04-28 19:32:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/275/1d208a46a9b9ad13521d1ad8ca97ab290a864d18a5dbee60403232e8bc63c1ee.txt"},{"canonical_hash":"f0c9813fdf93be50250018476b96de899287f0db5ae63b8f95dcd7d750ab1f69","size":275,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,9,5,7,6,2,4,274,3,8,31,32,38,30,37,35,39,34,256,33,36,213,214,216,215,219,217,211,210,251,212,218,122,123,120,126,128,127,124,125,252,121,129,165,169,160,166,164,161,163,162,263,167,168,94,98,90,93,95,99,91,96,271,92,97,233,234,231,232,236,235,237,238,259,230,239,248,241,247,245,249,246,243,242,254,244,240,148,147,146,140,149,144,145,142,267,141,143,87,81,83,88,86,82,85,84,261,89,80,155,153,157,152,151,158,156,159,262,154,150,185,182,188,181,186,184,183,187,264,180,189,58,52,54,59,57,53,56,55,270,50,51,73,77,79,74,72,78,70,71,266,75,76,179,176,172,171,175,177,173,174,257,170,178,101,107,106,100,103,102,104,109,272,108,105,26,24,27,22,23,29,20,21,255,25,28,207,203,201,200,205,202,208,204,268,206,209,119,114,117,113,111,116,110,112,253,118,115,199,193,195,191,198,194,197,196,265,190,192,63,65,60,66,61,68,67,64,258,69,62,42,49,40,45,46,47,43,41,250,48,44,10,15,17,12,11,16,19,18,260,13,14,226,220,228,229,221,222,227,225,273,224,223,132,136,138,133,131,137,130,139,269,134,135","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_11(4,8).","submitted_at":"2026-04-28 19:32:15","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/275/f0c9813fdf93be50250018476b96de899287f0db5ae63b8f95dcd7d750ab1f69.txt"},{"canonical_hash":"624c20fb2112972ba3054cf831d49cc39a19a8c3e013e3548f0140c622f3f518","size":275,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,9,7,6,4,3,5,274,2,8,39,30,34,31,36,38,37,33,256,35,32,212,214,219,215,210,218,211,213,251,217,216,123,121,120,129,128,126,122,127,252,124,125,163,166,164,165,167,162,169,160,263,161,168,93,99,95,96,94,90,91,92,271,98,97,232,237,235,234,238,231,239,230,259,236,233,241,246,249,240,243,245,247,248,254,244,242,142,146,149,145,147,148,141,140,267,143,144,84,83,81,80,82,85,87,88,261,89,86,158,157,151,152,153,159,150,155,262,154,156,180,186,184,181,183,185,188,187,264,182,189,54,53,50,51,52,55,56,59,270,58,57,76,79,73,72,78,77,71,75,266,74,70,175,179,173,172,177,178,174,176,257,170,171,100,101,103,102,109,106,107,105,272,104,108,23,20,22,27,24,25,28,21,255,26,29,200,201,207,208,204,205,202,209,268,203,206,116,118,115,114,117,113,112,110,253,111,119,191,194,199,198,195,190,193,197,265,196,192,65,63,67,62,68,61,60,64,258,69,66,45,43,47,40,41,42,49,46,250,44,48,19,11,17,16,10,18,14,12,260,13,15,227,224,222,229,225,228,223,226,273,220,221,138,131,136,137,130,139,134,132,269,133,135","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_11(5,7).","submitted_at":"2026-04-28 19:32:23","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/275/624c20fb2112972ba3054cf831d49cc39a19a8c3e013e3548f0140c622f3f518.txt"},{"canonical_hash":"127b6c013db3bb62967d79c7501f39120a9fa6c16a37f0793ae5f1f8143ca97c","size":275,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,7,3,4,8,2,9,6,274,5,31,39,36,33,34,35,32,38,37,256,30,211,212,214,218,215,217,210,213,219,251,216,127,121,124,129,128,125,120,126,122,252,123,162,169,163,165,161,168,164,167,166,263,160,93,91,95,90,98,97,94,96,92,271,99,237,231,232,235,239,230,236,238,234,259,233,243,240,248,247,241,245,242,244,246,254,249,145,144,142,148,149,143,146,147,140,267,141,87,84,88,81,85,83,89,82,80,261,86,153,157,159,155,156,150,152,154,151,262,158,182,181,187,184,188,183,185,180,186,264,189,53,51,54,56,50,59,55,58,57,270,52,72,79,73,75,71,78,74,77,76,266,70,173,175,174,179,171,177,172,170,178,257,176,100,102,104,108,109,101,106,107,105,272,103,20,25,21,22,29,28,26,27,23,255,24,207,206,201,209,208,203,205,200,202,268,204,111,113,115,110,119,114,112,118,117,253,116,197,194,198,191,195,193,199,192,190,265,196,67,64,68,61,65,63,69,62,60,258,66,48,40,44,43,47,45,49,41,42,250,46,12,19,13,15,10,18,14,17,16,260,11,227,226,222,229,228,225,224,223,221,273,220,138,135,139,131,136,134,130,133,132,269,137","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_11(6,6).","submitted_at":"2026-04-28 19:32:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/275/127b6c013db3bb62967d79c7501f39120a9fa6c16a37f0793ae5f1f8143ca97c.txt"},{"canonical_hash":"e16d69d9e60d9e2d4dafdbe055df47040af2d3fbb6a526b6c6b42fef7b6d0272","size":277,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"276,0,57,114,16,270,165,251,67,233,229,212,124,68,210,19,26,204,192,54,188,6,263,201,175,164,27,74,261,112,70,97,77,53,255,145,243,85,13,176,239,76,51,208,222,127,252,100,134,126,123,45,78,184,33,106,220,162,163,20,29,8,148,108,36,240,12,269,214,42,104,241,202,90,44,191,64,179,135,166,198,182,35,96,10,98,259,231,273,156,178,221,211,216,151,226,93,91,177,161,174,186,2,236,37,264,235,103,84,15,157,101,271,40,121,95,122,203,71,171,80,140,48,92,107,69,159,196,87,49,199,14,63,207,228,246,265,109,5,47,155,219,200,274,253,17,60,245,3,41,242,113,23,153,138,4,94,34,125,25,249,168,141,167,86,225,147,111,61,38,149,189,218,83,190,50,232,128,115,131,137,139,272,105,262,257,267,132,110,227,185,213,144,56,142,81,136,244,120,181,133,18,237,9,55,248,195,150,88,260,223,58,194,82,154,102,43,75,66,117,116,266,152,79,230,32,7,169,172,180,146,206,173,268,254,1,30,193,130,59,39,197,99,209,275,31,143,24,158,215,28,73,118,129,247,217,46,234,89,238,250,72,65,256,22,170,258,183,187,21,205,119,224,62,160,11,52","comment":"Linear magma over Z/277Z (the prime field F_277): x ◇ y = 116x + 164y (mod 277).","submitted_at":"2026-04-28 16:22:10","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/277/e16d69d9e60d9e2d4dafdbe055df47040af2d3fbb6a526b6c6b42fef7b6d0272.txt"},{"canonical_hash":"099e9d3d5eecc86e1837c3b5f17da0da3490ff44d471c8cd74b90fb8d4a5fe12","size":277,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"276,0,204,61,123,268,151,112,213,31,35,181,70,117,259,215,37,166,178,12,182,116,100,17,240,76,207,1,26,82,39,150,184,185,108,148,97,199,202,87,101,132,206,162,270,242,164,71,64,49,246,193,11,163,205,46,173,59,229,119,186,195,69,86,126,176,127,18,255,44,90,23,267,183,118,103,121,236,234,55,271,62,222,75,10,54,104,109,14,84,66,20,106,177,241,266,154,232,139,155,47,260,135,180,201,175,105,243,124,219,159,146,92,122,149,251,53,91,209,244,128,77,114,79,239,192,233,174,216,189,95,6,217,110,165,269,22,138,191,210,237,98,170,264,34,198,125,19,208,197,273,157,211,140,60,38,58,9,145,190,15,72,152,248,3,16,245,235,200,5,144,29,274,220,256,275,161,89,231,238,156,230,167,142,253,30,96,85,65,113,33,28,73,129,56,203,81,172,74,158,137,2,27,42,225,168,99,48,120,179,94,8,252,7,67,50,214,228,43,153,78,272,88,224,262,130,212,147,68,83,52,263,143,171,261,187,13,25,45,221,218,21,247,32,227,226,249,115,63,102,134,188,57,141,93,24,40,258,131,254,265,136,196,160,41,51,257,111,107,194,36,250,169,4,80,223,133","comment":"Linear magma over Z/277Z (the prime field F_277): x ◇ y = 160x + 190y (mod 277).","submitted_at":"2026-04-28 16:22:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/277/099e9d3d5eecc86e1837c3b5f17da0da3490ff44d471c8cd74b90fb8d4a5fe12.txt"},{"canonical_hash":"03afda3ba57d078005b49cd7545169526067945042de21c5a08ffebf981887f9","size":277,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"276,0,71,268,170,88,115,233,143,186,187,28,214,157,103,155,5,30,33,15,34,174,230,194,61,204,153,10,202,217,11,132,66,72,232,120,235,87,82,224,236,178,147,29,100,50,41,220,263,265,51,74,9,35,77,270,26,256,64,169,78,86,208,218,165,21,171,200,102,18,219,184,105,83,163,248,158,60,48,255,106,274,151,221,1,272,231,238,199,206,252,189,243,27,44,99,133,59,112,116,253,109,173,22,76,38,237,56,176,156,117,131,251,164,126,58,266,245,142,62,177,210,162,222,55,68,42,32,138,73,246,8,144,244,24,94,201,129,85,148,43,241,31,110,181,81,159,183,136,75,95,128,154,118,262,275,273,3,125,79,182,203,121,63,227,188,45,54,70,2,119,197,101,139,108,16,23,213,53,49,122,47,36,130,90,180,229,212,269,239,198,191,209,160,261,65,211,20,215,111,123,7,185,226,146,19,247,259,175,39,240,14,107,228,258,271,149,141,12,127,216,89,207,140,98,166,137,114,225,223,260,104,113,37,92,84,4,196,264,145,150,195,57,192,135,152,46,168,257,242,167,67,267,124,234,190,17,97,172,96,93,179,69,40,6,254,91,250,249,80,193,52,25,13,205,134,161","comment":"Linear magma over Z/277Z (the prime field F_277): x ◇ y = 116x + 229y (mod 277).","submitted_at":"2026-04-28 16:22:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/277/03afda3ba57d078005b49cd7545169526067945042de21c5a08ffebf981887f9.txt"},{"canonical_hash":"952bea5a4e8224c71acc1aa0329fa11754574dae626c8fb4d49fe8f3c9d7d6ad","size":277,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"276,0,9,135,28,184,126,24,19,223,175,178,117,101,48,272,43,82,214,71,166,113,169,115,108,2,92,12,39,249,263,138,34,266,73,162,205,98,62,189,157,197,104,130,160,84,106,105,99,35,11,170,83,118,25,8,274,159,240,77,254,146,129,201,269,238,257,103,64,203,153,4,196,46,89,133,53,156,180,207,148,123,188,57,95,219,121,61,151,225,75,79,97,226,96,208,90,204,270,78,26,36,161,190,74,250,109,72,16,224,29,186,265,6,150,252,231,33,68,60,245,14,137,41,120,182,192,262,260,218,229,143,248,49,94,172,55,38,194,56,144,193,13,232,187,110,37,91,80,122,124,54,3,258,147,31,171,107,198,206,139,93,114,44,179,127,275,168,86,155,210,247,112,212,52,22,142,165,216,132,66,228,70,234,88,235,217,213,87,45,199,259,81,233,195,50,261,42,69,5,17,191,271,227,152,58,181,47,65,202,241,119,100,131,63,267,40,116,215,102,20,136,177,164,256,221,15,174,141,237,243,244,222,21,268,242,59,18,51,200,236,67,23,211,128,140,32,125,111,145,173,230,183,246,253,30,251,27,209,76,220,149,134,154,239,255,7,10,85,158,163,264,1,167,273,176,185","comment":"Linear magma over Z/277Z (the prime field F_277): x ◇ y = 160x + 247y (mod 277).","submitted_at":"2026-04-28 16:22:17","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/277/952bea5a4e8224c71acc1aa0329fa11754574dae626c8fb4d49fe8f3c9d7d6ad.txt"},{"canonical_hash":"d999bf8fe983f5372d309aebd9266883b56b8fb4beddc8adf1e3d011f4feac87","size":281,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,267,209,88,149,256,251,223,98,142,57,167,222,68,102,90,232,186,39,96,202,163,93,136,173,101,41,143,270,229,114,274,124,211,94,265,65,213,162,6,16,266,237,54,188,129,80,252,280,112,220,269,48,194,97,126,156,146,22,73,205,125,234,71,264,134,254,89,130,3,181,241,33,276,233,23,62,236,179,46,92,230,242,208,82,27,197,2,238,83,111,116,9,228,69,127,141,140,104,11,61,42,131,155,170,246,64,152,7,231,154,160,200,207,58,49,70,118,36,53,190,137,135,153,25,87,110,272,66,180,191,75,219,216,224,113,117,217,56,139,177,203,235,171,249,145,248,107,212,24,119,185,169,85,150,81,239,192,263,184,278,187,74,43,172,159,260,148,115,34,59,240,262,78,268,55,28,273,35,121,166,103,157,105,178,158,226,21,144,4,161,86,18,38,245,17,243,26,261,175,133,168,195,128,218,122,100,199,174,255,8,120,19,32,183,214,47,138,44,123,52,99,221,10,225,29,45,259,164,72,247,108,5,109,31,95,63,37,279,196,77,257,253,84,76,79,215,51,40,206,132,250,227,165,13,275,277,50,193,176,258,210,189,198,67,60,20,14,91,147,12,204,106,30,15,271,182,201,151,244","comment":"Linear magma over Z/281Z (the prime field F_281): x ◇ y = 233x + 49y (mod 281).","submitted_at":"2026-04-28 16:22:19","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/281/d999bf8fe983f5372d309aebd9266883b56b8fb4beddc8adf1e3d011f4feac87.txt"},{"canonical_hash":"bf6aecd488308562384b24d801106c8d1d190922b97628ffa45502c100959342","size":281,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,40,230,102,236,53,218,221,160,216,233,192,125,178,37,30,68,185,172,153,199,46,251,223,151,273,228,152,117,60,191,143,109,101,245,47,253,84,7,107,55,28,204,173,261,89,16,74,92,86,137,31,15,201,87,6,115,104,190,126,63,250,17,276,36,98,49,217,212,188,174,26,181,149,42,219,269,148,56,139,97,43,80,103,24,169,85,70,82,27,197,2,100,122,246,272,94,213,184,22,145,215,144,135,39,99,165,66,23,278,118,268,209,18,211,131,95,62,274,264,14,127,58,260,123,256,252,280,112,116,263,120,198,267,154,124,134,202,235,271,71,158,69,128,258,138,163,206,25,239,179,275,4,75,5,162,44,73,234,132,106,262,240,142,57,167,222,210,225,29,164,243,220,183,237,279,196,8,129,79,182,9,41,166,34,48,72,77,189,238,176,136,157,110,203,266,50,244,255,146,227,61,155,171,277,226,232,214,156,229,121,33,64,168,195,247,147,224,113,187,105,241,249,3,51,200,257,12,88,133,11,83,111,186,59,13,32,45,208,170,177,38,265,52,93,76,20,81,78,193,96,242,90,180,141,140,35,161,19,114,205,207,91,270,10,54,119,248,108,259,194,150,130,231,67,65,254,159,21,175","comment":"Linear magma over Z/281Z (the prime field F_281): x ◇ y = 154x + 128y (mod 281).","submitted_at":"2026-04-28 16:22:21","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/281/bf6aecd488308562384b24d801106c8d1d190922b97628ffa45502c100959342.txt"},{"canonical_hash":"752b4ba3c758add85c82af7e86e84c06f7c31525f35e05aebab274ab16c7d99d","size":281,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,187,49,73,25,171,163,144,257,12,256,21,123,251,223,18,115,181,32,269,96,114,177,206,209,52,261,188,244,193,246,81,208,242,34,124,253,84,259,273,75,170,149,207,203,214,234,110,175,136,276,35,250,94,74,63,67,9,30,215,133,119,224,113,264,174,102,68,221,106,53,104,48,121,192,69,66,37,254,236,129,172,41,255,158,83,111,263,161,116,152,117,4,23,31,165,213,189,47,141,140,7,107,279,196,260,61,93,145,128,130,92,198,137,143,239,33,87,118,59,160,134,238,231,194,17,108,148,266,105,217,212,76,230,138,13,205,42,275,45,36,168,195,97,211,24,271,80,225,29,14,82,27,197,2,44,122,78,272,150,101,240,22,89,159,200,79,95,155,109,178,191,166,6,156,265,186,43,243,39,62,50,40,70,127,226,204,11,88,252,280,112,228,151,64,86,267,210,180,190,202,179,103,183,46,125,16,146,26,51,38,249,15,235,219,60,19,229,162,100,241,10,132,218,262,184,142,57,167,222,154,169,85,220,131,164,71,237,55,28,176,185,135,182,65,153,278,90,216,72,77,245,126,8,248,157,54,91,98,274,20,199,258,227,173,99,3,277,58,232,270,268,5,233,201,120,56,139,247,147","comment":"Linear magma over Z/281Z (the prime field F_281): x ◇ y = 91x + 191y (mod 281).","submitted_at":"2026-04-28 16:22:23","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/281/752b4ba3c758add85c82af7e86e84c06f7c31525f35e05aebab274ab16c7d99d.txt"},{"canonical_hash":"9eb724883f7a8047ecfefc40d61373b4d93637db762cef2e74a511f3d58b9c04","size":281,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,117,217,168,195,177,91,179,3,25,89,136,107,212,80,175,129,225,29,94,193,15,192,151,240,166,187,130,211,172,215,204,36,59,90,115,184,262,246,156,279,196,161,259,233,278,271,157,49,66,46,58,133,200,60,273,198,186,206,189,17,131,138,93,119,21,56,139,16,106,122,44,255,230,199,176,64,75,32,71,270,47,26,100,11,52,155,53,234,169,85,269,35,220,72,247,276,229,165,143,39,231,37,55,28,77,257,141,140,188,135,159,163,264,38,132,194,227,109,181,219,277,274,81,8,146,154,245,86,67,4,244,70,203,147,12,260,218,254,239,103,182,33,263,20,224,113,267,265,256,205,88,83,111,266,142,57,167,222,236,102,34,232,18,95,208,202,51,261,248,61,213,153,31,214,5,170,50,180,43,150,209,9,101,162,118,128,98,237,110,76,185,24,252,280,112,164,45,216,250,97,238,268,258,22,241,149,69,10,183,40,190,30,145,74,171,13,73,201,108,121,191,62,68,235,158,92,174,242,96,82,27,197,2,126,251,223,228,65,116,125,127,253,84,160,123,173,42,243,99,114,78,120,152,7,63,210,104,144,207,226,105,14,6,148,221,134,137,79,41,249,87,54,272,178,124,23,19,275,48","comment":"Linear magma over Z/281Z (the prime field F_281): x ◇ y = 87x + 195y (mod 281).","submitted_at":"2026-04-28 16:22:24","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/281/9eb724883f7a8047ecfefc40d61373b4d93637db762cef2e74a511f3d58b9c04.txt"},{"canonical_hash":"a586ea9852731c2e66d0fd9071e113176fb0ba0da12b9938f45faa204e7e3901","size":289,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"288,284,179,49,74,268,227,17,243,106,163,90,122,211,195,33,138,25,159,139,183,109,60,213,275,7,11,277,72,63,249,191,283,12,203,189,54,172,34,250,78,241,278,144,238,77,108,178,170,199,185,82,261,111,216,40,14,196,64,239,240,59,48,157,42,69,117,120,98,30,75,133,232,255,58,286,212,73,145,65,256,85,136,80,182,9,259,166,84,56,143,274,267,44,47,123,269,279,197,224,167,252,251,135,156,237,6,226,102,52,287,220,192,247,91,3,233,15,134,41,76,10,16,208,23,265,175,229,88,37,125,27,207,164,8,79,276,242,217,31,253,234,28,151,127,263,150,22,236,258,181,68,107,130,244,214,35,112,99,168,4,126,264,5,165,97,116,177,71,105,187,1,154,18,61,173,262,174,225,92,38,128,169,62,162,147,222,114,271,161,96,149,228,110,55,83,81,198,248,89,152,100,19,272,155,115,21,87,51,142,132,260,184,190,121,137,280,193,230,29,113,235,36,0,273,231,119,202,282,210,66,140,204,118,86,270,221,176,219,266,254,215,188,20,194,205,94,93,201,50,160,186,70,257,124,57,39,53,24,32,245,223,101,281,141,95,2,104,180,26,200,43,171,158,146,45,103,209,218,131,148,153,129,67,206,246,46,285,13","comment":"Linear magma over the extension field F_289 = F_17[α]/⟨α² − 3⟩.\n\nOperation: x ◇ y = a·x + b·y in F_289 with a = 8 + 15α, b = 6 + 5α. Here β = 6 + 5α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_289, and α_coef = -β³ - β - 1. This is Pace Nielsen's \"Type 2\" non-fully-idempotent linear 677 magma family.\n\nNote: 10 ∤ (17² − 1) = 288, so F_289 has no primitive 10th roots of unity → no Type-1 (translation-invariant fully-idempotent) linear 677 magma exists at this size. But Φ_2_5 has 4 roots in F_289 (forming 2 Galois-conjugate orbits under Frobenius), giving 2 distinct iso classes of Type-2 magmas at this size.\n\nF_289 is the proper degree-2 extension of F_17; do NOT confuse with the ring Z/289Z (which has zero divisors and is NOT a field).\n\nSize 289, not fully idempotent, right-cancellative. This iso class is one of the two known Eq 677 magmas at size 289 in the DB.\n\n[text written by Claude]","submitted_at":"2026-05-16 12:58:16","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/289/a586ea9852731c2e66d0fd9071e113176fb0ba0da12b9938f45faa204e7e3901.txt"},{"canonical_hash":"2d5005e6916ba6e431a8f0f36b35ada32b5b5bfe1115af31b207467bd704e353","size":289,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"288,284,264,262,276,270,274,266,256,272,282,258,286,260,278,280,268,257,98,244,103,168,181,212,22,43,195,237,44,77,80,127,287,138,269,207,110,249,224,56,115,89,180,92,161,139,192,19,10,150,55,267,222,87,108,12,90,254,53,137,113,205,21,178,247,148,159,54,281,72,219,173,122,151,229,204,236,7,36,29,95,130,69,35,160,275,4,145,186,62,116,61,13,167,63,230,213,156,198,66,121,223,279,125,202,217,67,9,120,190,0,227,70,128,234,171,33,34,149,271,163,251,17,117,57,94,112,194,58,152,182,209,141,226,8,91,261,27,84,48,199,18,185,107,102,142,131,81,241,47,216,172,248,277,232,188,200,31,225,65,147,158,118,123,169,2,215,32,68,11,255,75,24,242,157,193,166,136,42,210,96,78,41,101,1,235,179,263,133,50,49,187,250,144,86,243,16,174,104,25,83,201,218,109,259,239,105,82,214,140,197,246,79,183,30,45,100,46,170,129,20,265,176,51,85,146,111,14,52,23,252,220,245,135,106,189,203,88,283,38,175,132,231,162,5,221,97,153,37,238,74,28,124,71,206,285,39,134,26,3,208,155,177,76,164,73,99,40,240,233,126,191,273,154,15,143,64,93,60,253,211,59,6,196,165,184,119,228,114","comment":"Linear magma over the extension field F_289 = F_17[α]/⟨α² − 3⟩.\n\nOperation: x ◇ y = a·x + b·y in F_289 with a = 8 + 2α, b = 2 + 7α. Here β = 2 + 7α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_289, and α_coef = -β³ - β - 1. This is Pace Nielsen's \"Type 2\" non-fully-idempotent linear 677 magma family.\n\nNote: 10 ∤ (17² − 1) = 288, so F_289 has no primitive 10th roots of unity → no Type-1 (translation-invariant fully-idempotent) linear 677 magma exists at this size. But Φ_2_5 has 4 roots in F_289 (forming 2 Galois-conjugate orbits under Frobenius), giving 2 distinct iso classes of Type-2 magmas at this size.\n\nF_289 is the proper degree-2 extension of F_17; do NOT confuse with the ring Z/289Z (which has zero divisors and is NOT a field).\n\nSize 289, not fully idempotent, right-cancellative. This iso class is one of the two known Eq 677 magmas at size 289 in the DB.\n\n[text written by Claude]","submitted_at":"2026-05-16 12:58:18","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/289/2d5005e6916ba6e431a8f0f36b35ada32b5b5bfe1115af31b207467bd704e353.txt"},{"canonical_hash":"d5965040574f5390aa3e153c1743e8786570addb984a9aac5764d08b9363f723","size":307,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"306,0,242,68,137,234,269,91,9,95,129,201,164,216,292,261,233,245,296,12,17,118,96,31,59,121,111,122,187,37,156,286,128,228,140,284,191,57,230,243,225,127,28,66,297,288,211,46,260,141,25,272,35,279,24,88,82,56,205,124,51,202,181,145,18,103,123,300,6,4,179,67,86,29,258,148,125,251,138,42,120,149,19,16,214,132,267,10,192,45,183,266,106,34,247,222,155,53,5,255,217,263,167,215,207,36,174,265,218,303,289,84,283,101,257,203,100,270,22,295,252,55,97,154,76,33,1,231,224,93,304,240,23,79,195,32,236,180,238,262,74,73,268,70,287,197,213,168,153,47,43,186,21,299,146,173,8,196,200,41,26,60,44,134,223,115,226,227,109,85,14,83,162,305,232,171,87,151,246,71,78,193,161,229,40,250,208,99,142,172,117,253,50,104,254,130,237,136,150,65,112,20,158,54,62,27,110,64,102,189,206,39,69,94,160,259,113,11,198,2,184,114,285,61,178,175,302,273,152,291,98,278,301,105,165,239,220,15,190,188,147,276,256,176,298,13,49,204,277,52,209,235,241,170,126,159,119,169,294,107,199,58,135,144,219,166,280,72,90,77,210,3,131,293,75,281,133,38,157,7,275,264,274,212,163,249,271,177,182,143,92,80,108,139,63,30,48,282,248,185,244,116,81,290,221,89,194","comment":"Linear magma over Z/307Z (the prime field F_307): x ◇ y = 289x + 120y (mod 307).","submitted_at":"2026-04-28 16:22:28","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/307/d5965040574f5390aa3e153c1743e8786570addb984a9aac5764d08b9363f723.txt"},{"canonical_hash":"428de17a5b92b6496df84c403129358a8b22a6d964eab8441754b1921afead26","size":307,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"306,0,141,84,174,37,117,17,207,78,70,115,150,235,50,13,240,7,4,234,103,302,148,71,183,257,286,54,83,125,64,122,273,2,129,237,126,25,285,229,136,185,44,199,181,298,104,239,216,217,290,90,28,106,87,62,116,228,176,230,97,203,155,278,15,164,142,154,162,47,270,287,177,247,58,233,27,42,262,303,169,30,218,191,77,43,250,119,232,151,40,144,137,9,272,163,267,255,268,85,32,189,123,147,61,231,139,74,120,109,95,292,149,297,261,291,209,205,263,23,112,140,236,161,188,186,20,82,48,193,197,256,175,143,187,274,213,67,98,101,12,215,29,260,210,72,280,211,91,36,284,304,60,66,75,51,295,275,45,100,202,271,81,201,251,38,224,21,3,89,76,204,283,196,152,166,265,206,184,57,73,11,195,179,170,245,131,121,14,254,214,200,300,252,288,158,301,86,118,111,65,130,222,52,156,114,180,41,94,259,264,258,172,281,1,128,153,31,160,223,110,241,34,68,182,227,39,178,294,253,33,18,242,49,238,168,296,279,56,171,145,133,173,24,269,146,212,88,221,167,219,107,53,96,8,19,99,299,226,225,248,6,289,190,208,35,194,127,220,276,16,135,246,138,305,282,113,55,134,92,63,277,266,192,80,157,293,5,243,102,105,249,22,59,244,159,124,79,69,198,26,108,46,165,93,132,10","comment":"Linear magma over Z/307Z (the prime field F_307): x ◇ y = 289x + 169y (mod 307).","submitted_at":"2026-04-28 16:22:31","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/307/428de17a5b92b6496df84c403129358a8b22a6d964eab8441754b1921afead26.txt"},{"canonical_hash":"e6d0796a16829303762badb426dc40b8513d7046a77d18a413fc1217a19d7963","size":311,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,232,276,273,117,63,32,58,48,226,265,193,86,207,269,161,57,8,242,97,112,15,49,220,245,36,158,149,102,37,201,25,144,268,29,216,280,2,177,82,119,309,279,228,9,153,271,293,258,99,14,30,247,68,251,39,224,94,31,227,140,84,183,126,11,262,159,101,261,301,253,240,306,229,233,206,13,122,165,303,141,243,235,288,215,305,147,123,217,197,129,199,111,93,310,248,266,44,284,42,62,278,302,150,60,133,80,88,296,148,10,277,168,51,78,74,151,85,98,146,106,256,4,107,166,281,28,239,295,72,186,249,69,194,96,223,92,185,169,254,103,138,116,308,164,73,124,154,274,237,22,157,125,61,184,113,299,180,46,192,257,304,3,191,90,65,204,170,267,252,87,163,212,6,114,52,241,38,110,71,203,213,187,218,272,118,121,77,156,155,134,127,16,35,182,41,91,5,142,178,172,264,292,214,255,45,40,208,175,189,143,300,79,307,202,18,131,19,7,250,198,294,64,291,210,135,275,81,12,50,21,76,209,66,108,244,83,283,222,211,188,104,285,225,270,287,105,179,181,75,230,26,24,260,132,115,70,130,259,33,56,67,128,238,89,263,221,54,231,176,205,167,236,120,290,55,136,219,139,43,95,162,174,286,173,47,152,234,145,298,34,20,53,195,200,100,59,137,109,17,23,297,160,246,196,27,190,171,282,289","comment":"Linear magma over Z/311Z (the prime field F_311): x ◇ y = 217x + 95y (mod 311).","submitted_at":"2026-04-28 16:22:34","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/311/e6d0796a16829303762badb426dc40b8513d7046a77d18a413fc1217a19d7963.txt"},{"canonical_hash":"ba29669920b63a23d46e49e8e901ece1d23cdd9e516c70898b9a1d96f6d1cb30","size":311,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,5,199,262,186,164,37,2,304,63,121,129,278,210,6,290,31,118,162,13,100,200,249,194,285,258,138,10,263,43,229,98,58,307,297,187,235,260,242,39,204,143,165,21,216,128,161,257,57,38,160,266,244,267,15,271,3,158,182,106,245,176,80,305,94,66,191,268,218,60,64,212,113,224,16,29,55,122,185,169,48,272,96,46,130,91,140,221,4,303,289,248,42,234,20,159,157,93,211,184,90,41,183,102,149,7,103,276,174,107,109,72,291,150,214,232,246,87,309,32,8,53,154,177,207,125,119,104,172,132,81,68,281,163,277,12,137,306,203,256,14,175,217,28,95,302,156,101,108,86,206,67,202,301,201,110,146,134,192,111,51,250,73,115,35,269,147,299,195,292,252,240,219,135,179,286,151,198,62,61,193,228,259,215,265,181,65,112,168,139,233,89,275,213,52,171,11,247,85,145,114,251,197,264,88,84,83,225,74,295,44,279,226,77,17,116,189,230,33,75,24,30,36,209,99,9,296,142,56,270,79,59,54,45,288,123,148,71,308,124,280,255,155,300,50,298,178,227,167,170,196,294,188,208,78,70,49,293,310,236,126,18,26,273,253,237,261,120,117,284,97,241,127,243,105,190,223,47,220,19,40,173,231,153,131,136,27,205,133,34,239,92,180,274,144,82,76,23,141,287,254,166,69,25,283,222,152,238,22,282","comment":"Linear magma over Z/311Z (the prime field F_311): x ◇ y = 53x + 259y (mod 311).","submitted_at":"2026-04-28 16:22:36","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/311/ba29669920b63a23d46e49e8e901ece1d23cdd9e516c70898b9a1d96f6d1cb30.txt"},{"canonical_hash":"3d8e4556e0cfd6604d4ce7d355ad4f979f32665e6638e8c1b8795bd544996177","size":311,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,131,256,220,99,92,123,231,6,289,14,240,184,226,259,186,216,26,237,22,157,63,185,246,299,51,118,170,192,257,56,189,5,28,3,266,108,267,252,87,39,212,130,176,52,55,224,48,195,79,89,187,94,272,304,245,77,280,93,196,127,140,283,182,165,215,253,142,54,172,16,292,276,193,293,288,84,113,251,19,238,141,307,202,204,255,81,7,188,74,46,126,105,148,73,213,205,12,298,145,200,271,190,294,306,269,159,222,25,64,166,223,163,208,287,43,241,305,13,168,150,86,198,132,53,8,68,11,219,180,67,4,114,151,139,35,116,45,300,143,167,50,58,228,303,260,281,201,229,33,162,236,100,49,47,152,296,83,174,96,268,239,133,138,38,121,137,171,17,209,297,98,60,10,27,128,295,282,41,248,125,232,90,149,117,249,32,244,234,40,203,69,210,207,21,285,57,194,242,97,112,263,111,158,183,160,34,211,102,37,15,273,206,144,91,30,218,2,177,82,181,61,31,104,71,29,85,169,134,161,76,278,247,254,65,101,286,156,155,227,78,146,59,250,135,262,221,225,75,115,129,178,120,291,109,20,199,122,103,179,265,119,173,164,153,243,147,309,217,197,191,261,235,279,310,124,80,106,36,42,62,154,302,88,308,9,18,274,110,24,258,277,44,175,264,136,275,23,284,270,230,70,66,107,290,95,214,301,233,72","comment":"Linear magma over Z/311Z (the prime field F_311): x ◇ y = 37x + 275y (mod 311).","submitted_at":"2026-04-28 16:22:38","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/311/3d8e4556e0cfd6604d4ce7d355ad4f979f32665e6638e8c1b8795bd544996177.txt"},{"canonical_hash":"d6a74af0719889acfe019025f942b59ba7a32239138531b5620877ab9fb67510","size":311,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,70,98,33,155,13,36,14,131,83,259,111,268,46,112,168,172,26,9,49,54,27,274,144,193,96,266,272,145,124,256,281,147,59,220,125,227,181,87,185,141,39,126,22,215,62,32,67,299,40,224,287,258,2,175,206,68,109,25,279,37,285,283,3,192,137,78,269,120,294,280,5,149,72,10,233,86,138,248,240,230,194,61,100,6,198,304,154,257,52,254,139,222,35,278,228,252,75,101,45,77,80,127,157,212,53,71,237,161,300,103,271,229,15,106,188,176,219,153,81,47,122,183,38,277,292,238,50,43,298,79,296,89,16,97,205,160,150,263,91,82,282,187,133,249,307,171,293,182,18,129,7,143,85,297,23,118,246,255,99,159,151,41,261,180,253,132,243,134,207,214,74,128,113,202,19,286,211,245,162,55,12,24,270,179,65,107,267,136,152,73,235,217,48,148,291,244,241,209,265,239,88,64,114,199,58,303,90,216,93,163,140,34,170,264,225,30,66,76,84,302,250,69,174,236,158,169,116,130,284,105,242,301,28,167,119,121,201,115,189,273,232,42,11,166,94,123,60,204,135,231,196,226,51,186,290,203,305,21,251,17,63,289,56,223,156,117,92,288,309,108,102,260,29,308,110,191,218,213,173,190,8,4,276,210,104,275,95,247,295,178,200,177,146,197,262,234,165,164,184,221,306,208,195,310,31,44,142,57,20","comment":"Linear magma over Z/311Z (the prime field F_311): x ◇ y = 7x + 305y (mod 311).","submitted_at":"2026-04-28 16:22:41","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/311/d6a74af0719889acfe019025f942b59ba7a32239138531b5620877ab9fb67510.txt"},{"canonical_hash":"acd78d74788e3d7841e80438eec8b0380b2a0b9039f4903716a031ad0d71aafd","size":321,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"244,218,213,170,148,270,101,266,174,93,89,144,222,240,209,105,42,186,259,203,167,68,143,64,207,83,87,163,182,38,263,139,118,304,314,276,298,113,14,109,280,285,289,294,308,122,318,10,133,248,230,22,31,156,192,152,26,75,79,35,252,129,234,196,117,9,311,313,283,297,112,13,108,279,284,288,293,307,121,317,243,104,217,212,169,147,269,100,265,173,92,88,151,221,247,208,41,138,185,258,202,166,67,142,71,206,82,86,162,181,37,262,132,195,255,229,21,30,155,199,159,25,74,78,34,251,128,233,226,273,44,49,55,62,176,127,51,18,97,272,191,50,227,178,0,56,225,238,48,1,46,239,177,47,189,6,99,237,53,57,301,303,320,302,45,58,275,224,5,16,98,59,190,124,52,4,63,54,236,7,179,126,61,2,60,17,188,96,274,125,19,3,23,134,153,28,231,32,130,249,253,157,72,27,197,235,76,193,204,43,65,164,260,160,39,187,183,69,80,200,140,256,84,136,171,245,267,145,214,149,241,219,223,271,90,175,106,210,94,102,277,119,110,295,315,299,123,305,309,114,290,281,11,319,286,15,36,66,201,85,81,165,184,40,257,141,180,261,205,161,70,137,246,268,168,95,91,146,216,242,211,107,220,215,172,150,264,103,135,154,20,77,73,29,254,131,228,198,250,232,24,33,158,194,120,111,282,287,291,296,310,116,312,12,306,316,278,292,115,8,300","comment":null,"submitted_at":"2026-05-17 14:54:31","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/321/acd78d74788e3d7841e80438eec8b0380b2a0b9039f4903716a031ad0d71aafd.txt"},{"canonical_hash":"8b5d0724ed8c88a3f808150d5693e831f53ba97392163a34ecf3ebc914540df8","size":325,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"300,5,84,270,42,72,60,121,97,18,30,109,54,301,4,95,269,41,83,71,131,107,17,29,119,53,318,256,170,280,220,194,182,158,134,244,208,146,231,313,254,172,278,218,196,184,160,136,242,206,148,230,309,9,88,274,46,76,64,124,100,22,34,112,58,303,6,85,271,43,73,61,120,96,19,31,108,55,304,1,91,265,36,79,67,127,103,13,24,115,48,308,2,93,267,39,81,69,129,105,15,27,117,51,315,259,175,283,223,199,187,163,139,247,211,151,233,319,258,177,282,222,201,189,165,141,246,210,153,236,307,8,87,273,45,75,63,123,99,21,33,111,57,324,289,297,290,293,296,298,299,294,288,292,295,291,305,7,86,272,44,74,62,122,98,20,32,110,56,320,261,169,285,225,193,181,156,132,249,213,144,237,314,253,173,277,217,197,185,161,137,240,205,149,229,321,262,168,286,226,192,180,157,133,250,214,145,238,322,252,178,276,216,202,190,166,142,241,204,154,228,312,255,171,279,219,195,183,159,135,243,207,147,235,316,260,174,284,224,198,186,162,138,248,212,150,234,302,0,90,264,37,78,66,126,102,14,25,114,49,311,10,89,275,47,77,65,125,101,23,35,113,59,317,257,176,281,221,200,188,164,140,245,209,152,232,310,3,94,268,40,82,70,130,106,16,28,118,52,306,11,92,266,38,80,68,128,104,12,26,116,50,323,263,179,287,227,203,191,167,143,251,215,155,239","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_13(9,11).","submitted_at":"2026-04-28 19:32:40","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/325/8b5d0724ed8c88a3f808150d5693e831f53ba97392163a34ecf3ebc914540df8.txt"},{"canonical_hash":"0fc39c877771ff7e57824856eedffe8e9b9bfbcaf85eac57e28ffbfed22dc87f","size":331,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,318,286,293,239,269,115,330,44,184,209,67,60,92,127,126,62,119,308,151,212,226,144,225,260,121,76,273,251,15,167,250,266,95,146,305,194,243,247,304,40,284,298,220,287,135,65,297,198,275,231,210,268,105,172,329,13,290,309,154,59,245,203,12,160,77,295,322,150,326,300,11,147,180,51,46,75,5,99,299,113,49,315,234,94,124,232,4,270,81,258,37,39,310,102,93,108,292,254,164,296,55,227,36,218,208,205,52,171,16,57,253,30,118,316,324,244,86,19,207,97,259,157,136,149,2,187,29,255,249,106,33,45,7,241,206,280,246,222,63,314,191,317,186,327,134,261,200,80,158,43,6,129,267,178,189,107,22,125,313,41,153,26,223,35,311,143,199,264,294,262,140,56,282,14,177,68,179,229,17,85,161,193,152,27,112,87,54,148,278,274,263,182,3,132,114,32,306,230,176,8,101,271,91,221,88,289,192,216,109,236,211,133,116,159,277,219,170,155,272,128,23,10,31,174,323,237,145,312,214,98,90,47,156,168,283,142,256,123,235,238,248,162,197,281,70,38,169,66,279,319,328,84,110,163,173,307,185,130,202,53,320,204,89,120,42,73,325,131,301,117,122,265,21,137,74,100,24,96,69,303,34,138,233,215,285,28,83,64,139,103,257,276,183,240,201,104,228,71,291,9,61,190,72,58,111,78,217,213,224,79,20,321,181,165,252,141,166,188,302,50,175,195,18,196,242,25,82,48,288","comment":"Linear magma over Z/331Z (the prime field F_331): x ◇ y = 324x + 8y (mod 331).","submitted_at":"2026-04-28 16:22:46","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/331/0fc39c877771ff7e57824856eedffe8e9b9bfbcaf85eac57e28ffbfed22dc87f.txt"},{"canonical_hash":"0b92141afcd8a4ecd297f68c9f46464e0ee74f9990c584c168839bc6d3a2941b","size":331,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"330,0,309,269,124,122,194,80,64,154,62,199,58,317,226,56,320,220,94,158,318,296,24,257,280,316,132,329,151,249,278,232,135,99,145,149,240,193,98,202,133,313,111,306,285,238,182,227,205,31,131,105,72,106,310,283,91,216,174,211,203,42,157,181,75,70,245,213,85,142,89,196,165,76,57,201,244,116,21,322,73,270,128,298,2,83,121,134,210,120,163,234,46,117,152,242,18,303,253,315,71,321,8,184,328,4,7,107,125,294,208,93,237,164,314,44,38,102,12,247,20,250,264,198,97,69,45,246,221,191,326,272,170,185,311,123,231,173,82,236,235,112,60,16,29,36,222,323,279,104,26,5,169,39,214,95,288,53,137,40,219,284,195,252,68,168,113,47,307,140,229,274,61,192,74,233,13,35,218,114,27,86,159,224,268,277,215,3,92,81,167,290,291,22,118,286,178,256,130,115,327,271,136,276,301,66,48,11,143,319,305,88,302,96,6,217,65,259,109,292,15,153,239,180,162,101,28,273,129,100,266,50,260,308,248,90,297,207,172,67,289,108,175,155,189,176,23,30,243,183,325,52,267,87,171,299,146,78,55,110,141,19,197,25,34,300,49,54,126,212,63,148,156,119,37,17,228,255,161,51,160,186,1,150,282,127,293,230,251,166,258,188,147,10,138,295,204,200,9,190,287,223,304,206,33,187,261,225,312,84,241,263,103,14,275,265,77,281,262,79,144,41,209,43,59,139,177,179,324,254,32","comment":"Linear magma over Z/331Z (the prime field F_331): x ◇ y = 299x + 88y (mod 331).","submitted_at":"2026-04-28 16:22:49","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/331/0b92141afcd8a4ecd297f68c9f46464e0ee74f9990c584c168839bc6d3a2941b.txt"},{"canonical_hash":"eb64c92edb5a465683c672885d9e9fb280521e6dff03c96e69beb38fb5d88d1a","size":331,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,318,102,105,62,207,64,232,5,190,155,326,179,41,305,250,96,124,271,210,135,60,287,9,152,7,50,47,263,56,55,298,145,167,174,8,27,23,100,292,123,136,58,315,181,325,121,251,276,164,206,329,161,156,15,109,33,310,170,208,81,169,75,98,34,2,160,308,149,91,220,120,241,227,30,69,122,238,17,141,25,173,137,127,107,214,262,247,28,110,295,286,246,248,299,71,95,172,280,138,51,154,68,234,130,239,61,90,321,284,39,242,97,37,143,12,77,309,327,86,265,259,328,76,65,197,218,324,38,311,319,53,291,129,322,162,113,166,279,147,235,252,46,245,188,223,281,59,261,194,132,195,249,24,222,186,158,189,29,146,212,230,104,148,128,48,116,199,74,323,18,288,44,32,258,312,228,125,205,11,330,66,150,180,283,257,313,87,99,233,73,268,19,144,171,103,183,203,49,285,157,201,84,134,213,131,277,79,304,140,187,139,316,4,226,278,133,300,101,307,290,202,224,111,168,217,267,184,236,108,264,256,93,269,163,142,10,21,273,314,320,31,272,254,22,67,198,92,42,297,94,229,266,35,6,294,185,289,13,209,106,193,225,117,40,16,244,303,301,231,240,165,83,302,317,159,52,182,192,118,80,196,72,293,177,14,85,282,296,175,275,36,204,253,215,57,89,43,20,114,26,153,115,255,88,54,70,211,216,274,151,219,221,306,176,270,126,260,3,191,178,237,45,78,82,63,119,112,200,243","comment":"Linear magma over Z/331Z (the prime field F_331): x ◇ y = 151x + 181y (mod 331).","submitted_at":"2026-04-28 16:22:52","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/331/eb64c92edb5a465683c672885d9e9fb280521e6dff03c96e69beb38fb5d88d1a.txt"},{"canonical_hash":"bc44f5670b2dca72e060d8d0f3cd0bfc4293ec747469524fa32893cdce48521c","size":331,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,7,205,325,162,210,208,232,119,310,133,305,143,70,170,297,238,72,10,39,65,198,286,319,254,22,83,151,19,67,4,176,46,160,57,329,184,154,193,98,236,153,3,318,237,309,204,17,243,86,301,99,27,59,234,43,62,116,194,216,323,25,79,105,32,155,172,295,30,226,180,271,185,257,149,278,280,245,200,275,102,96,95,148,294,322,58,203,97,45,21,9,304,161,168,103,128,289,267,248,47,81,276,121,89,165,92,177,191,201,109,283,130,228,5,299,246,139,124,111,220,68,77,281,123,282,88,288,20,147,279,225,78,42,242,152,56,150,64,69,207,54,84,265,258,13,221,260,141,23,107,186,312,112,50,252,255,75,272,188,125,291,182,320,240,181,251,140,53,241,287,274,227,91,247,303,321,199,270,31,115,300,317,183,66,285,296,118,6,327,292,40,315,173,36,229,15,126,11,34,156,135,131,214,189,73,330,33,314,284,269,273,239,74,106,264,55,146,76,298,190,80,167,202,101,256,171,215,26,308,192,175,253,71,132,324,196,178,164,51,144,136,217,158,93,223,113,306,157,195,307,166,263,313,134,35,117,114,90,250,187,311,12,63,224,122,138,108,120,127,44,94,277,29,24,233,16,235,159,82,38,142,209,230,60,218,48,212,261,211,37,28,137,249,262,222,163,174,100,145,268,213,14,326,316,302,52,290,49,259,206,41,87,110,129,219,266,8,293,244,179,104,61,85,2,328,18,197,169,231","comment":"Linear magma over Z/331Z (the prime field F_331): x ◇ y = 125x + 207y (mod 331).","submitted_at":"2026-04-28 16:22:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/331/bc44f5670b2dca72e060d8d0f3cd0bfc4293ec747469524fa32893cdce48521c.txt"},{"canonical_hash":"628c335200ee831f71fb491697165170a3a02c0efebd54ed70af78bd29059a17","size":331,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"330,0,234,114,296,290,54,194,146,3,140,250,191,258,38,185,86,20,236,15,80,301,312,243,35,74,320,116,106,219,29,274,223,70,253,100,298,232,248,78,217,246,151,92,162,292,305,153,103,46,211,133,170,24,56,156,94,128,281,121,97,143,124,196,285,164,207,7,315,63,327,60,148,182,294,256,310,272,215,44,279,5,308,307,43,309,181,326,6,284,142,280,155,169,45,304,91,216,231,252,273,105,73,311,14,85,257,139,193,295,48,52,183,33,68,149,131,260,61,213,324,328,83,66,64,267,40,316,135,226,8,11,269,208,240,187,165,172,200,286,177,1,197,49,88,125,26,111,144,18,318,98,160,22,122,58,277,282,229,137,129,265,238,95,158,263,157,264,228,57,159,17,25,96,176,171,239,10,134,266,82,212,130,32,47,138,13,104,230,303,154,283,180,306,278,271,293,59,314,163,123,120,93,23,210,152,161,245,247,99,222,218,319,242,79,19,37,249,145,289,233,112,189,299,27,76,101,126,205,254,89,167,71,50,322,224,198,109,275,329,174,30,178,118,220,287,203,107,201,202,117,173,108,321,166,204,75,188,288,36,241,221,244,209,119,313,270,179,302,12,31,81,9,175,16,227,262,237,136,276,21,317,110,87,41,199,186,268,225,39,65,323,259,67,51,192,84,72,251,90,168,141,325,42,4,214,255,147,62,206,195,261,127,55,132,102,291,150,77,297,69,28,115,34,300,235,184,190,2,53,113","comment":"Linear magma over Z/331Z (the prime field F_331): x ◇ y = 299x + 211y (mod 331).","submitted_at":"2026-04-28 16:22:58","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/331/628c335200ee831f71fb491697165170a3a02c0efebd54ed70af78bd29059a17.txt"},{"canonical_hash":"0c425c2c9885818c2ed85f236e100327110c4c04fa573129500d131698963831","size":331,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,68,4,20,114,181,147,105,224,28,146,57,141,286,275,40,85,317,213,229,38,140,155,96,92,310,59,290,119,112,269,8,212,200,76,225,255,6,167,207,189,230,121,91,47,323,36,270,171,65,13,176,294,231,268,26,67,53,325,295,185,237,248,253,148,254,285,104,101,257,318,251,308,298,250,70,120,234,307,16,292,273,208,50,161,233,23,170,14,228,18,215,195,115,238,62,49,99,267,41,309,320,30,278,88,60,51,227,126,184,204,7,239,3,159,34,222,172,61,219,284,303,5,296,223,131,81,261,287,319,262,329,246,90,93,274,243,137,242,259,226,196,306,314,64,78,37,279,220,305,187,2,54,160,281,25,312,58,102,110,241,178,218,156,17,244,236,87,211,201,19,280,123,130,301,48,321,103,107,166,151,27,240,202,328,74,29,264,297,152,46,135,39,235,94,136,192,125,9,15,79,12,11,139,122,42,313,133,158,32,232,205,66,132,289,106,149,304,108,283,117,214,71,247,153,199,327,113,24,315,80,163,98,190,100,282,206,45,145,177,127,245,72,277,182,249,198,322,191,84,86,299,263,265,183,175,291,162,197,10,154,129,168,63,55,33,330,22,44,52,157,118,165,21,186,173,302,164,194,276,252,288,75,73,180,311,209,260,193,266,83,256,116,188,134,56,217,271,89,179,109,174,69,326,35,124,316,210,142,258,82,203,128,272,97,293,138,95,300,143,77,216,221,43,169,144,324,31,111,150","comment":"Linear magma over Z/331Z (the prime field F_331): x ◇ y = 65x + 267y (mod 331).","submitted_at":"2026-04-28 16:23:01","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/331/0c425c2c9885818c2ed85f236e100327110c4c04fa573129500d131698963831.txt"},{"canonical_hash":"bd389c9b22f836839430da2a096719921c6fc565e9d4f5bac85d9cfd0db5d754","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,54,7,111,92,72,44,58,11,115,276,76,19,62,15,119,99,80,23,66,5,34,103,84,27,70,50,38,107,88,69,49,37,106,87,30,4,53,6,110,91,275,43,57,10,114,95,75,47,61,14,118,98,79,22,65,18,33,102,83,26,325,326,327,328,329,330,331,332,333,334,335,336,315,316,309,310,311,307,318,319,320,321,322,323,338,317,312,313,314,308,324,116,96,77,20,63,16,31,100,81,24,67,277,35,104,85,28,71,51,39,108,89,2,41,55,8,112,93,73,45,59,12,135,138,132,142,140,131,126,130,149,148,136,340,120,133,134,145,141,146,125,127,147,123,121,128,144,137,124,139,122,129,143,250,254,258,262,266,181,185,189,158,162,166,273,201,205,209,213,217,221,191,195,170,174,178,152,223,227,231,235,239,243,246,300,295,288,291,281,306,301,296,283,292,282,339,302,297,284,293,278,286,303,298,285,294,289,287,304,299,279,337,290,280,305,203,207,211,215,219,154,193,197,172,176,180,271,225,229,233,237,241,245,248,252,256,260,264,268,183,187,156,160,164,168,199,194,169,173,177,151,222,226,230,234,238,242,272,249,253,257,261,265,269,184,188,157,161,165,155,200,204,208,212,216,220,150,186,190,159,163,167,198,202,206,210,214,218,270,192,196,171,175,179,153,224,228,232,236,240,244,247,251,255,259,263,267,182,17,32,101,82,25,68,48,36,105,86,29,274,52,40,109,90,3,42,56,9,113,94,74,46,60,13,117,97,78,21,64","comment":"Tao(F_11,β=5) × F_31(ζ=2,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 16:53:56","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/bd389c9b22f836839430da2a096719921c6fc565e9d4f5bac85d9cfd0db5d754.txt"},{"canonical_hash":"fb872af1c3f39302737f5ef4a3fbbc48f5be9a96c37e27864477679097fe8ef7","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,7,62,50,32,20,111,99,88,76,12,44,66,54,36,24,115,103,92,80,11,16,70,58,40,28,119,107,276,84,72,61,49,31,19,110,98,87,75,15,43,65,53,35,23,114,102,91,79,10,47,69,57,39,27,118,106,95,83,275,3,6,317,334,338,333,323,332,322,331,321,330,320,329,319,328,318,327,316,326,315,325,314,324,313,310,312,308,311,307,336,309,335,108,96,85,73,13,41,63,51,33,21,112,100,89,77,8,45,67,55,37,25,116,104,93,81,4,5,71,59,277,29,17,147,128,124,129,138,140,130,136,133,141,127,121,137,122,135,142,126,148,120,145,125,123,144,139,143,132,131,149,340,134,146,227,183,223,179,154,175,158,171,163,167,155,266,195,262,191,258,221,254,217,250,213,246,209,243,205,239,201,235,273,231,187,298,295,278,337,292,289,285,282,305,302,299,296,279,288,293,290,286,283,306,303,300,297,281,280,294,291,287,284,339,304,301,173,165,169,153,268,197,264,193,260,156,256,219,252,215,248,211,245,207,241,203,237,199,233,189,229,185,225,181,271,177,160,204,238,200,234,190,230,186,226,182,222,178,161,174,162,170,151,269,166,265,194,261,157,257,220,253,216,249,212,272,208,242,251,214,247,210,244,206,240,202,236,198,232,188,228,184,224,180,150,176,159,172,164,168,152,267,196,263,192,259,270,255,218,30,18,109,97,86,74,14,42,64,52,34,22,113,101,90,78,9,46,68,56,38,26,117,105,94,82,1,2,274,60,48","comment":"Tao(F_11,β=5) × F_31(ζ=2,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:58:48","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/fb872af1c3f39302737f5ef4a3fbbc48f5be9a96c37e27864477679097fe8ef7.txt"},{"canonical_hash":"b0e92fc5a67e50287d47bc4eed165be55d271661a3b82829c20d7b97a28c4220","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,115,10,88,61,38,107,17,80,53,30,99,65,72,119,70,92,23,42,111,6,84,57,34,103,13,76,49,26,276,2,116,67,89,62,39,108,18,81,54,31,100,66,73,46,71,93,24,43,112,7,85,58,35,104,14,77,50,27,96,277,294,300,283,288,305,280,298,291,286,303,281,296,289,284,301,278,279,306,337,299,292,287,304,282,297,290,285,302,293,295,339,236,201,218,232,197,158,228,267,169,224,263,165,153,259,161,194,255,213,190,251,154,186,247,171,182,244,209,178,240,205,270,118,69,91,22,41,110,20,83,56,33,102,12,75,48,25,95,5,45,114,9,87,60,37,106,16,79,52,29,98,64,275,142,139,121,136,137,132,141,148,143,149,131,129,125,138,130,145,123,140,144,146,134,128,133,126,147,122,120,135,124,127,340,260,162,195,256,214,191,252,155,187,248,172,183,245,210,179,241,206,175,237,202,219,233,198,159,229,268,170,225,264,166,271,94,4,44,113,8,86,59,36,105,15,78,51,28,97,63,3,117,68,90,21,40,109,19,82,55,32,101,11,74,47,274,309,325,335,311,324,334,310,308,333,322,317,332,307,316,331,312,315,330,321,314,329,320,313,328,319,323,327,318,338,326,336,189,250,174,185,246,212,181,243,208,177,239,204,221,235,200,217,231,196,157,227,266,168,223,262,164,152,258,216,193,254,273,211,180,242,207,176,238,203,220,234,199,160,230,269,156,226,265,167,222,261,163,150,257,215,192,253,151,188,249,173,184,272","comment":"Tao(F_11,β=5) × F_31(ζ=4,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:58:52","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/b0e92fc5a67e50287d47bc4eed165be55d271661a3b82829c20d7b97a28c4220.txt"},{"canonical_hash":"51c4af6678263c10ba8620f1335d26c4bc75e24246b38c0a2f342e1cc6d9d260","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,105,15,34,90,37,6,74,109,63,22,94,41,68,78,113,18,26,97,45,274,82,117,11,30,101,49,57,86,60,44,71,81,116,10,29,100,48,56,85,59,14,4,104,52,33,89,53,5,73,108,277,21,93,40,67,77,112,66,25,96,192,225,166,237,162,248,219,260,185,211,181,196,229,214,241,152,252,204,264,173,188,271,200,233,169,245,157,256,208,268,177,84,119,13,9,103,51,32,88,62,3,72,107,17,36,92,39,8,76,111,65,24,276,43,70,80,115,20,28,99,47,55,128,140,138,149,132,139,124,147,134,123,125,143,137,142,135,126,146,145,129,148,136,340,120,133,144,130,131,141,121,127,122,163,249,220,261,186,212,159,197,230,215,242,153,253,205,265,174,189,222,201,234,170,272,158,257,182,269,178,193,226,167,238,23,95,42,69,79,114,19,27,98,46,54,83,118,12,31,102,50,58,87,61,2,275,106,16,35,91,38,7,75,110,64,231,216,243,155,254,206,266,175,190,223,202,235,160,246,217,258,183,209,179,194,227,273,239,164,250,221,262,171,203,154,198,255,207,267,176,191,224,165,236,161,247,218,259,184,210,180,195,228,213,240,151,251,270,263,172,187,150,199,232,168,244,156,312,321,307,318,326,322,329,308,332,320,335,313,316,324,319,327,309,330,338,333,315,336,314,317,325,311,328,310,331,323,334,304,282,283,300,287,337,296,305,293,284,301,288,294,297,306,280,285,302,289,291,298,339,281,278,303,290,286,299,292,279,295","comment":"Tao(F_11,β=5) × F_31(ζ=4,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:58:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/51c4af6678263c10ba8620f1335d26c4bc75e24246b38c0a2f342e1cc6d9d260.txt"},{"canonical_hash":"ea5bede66a47b065320820a3343cdface025ead09a0df017a763becdb37a6798","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,24,29,27,21,22,4,9,25,274,3,8,12,10,13,16,19,26,17,5,18,23,7,14,20,15,2,28,11,6,68,82,63,65,78,62,64,73,77,85,276,75,60,69,71,70,61,74,81,89,76,72,83,80,79,84,87,67,66,86,88,338,321,335,312,333,322,324,308,327,315,336,320,313,326,311,325,314,318,331,332,334,328,317,309,330,319,323,310,329,316,307,108,114,109,116,94,105,106,90,118,115,277,99,102,107,91,104,110,100,93,98,92,111,113,117,103,112,96,119,101,97,95,122,138,140,125,135,141,123,128,120,143,340,136,147,133,131,137,142,130,145,146,148,124,121,132,144,134,126,139,127,149,129,252,243,253,245,255,249,250,267,247,244,273,260,263,251,266,265,254,261,269,259,268,241,242,246,264,240,257,248,262,258,256,287,301,303,282,286,304,278,290,305,296,339,293,337,294,299,285,291,295,292,281,288,289,284,279,306,300,280,302,297,298,283,210,231,228,238,212,226,225,230,236,229,272,211,233,217,216,235,221,223,218,214,213,222,227,237,232,224,220,239,234,219,215,158,176,164,156,171,153,169,157,161,177,270,166,173,178,179,175,163,168,152,174,159,160,155,165,150,154,162,167,170,151,172,184,190,185,192,201,181,182,198,194,191,271,206,209,183,197,196,186,207,200,205,199,187,189,193,195,188,203,180,208,204,202,54,45,55,47,41,51,52,38,49,46,275,31,34,53,37,36,56,32,40,30,39,57,59,48,35,58,43,50,33,44,42","comment":"Tao(F_11,β=5) × F_31(ζ=8,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:58:59","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/ea5bede66a47b065320820a3343cdface025ead09a0df017a763becdb37a6798.txt"},{"canonical_hash":"19d43629ea9664a2cd42378cd46ff7ac7d493d826c910f7bdc5b517901007871","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,27,29,26,14,12,16,17,9,6,4,274,28,25,22,23,19,20,13,11,21,2,24,7,15,8,5,18,10,3,61,81,76,62,75,63,82,79,78,85,64,70,276,66,67,77,86,87,74,68,83,69,84,73,80,60,88,72,89,65,71,323,307,325,308,322,338,316,314,318,329,315,330,336,320,333,327,313,319,309,334,326,328,312,317,310,335,311,324,332,321,331,94,92,105,111,106,113,90,117,118,103,115,112,277,96,99,119,102,101,107,97,91,95,104,108,110,114,100,109,93,116,98,135,149,142,124,123,121,128,132,120,145,141,134,340,126,136,138,148,127,133,147,131,129,137,122,143,140,130,139,146,125,144,265,263,244,250,245,252,262,240,242,259,254,251,273,267,255,243,258,257,246,268,261,266,260,247,249,253,256,248,264,241,269,296,289,304,297,282,278,285,291,305,306,294,287,339,280,281,302,337,301,290,288,292,293,286,284,283,303,279,300,298,299,295,215,214,213,238,219,236,220,232,231,222,234,237,272,229,226,239,223,224,216,228,212,217,230,218,210,235,225,221,211,233,227,156,164,151,158,171,173,154,162,150,155,152,169,270,166,177,168,174,170,178,167,179,160,157,163,175,159,176,153,165,161,172,201,199,181,187,182,189,198,193,194,195,191,188,271,203,206,180,209,208,183,204,197,202,196,184,186,190,207,185,200,192,205,31,44,56,47,57,49,43,53,54,40,51,48,275,33,36,55,39,38,58,34,42,32,41,59,46,50,37,45,30,52,35","comment":"Tao(F_11,β=5) × F_31(ζ=8,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:01","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/19d43629ea9664a2cd42378cd46ff7ac7d493d826c910f7bdc5b517901007871.txt"},{"canonical_hash":"84cdffa0fb5760964e8f75865f064f4e71c5a9c7a44189c314f49f8bd2894400","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,62,107,80,31,10,119,92,43,22,58,103,76,27,3,115,88,39,18,54,99,72,70,66,111,84,35,14,50,276,69,65,110,83,34,13,49,95,46,7,61,106,79,30,9,118,91,42,21,57,102,75,26,6,114,87,38,17,53,98,275,325,311,334,308,309,332,316,322,330,314,320,328,323,318,326,312,335,324,310,333,317,307,331,315,321,329,313,319,327,338,336,116,89,40,19,55,100,73,71,25,112,85,36,15,51,96,4,67,63,108,81,32,11,47,93,44,23,59,104,77,28,277,129,123,130,147,149,124,127,141,131,143,122,148,140,120,121,135,136,125,133,137,128,146,126,142,139,134,132,145,138,144,340,250,186,213,243,178,205,235,217,197,227,169,262,154,161,254,190,175,246,182,209,239,221,201,231,173,266,223,165,258,194,273,300,288,283,291,303,296,284,278,306,299,287,282,290,302,295,294,293,305,298,286,281,289,301,279,337,292,304,297,285,280,339,163,256,192,156,248,184,211,241,176,203,233,157,268,225,167,260,196,159,252,188,215,245,180,207,237,219,199,229,171,264,271,181,208,238,220,200,230,172,265,222,164,257,193,153,249,185,212,242,177,204,234,150,269,226,168,261,151,160,253,189,216,272,202,232,174,267,224,166,259,195,158,251,187,214,244,179,206,236,218,198,228,170,263,152,162,255,191,155,247,183,210,240,270,5,113,86,37,16,52,97,2,68,64,109,82,33,12,48,94,45,24,60,105,78,29,8,117,90,41,20,56,101,74,274","comment":"Tao(F_11,β=5) × F_31(ζ=16,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:04","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/84cdffa0fb5760964e8f75865f064f4e71c5a9c7a44189c314f49f8bd2894400.txt"},{"canonical_hash":"f50ba99c18a7be1006163fb5cc960fa0d3ad9576e79115396f949c5696842c4c","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,72,103,10,70,76,107,14,47,80,111,18,51,84,115,36,55,88,119,22,59,92,44,26,63,276,39,30,6,99,56,89,41,23,60,93,45,27,64,96,40,31,3,100,7,67,73,104,11,71,77,108,15,48,81,112,277,52,85,116,19,284,293,301,287,285,278,302,279,337,295,303,280,294,296,304,281,289,297,305,282,290,298,306,286,291,299,339,283,292,300,288,263,228,218,154,244,207,184,259,224,182,187,240,203,166,255,152,178,192,236,199,162,251,215,174,267,232,270,158,247,211,170,106,13,46,79,110,17,50,83,114,35,54,87,118,21,58,91,43,25,62,95,38,29,66,98,5,33,275,102,9,69,75,138,143,146,130,121,132,141,137,129,140,139,124,125,144,122,126,147,135,145,131,128,123,120,134,127,133,340,148,142,149,136,163,252,216,175,268,233,196,159,248,212,171,264,229,219,155,245,208,185,260,225,183,188,241,204,167,256,271,179,193,237,200,82,113,34,53,86,117,20,57,90,42,24,61,94,37,28,65,97,4,32,2,101,8,68,74,105,12,274,78,109,16,49,322,312,335,326,323,308,330,321,315,334,325,338,316,329,320,311,333,324,314,317,328,319,310,332,307,313,336,327,318,309,331,239,202,165,254,153,177,191,235,198,161,250,214,173,266,231,221,157,246,210,169,262,227,217,190,243,206,273,258,223,181,195,150,189,242,205,168,257,222,180,194,238,201,164,253,156,176,269,234,197,160,249,213,172,265,230,220,151,272,209,186,261,226","comment":"Tao(F_11,β=5) × F_31(ζ=16,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:07","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/f50ba99c18a7be1006163fb5cc960fa0d3ad9576e79115396f949c5696842c4c.txt"},{"canonical_hash":"2f34c182f10e0e745f2a3760d91289a63b913a32ef2748f56541008f406821d1","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,13,4,16,25,20,11,3,8,18,6,29,21,17,14,2,27,10,23,19,335,24,28,15,22,7,9,12,26,5,71,68,60,63,86,72,80,70,61,82,65,87,83,81,66,89,74,88,67,79,85,331,69,84,64,76,62,77,73,75,78,40,56,36,50,43,41,45,38,33,49,30,44,57,48,46,31,39,34,55,54,32,334,37,58,59,51,47,52,42,35,53,271,280,290,288,299,286,285,284,289,291,273,287,276,296,270,275,294,279,295,278,272,333,283,282,281,298,293,292,274,297,277,258,255,263,249,242,259,244,257,264,248,241,243,267,247,245,266,261,265,254,253,240,340,256,268,269,250,246,251,260,262,252,145,144,126,142,129,134,139,124,147,131,149,140,148,123,130,127,146,136,133,121,138,338,120,137,128,122,141,132,125,135,143,170,167,175,161,154,171,156,169,176,160,152,155,179,159,157,178,173,177,166,165,153,337,168,151,150,162,158,163,172,174,164,194,189,186,203,209,200,181,193,207,202,182,180,188,192,190,184,195,183,197,198,208,336,199,185,206,204,191,196,201,187,205,90,102,91,96,118,108,107,116,113,98,92,109,101,95,114,100,110,97,103,106,112,330,111,105,104,115,93,99,117,94,119,311,328,301,317,310,326,312,309,318,319,305,314,306,329,304,325,315,307,321,302,308,332,323,322,320,300,303,324,313,316,327,232,238,212,216,214,233,227,220,231,221,224,225,239,228,237,234,230,211,223,218,226,339,219,210,236,217,235,222,229,213,215","comment":"Tao(F_11,β=9) × F_31(ζ=2,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/2f34c182f10e0e745f2a3760d91289a63b913a32ef2748f56541008f406821d1.txt"},{"canonical_hash":"cb9a0c4bab3386f467f1236f9a71d1c147951d866e5de4abd3f0ea84e357b8b3","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,13,29,16,21,26,11,3,8,5,6,4,27,17,14,2,23,10,19,25,335,20,24,15,28,7,9,12,22,18,89,62,83,61,74,60,64,88,75,68,72,69,78,67,65,77,81,76,79,86,73,331,63,70,71,87,66,84,80,82,85,38,58,43,57,52,39,31,37,44,56,50,53,47,55,30,46,41,45,36,35,51,334,59,48,49,32,54,33,40,42,34,299,286,274,290,272,291,289,296,273,275,285,298,294,276,292,279,278,270,288,282,284,333,283,281,280,271,277,297,287,293,295,242,269,247,263,256,243,258,240,248,262,254,257,251,261,259,250,245,249,268,267,255,340,241,252,253,264,260,265,244,246,266,141,140,126,148,122,136,131,137,143,121,145,146,144,132,123,124,142,128,139,134,130,338,135,129,125,133,147,120,138,127,149,158,155,163,179,172,159,174,157,164,178,170,173,167,177,175,166,161,165,154,153,171,337,156,168,169,151,176,150,160,162,152,191,196,183,197,208,192,201,190,181,186,185,200,207,194,203,184,188,204,205,202,199,336,189,182,180,206,193,198,187,209,195,98,105,115,104,109,96,112,108,103,116,90,97,118,110,102,92,100,106,113,95,114,330,94,117,91,111,99,93,101,119,107,306,301,315,300,309,305,308,323,313,314,322,307,304,325,302,317,312,318,321,329,310,332,311,328,320,319,327,316,303,324,326,223,235,228,234,231,226,236,222,239,220,225,237,233,232,210,229,213,212,221,217,211,339,218,238,230,224,219,215,227,214,216","comment":"Tao(F_11,β=9) × F_31(ζ=2,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:17","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/cb9a0c4bab3386f467f1236f9a71d1c147951d866e5de4abd3f0ea84e357b8b3.txt"},{"canonical_hash":"ae32787f0f75c489a2f4434df9489e173cac075c0f5f89b93796a55d6629d49f","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,9,19,20,18,7,28,15,13,335,8,10,23,12,4,25,24,14,5,29,3,27,16,26,11,6,21,2,22,17,85,82,84,61,69,71,70,76,73,81,331,67,80,86,77,78,62,66,74,68,75,60,83,64,79,63,88,72,65,87,89,42,51,41,49,38,45,44,53,47,50,334,33,31,43,54,55,40,32,39,34,52,59,57,48,56,58,36,46,30,35,37,270,292,273,282,274,276,280,285,293,299,333,275,295,286,281,277,284,283,294,291,271,278,296,290,298,287,288,272,289,297,279,254,248,253,246,261,242,240,264,244,247,340,256,268,241,265,266,252,255,262,257,263,251,249,245,267,250,259,243,269,258,260,140,144,131,128,129,148,139,127,137,135,338,130,132,122,134,143,124,123,136,149,145,142,126,146,125,133,138,121,141,120,147,162,156,161,154,177,151,164,165,152,155,337,172,169,163,166,167,160,171,178,173,179,159,157,153,168,158,175,150,170,174,176,189,183,193,185,186,200,191,207,182,184,336,192,195,190,203,202,201,204,180,188,209,199,197,206,194,198,181,187,196,208,205,114,116,110,98,93,102,96,106,91,95,330,94,119,105,97,92,118,99,109,117,115,100,112,104,111,108,107,90,103,113,101,325,324,328,310,308,306,314,321,327,305,332,315,326,320,313,329,307,309,301,304,300,312,302,319,323,316,317,322,318,303,311,238,215,213,229,230,210,228,223,239,226,339,219,214,217,224,225,220,218,212,237,216,227,222,235,221,234,233,231,236,232,211","comment":"Tao(F_11,β=9) × F_31(ζ=4,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:22","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/ae32787f0f75c489a2f4434df9489e173cac075c0f5f89b93796a55d6629d49f.txt"},{"canonical_hash":"57a3c639207884afe28c31fb0adefac98939d613438c4c259abe1b608eb5e807","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,17,21,18,27,20,24,8,15,16,28,29,14,5,3,335,7,6,9,2,23,11,10,4,19,25,22,13,26,12,67,88,89,79,87,73,82,65,61,69,64,85,84,81,62,70,331,72,78,83,75,76,63,71,60,86,80,68,66,74,77,38,48,51,30,47,31,42,36,41,34,52,50,49,55,32,35,334,45,59,43,56,57,40,44,53,46,54,39,37,33,58,270,299,279,293,282,292,285,277,273,274,298,297,281,295,290,287,333,288,284,294,280,276,296,272,289,271,286,275,283,291,278,259,254,267,249,253,241,263,257,262,255,240,266,265,244,268,256,340,251,248,264,245,246,261,250,242,252,243,260,258,269,247,142,144,128,135,129,141,134,138,147,126,127,132,145,125,149,121,338,146,148,130,143,137,122,131,120,133,139,136,124,140,123,173,161,166,156,160,162,177,171,176,169,163,165,179,150,167,170,337,158,155,178,152,153,175,157,164,159,151,174,172,168,154,201,209,183,195,205,189,204,199,198,194,190,184,185,208,203,181,336,186,182,188,206,207,197,196,191,187,192,202,200,193,180,111,112,93,118,102,96,107,105,95,92,91,103,113,110,99,114,330,117,98,109,116,104,115,108,94,106,100,97,101,119,90,323,305,320,324,321,306,313,309,301,311,318,328,322,302,317,300,332,327,316,329,307,326,319,312,308,310,314,303,315,325,304,232,216,210,228,225,215,227,238,230,239,236,211,217,213,226,222,339,218,231,214,221,237,235,234,223,219,224,229,212,233,220","comment":"Tao(F_11,β=9) × F_31(ζ=4,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:26","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/57a3c639207884afe28c31fb0adefac98939d613438c4c259abe1b608eb5e807.txt"},{"canonical_hash":"2676d71becda21685a3d9ef73d833f1101d489a159237b31a2e72b901602d451","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,25,13,17,10,5,16,6,28,23,7,11,18,15,12,8,20,3,2,14,22,4,24,26,335,21,19,29,27,9,81,69,86,85,73,64,89,72,80,71,60,78,65,74,68,88,77,76,62,79,84,63,66,87,82,331,61,75,70,67,83,41,47,38,39,54,30,52,44,40,49,58,32,56,55,46,51,34,33,31,36,43,59,57,50,42,334,37,53,48,45,35,286,298,291,295,280,283,288,274,293,281,275,292,284,287,282,289,294,290,297,285,273,270,278,277,299,333,276,279,272,271,296,268,256,251,249,252,247,264,262,250,261,258,241,259,253,255,266,242,240,248,244,267,246,260,265,269,340,245,254,263,257,243,147,136,133,149,139,128,145,138,146,121,131,148,127,122,126,120,123,141,143,142,125,130,144,132,134,338,129,140,137,135,124,160,162,169,170,176,152,158,178,168,177,155,173,153,174,164,157,172,171,151,166,159,150,154,156,161,337,167,175,179,163,165,186,181,208,207,200,193,196,199,206,183,191,190,180,195,209,205,189,185,194,188,204,202,198,201,187,336,203,184,197,182,192,119,98,113,111,105,116,93,104,109,118,100,108,91,94,117,106,110,112,90,92,103,101,96,107,114,330,115,95,97,99,102,326,303,322,320,309,302,311,307,324,304,300,325,312,319,301,310,321,323,313,305,308,328,306,317,315,332,316,318,314,327,329,225,223,210,239,231,215,213,218,238,217,219,234,216,221,222,214,232,233,236,227,211,235,229,220,212,339,228,230,224,237,226","comment":"Tao(F_11,β=9) × F_31(ζ=8,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/2676d71becda21685a3d9ef73d833f1101d489a159237b31a2e72b901602d451.txt"},{"canonical_hash":"5f6ae5f8915a53017760ca81659579ed6b5aea8196e05fa735d4cca5e71d003f","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,15,22,2,24,26,335,21,19,29,27,10,5,6,25,14,18,11,3,17,4,28,23,8,12,7,16,13,9,20,65,71,76,66,85,87,75,331,72,67,79,82,73,74,61,63,62,68,64,86,78,88,80,83,70,84,69,77,89,81,60,39,58,49,40,51,42,48,334,56,44,59,53,57,47,55,35,36,45,38,41,31,37,52,34,30,50,46,54,43,33,32,292,273,284,290,279,299,280,333,295,275,270,291,274,277,272,294,288,298,285,297,283,289,282,281,286,278,296,271,276,287,293,262,267,249,263,258,257,251,340,268,253,266,243,269,250,245,247,248,254,261,256,265,246,264,259,240,260,252,244,255,241,242,123,135,144,146,120,134,128,338,127,139,121,129,136,143,124,148,125,133,130,149,137,142,138,147,141,131,140,145,132,122,126,165,164,150,166,153,158,151,337,162,174,179,169,163,152,168,159,160,175,167,157,178,161,177,154,172,155,176,170,156,171,173,195,194,198,196,204,187,205,336,202,186,193,209,203,185,208,206,180,201,197,190,192,207,200,199,183,191,188,181,189,182,184,100,98,111,108,119,91,118,330,90,114,97,107,112,99,113,104,110,116,106,115,96,103,94,93,102,92,95,105,117,109,101,322,303,304,301,314,313,306,332,316,308,311,317,310,327,323,319,318,309,300,307,312,325,305,315,326,302,329,324,328,321,320,211,216,222,235,218,212,226,339,234,238,215,227,225,239,214,236,221,230,237,219,229,210,224,223,232,217,213,228,220,231,233","comment":"Tao(F_11,β=9) × F_31(ζ=8,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:35","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/5f6ae5f8915a53017760ca81659579ed6b5aea8196e05fa735d4cca5e71d003f.txt"},{"canonical_hash":"2bcca66eff097ace79f2b7640b025226383b865c37cebd3362ff202e230c04ec","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,2,23,9,12,4,27,16,21,25,335,20,26,11,22,18,17,14,28,7,5,6,13,29,10,19,24,15,3,8,74,87,64,85,79,76,62,84,89,75,88,331,81,71,82,65,67,61,86,78,83,80,70,66,77,69,68,72,73,60,63,38,51,39,49,54,30,59,35,57,31,56,334,32,46,33,40,42,47,50,53,34,55,45,41,52,44,43,36,37,48,58,281,272,289,285,298,295,277,274,275,282,279,333,273,292,276,297,278,294,299,286,290,270,280,284,296,288,293,291,287,271,283,248,269,257,267,253,250,245,243,256,249,255,340,241,264,240,258,260,265,268,252,242,254,263,259,251,262,261,246,247,266,244,138,137,139,142,127,130,124,145,134,140,121,338,148,144,129,141,149,135,132,146,120,125,126,131,122,128,147,143,133,123,136,176,167,155,165,150,178,173,171,154,177,153,337,168,162,169,156,158,163,166,151,170,152,161,157,179,160,159,174,175,164,172,209,202,194,193,185,199,188,186,196,182,195,336,198,183,207,200,208,191,190,206,205,189,184,187,197,204,203,181,180,192,201,119,101,105,107,92,114,112,97,110,91,94,330,95,90,111,98,113,96,117,108,106,100,118,99,102,104,116,115,103,93,109,306,322,317,319,312,308,305,329,326,314,325,332,324,315,304,328,310,309,311,318,316,313,327,302,300,320,307,301,321,323,303,211,229,234,232,225,222,223,239,231,214,237,339,213,230,221,215,217,238,210,218,227,212,226,216,228,220,219,236,233,235,224","comment":"Tao(F_11,β=9) × F_31(ζ=16,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:40","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/2bcca66eff097ace79f2b7640b025226383b865c37cebd3362ff202e230c04ec.txt"},{"canonical_hash":"dbd72a531d7052b057688b050bf75a250649546c130630af60809b45880bf0ed","size":341,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,2,27,17,10,29,21,14,25,19,335,24,20,9,26,7,15,12,22,5,18,4,11,6,8,23,28,13,3,16,61,73,68,86,82,79,64,77,67,60,66,331,74,72,75,87,89,84,83,81,76,65,71,88,80,70,69,62,63,85,78,57,33,45,30,41,59,34,56,44,58,43,334,53,52,54,46,48,38,32,40,55,42,51,47,39,50,49,35,36,37,31,290,288,277,279,287,285,281,283,294,291,270,333,275,299,295,282,280,274,286,278,276,272,289,271,293,273,297,296,298,292,284,242,263,251,261,247,244,269,267,250,243,249,340,264,258,265,252,254,259,262,246,266,248,257,253,245,256,255,241,240,260,268,145,144,146,128,123,137,148,132,125,126,130,338,135,131,136,127,143,120,139,133,141,149,140,138,142,121,134,129,124,147,122,152,173,161,171,157,154,179,177,160,153,159,337,174,168,175,162,164,169,172,156,176,158,167,163,155,166,165,151,150,170,178,205,182,196,200,187,184,198,204,203,185,202,336,206,190,207,193,191,201,180,186,181,188,189,194,209,195,208,192,199,197,183,100,109,95,117,108,97,110,104,111,91,90,330,101,102,112,103,92,98,107,118,96,119,99,106,116,93,114,113,94,115,105,317,303,304,307,314,301,315,319,327,300,311,332,312,318,326,320,305,306,313,308,328,302,316,329,324,309,322,323,310,325,321,231,239,215,214,233,218,238,221,235,212,219,339,226,220,225,213,227,216,229,222,223,232,210,228,211,224,237,236,230,234,217","comment":"Tao(F_11,β=9) × F_31(ζ=16,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:59:47","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/341/dbd72a531d7052b057688b050bf75a250649546c130630af60809b45880bf0ed.txt"},{"canonical_hash":"d25da012cffb19eec9a60d1bebd43a947e65b1cff4ad4e72b87fe1b273b80bfc","size":343,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"252,25,27,26,22,24,23,286,238,241,240,243,239,242,254,74,70,75,72,73,71,255,92,88,93,90,91,89,256,146,142,147,144,145,143,257,178,180,179,182,183,181,253,245,247,246,249,244,248,288,16,4,250,10,13,0,289,79,81,80,77,78,76,290,107,109,108,111,106,110,291,156,158,157,154,155,159,292,173,174,172,176,177,175,293,229,231,230,227,228,226,258,234,236,235,232,233,237,259,30,32,31,29,28,33,260,48,50,49,46,47,51,261,102,104,103,100,101,105,262,141,137,136,139,140,138,263,204,206,205,202,203,207,264,166,169,168,171,167,170,265,208,210,209,212,213,211,266,6,8,1,14,7,11,267,43,45,44,41,42,40,268,87,83,82,85,86,84,269,125,127,126,129,124,128,270,130,132,131,134,135,133,271,189,185,184,187,188,186,272,224,220,225,222,223,221,273,34,37,36,39,35,38,274,69,65,64,67,68,66,275,112,114,113,116,117,115,276,123,119,118,121,122,120,277,151,153,152,149,150,148,278,199,201,200,197,198,196,279,219,215,214,217,218,216,280,20,18,21,17,19,251,281,53,55,54,57,52,56,282,58,60,59,62,63,61,283,97,99,98,95,96,94,284,161,163,162,165,160,164,285,194,190,195,192,193,191,287,2,5,3,12,15,9,313,307,310,309,312,308,311,300,299,294,295,297,298,296,320,317,319,318,314,316,315,327,325,326,323,324,321,322,334,333,331,329,332,330,328,341,338,339,335,340,336,337,342,304,302,305,303,306,301","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_7(4,1).","submitted_at":"2026-04-28 19:33:41","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/343/d25da012cffb19eec9a60d1bebd43a947e65b1cff4ad4e72b87fe1b273b80bfc.txt"},{"canonical_hash":"102a77e69a309e3b404a69e2bdff896b4a86e4e7c2950493bd3d0e4e21fcb46e","size":343,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,1,2,3,4,287,5,157,265,160,158,156,161,159,8,10,6,9,288,7,11,14,15,17,13,12,16,283,20,19,284,23,22,21,18,26,29,24,285,27,25,28,32,286,34,30,31,35,33,204,206,207,208,209,259,205,210,214,211,213,260,212,215,180,183,185,181,182,184,261,186,187,262,191,190,189,188,192,197,194,263,195,193,196,198,264,202,200,199,203,201,242,272,245,243,240,241,244,248,249,250,251,247,273,246,218,221,216,220,274,219,217,224,226,223,222,225,227,275,230,228,276,229,233,232,231,236,235,237,271,238,234,239,61,65,62,292,63,60,64,67,258,70,68,66,71,69,37,38,39,40,41,293,36,43,46,42,45,289,44,47,49,51,53,48,50,52,290,55,54,291,59,58,57,56,96,97,255,101,98,100,99,102,107,105,256,106,103,104,72,257,74,75,73,77,76,78,81,82,80,83,252,79,84,86,85,88,253,87,89,90,94,95,91,93,92,254,133,135,137,132,134,136,282,139,138,277,143,142,141,140,109,113,110,278,111,108,112,115,279,118,116,114,119,117,121,122,123,124,125,280,120,127,130,126,129,281,128,131,168,172,169,171,267,170,173,174,177,179,175,176,178,268,145,144,269,149,148,147,146,150,155,152,270,153,151,154,163,164,165,166,167,266,162,334,297,299,296,294,298,295,331,309,311,306,307,310,308,332,321,323,320,319,322,318,333,327,329,326,324,328,325,330,315,317,312,313,316,314,335,302,304,305,301,303,300,342,336,341,337,339,338,340","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_7(4,3).","submitted_at":"2026-04-28 19:33:51","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/343/102a77e69a309e3b404a69e2bdff896b4a86e4e7c2950493bd3d0e4e21fcb46e.txt"},{"canonical_hash":"1ed733cf6330f0e7bbcb1f26d05f7985a4b1dd577a18626bff8cd25ba4ddc2da","size":343,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"252,48,84,187,142,47,98,269,66,137,6,176,110,96,254,231,227,228,226,230,229,255,127,166,27,107,211,28,256,183,53,160,205,64,8,257,154,89,75,16,116,199,253,38,193,131,2,148,170,283,39,194,132,40,149,171,284,71,134,70,173,113,93,285,182,52,159,204,63,59,286,21,81,190,145,44,101,287,123,4,23,109,213,30,282,219,217,215,216,218,251,271,225,222,221,220,224,223,272,157,86,78,19,119,202,273,50,80,189,144,43,100,274,36,191,129,9,146,168,275,184,54,161,206,65,5,270,67,138,7,177,111,97,259,68,139,69,178,112,92,260,126,165,26,106,210,33,261,35,196,128,20,151,167,262,243,240,238,239,242,241,263,12,82,185,140,45,102,258,155,90,76,17,117,200,289,156,91,77,18,118,201,290,181,57,158,203,62,58,291,237,234,233,232,236,235,292,73,136,10,175,115,95,293,37,192,130,3,147,169,288,124,250,24,104,214,31,277,125,164,25,105,209,32,278,49,85,188,143,42,99,279,72,135,51,174,114,94,280,153,88,74,15,121,198,281,249,246,245,244,248,247,276,179,55,162,207,60,1,265,180,56,163,208,61,0,266,34,195,133,41,150,172,267,152,87,79,14,120,197,268,122,11,22,108,212,29,264,13,83,186,141,46,103,336,324,325,329,326,328,327,337,307,309,310,308,311,306,338,300,303,304,302,305,301,339,314,313,317,315,312,316,340,330,332,334,331,333,335,341,297,298,296,295,299,294,342,318,319,323,320,321,322","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 d50b3565) × F_7(4,1).","submitted_at":"2026-04-28 19:39:22","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/343/1ed733cf6330f0e7bbcb1f26d05f7985a4b1dd577a18626bff8cd25ba4ddc2da.txt"},{"canonical_hash":"972795512fae1c98e88678811e91579009084624f888b41b5fbcf3537fda047c","size":343,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,1,278,5,4,2,3,186,190,187,188,264,189,191,42,47,45,279,44,43,46,84,280,88,87,85,89,86,127,129,128,130,131,281,126,168,172,169,170,282,171,173,212,213,210,211,214,215,277,25,24,254,29,28,26,27,67,71,69,255,68,66,70,109,256,112,111,108,113,110,151,153,152,154,155,257,150,193,196,192,194,258,195,197,235,236,239,234,237,238,253,7,6,272,11,10,8,9,49,53,51,273,50,48,52,91,274,94,93,90,95,92,133,135,134,136,137,275,132,175,178,174,176,276,177,179,217,218,221,216,219,220,271,31,30,290,35,34,32,33,73,77,75,291,74,72,76,115,292,118,117,114,119,116,157,159,158,160,161,252,156,199,202,198,200,293,201,203,241,242,245,240,243,244,289,12,13,266,17,16,14,15,54,59,57,267,56,55,58,96,268,100,99,97,101,98,138,141,140,142,143,269,139,180,184,181,182,270,183,185,222,224,227,223,225,226,265,36,37,284,41,40,38,39,78,83,81,285,80,79,82,120,286,124,123,121,125,122,162,165,164,166,167,287,163,204,208,205,206,288,207,209,246,248,251,247,249,250,283,18,19,260,23,22,20,21,60,65,63,261,62,61,64,102,262,106,105,103,107,104,144,147,146,148,149,263,145,228,230,233,229,231,232,259,337,324,329,327,328,326,325,336,320,321,318,319,322,323,338,333,331,335,332,330,334,339,305,304,301,300,303,302,340,307,308,310,309,311,306,341,316,312,314,317,313,315,342,299,297,298,294,295,296","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 d50b3565) × F_7(4,3).","submitted_at":"2026-04-28 19:39:32","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/343/972795512fae1c98e88678811e91579009084624f888b41b5fbcf3537fda047c.txt"},{"canonical_hash":"ff552011554d0a580284a44764032ad2f2ecc5a95a2f8c8a2a56d1ef8a74158c","size":343,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,3,342,18,24,6,21,2,168,325,134,257,90,154,165,96,331,160,131,8,254,339,233,139,20,36,73,55,93,5,328,260,157,162,128,76,333,142,39,58,227,23,230,79,136,61,26,336,42,1,218,261,232,104,174,145,222,252,223,57,269,313,243,66,120,338,71,298,163,278,251,80,40,92,340,198,141,284,277,11,187,75,320,106,300,211,140,149,205,82,291,280,191,193,203,268,28,314,224,171,267,151,229,7,101,274,317,17,103,184,281,72,258,310,220,249,54,219,266,208,88,137,288,146,297,202,117,169,335,275,68,63,304,197,34,190,311,200,286,265,77,204,37,138,98,248,337,29,10,112,19,270,253,49,302,235,332,295,247,33,279,324,161,91,83,237,38,129,84,111,45,53,318,167,228,319,110,118,209,150,242,125,12,133,102,213,312,64,178,179,293,159,186,59,182,192,177,4,264,107,148,221,226,166,69,341,301,272,123,65,323,287,14,78,100,271,181,31,283,196,262,308,194,206,307,216,217,263,246,255,60,201,245,43,334,135,74,95,85,303,143,199,294,214,152,256,32,115,273,52,13,22,41,327,94,240,132,155,86,236,322,121,144,119,113,212,185,173,153,62,195,296,180,27,305,326,250,282,238,289,170,87,48,321,231,114,47,67,15,105,306,172,127,207,16,259,109,46,25,35,276,116,239,124,122,215,316,147,241,30,329,285,292,299,244,130,70,99,175,210,9,309,158,44,97,126,89,330,234,290,188,156,189,183,176,56,108,164,51,225,50,81,315","comment":"Size-343 = 7³ idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group (Z/7)³ ≅ GF(7³) = F_343, with the magma translation-invariant under the full (Z/7)³ translation subgroup of Aut (verified by exhibiting three commuting order-7 fix-free magma automorphisms τ_1, τ_2, τ_3).\n\nDistinguishing features:\n  • L_0 = T[0, ·] has cycle structure (1, 18¹⁹) — order 18, with 19 orbits of length 18 covering F_343*.\n  • R_0 = T[·, 0] has cycle structure (1, 19¹⁸) — order 19, with 18 orbits of length 19.\n  • lcm(18, 19) = 342 = |F_343*|, and ord(L_0) · ord(R_0) = 342 exactly, so the multiplicative orders of L_0 and R_0 partition F_343* cleanly.\n  • The magma is 2-generated: <0, 1> = the full 343 elements (no AG-line-style sub-magma structure).\n  • L_0 is axis-additive on each of the three F_7-axes (e_1, e_2, e_3) — f(c·e_i) = c·f(e_i) for c ∈ F_7 — but NOT globally F_7-linear (only 25/343 ≈ 7.3% of cells match the F_7-linear prediction f(a, b, c) = a·f(e_1) + b·f(e_2) + c·f(e_3)).\n\nThis 'axis-additive but globally non-linear' fingerprint matches the near-field-based magmas at sizes 121 (= 11², magma#5ebfbb80) and 841 (= 29², magma#29114da6), but with a crucial difference: 7³ is NOT in the Zassenhaus exceptional near-field list {5², 7², 11², 23², 29², 59²}, so this cannot be an exceptional near-field magma. It is almost certainly a **Dickson near-field of order 7³** with the order-3 Frobenius x ↦ x⁷ as the twisting automorphism.\n\nWhy no simple-linear or AG-line construction exists at this size: F_343 has primitive 10th roots of unity iff 10 | |F_343*| = 342; since 10 ∤ 342, Φ_10(α) = α⁴ − α³ + α² − α + 1 has no roots in F_343, ruling out simple-linear x ◇ y = (1−α)x + αy. (Also 7³ ≠ q² for any q, so AG(2, q) line magmas don't apply.) The non-distributive Dickson multiplication is needed to satisfy Eq 677.\n\nWhy the F_p²-addition trick (used for the size-961 AG(2, 31) constant-α magmas) fails here: the multiplier c (with ord(c) = 18 in F_343*) is not in F_7 (since |F_7*| = 6 and 18 ∤ 6), so c· is not F_7-linear over (Z/7)³ as a vector space — its action on cross-axis vectors invokes the non-distributive near-field multiplication.\n\nDisplay reorder lays elements out as (i, j, k) ↦ τ_1^i τ_2^j τ_3^k(0) at new index 49·i + 7·j + k. Under this reorder the Cayley table is fully (Z/7)³-translation-invariant — every row is a shift of row 0 (= f) — exposing the cyclic translation structure as clean diagonal banding; finer within-block structure reflects the near-field non-distributivity.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:26:24","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/343/ff552011554d0a580284a44764032ad2f2ecc5a95a2f8c8a2a56d1ef8a74158c.txt"},{"canonical_hash":"f7c7ee5aad567c86fe39f6c95e00a98dfce77d47db410dc45b2b955c91068539","size":349,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"348,0,150,181,193,11,224,204,236,255,54,314,267,276,247,111,279,39,298,187,123,278,87,93,310,315,319,329,290,121,154,203,322,14,347,134,341,305,230,80,166,323,321,56,26,185,32,200,83,301,88,139,92,260,102,244,333,261,164,268,197,296,246,82,95,206,57,143,151,63,177,294,10,79,78,15,273,37,19,128,209,29,96,153,94,343,125,195,69,118,228,103,75,277,243,117,22,264,344,114,27,158,182,266,31,208,303,16,41,109,287,5,106,180,304,293,207,50,311,162,240,173,339,23,289,245,21,248,34,156,249,326,126,284,186,259,194,172,132,51,220,274,337,135,53,25,18,105,17,270,58,331,316,213,1,133,62,265,171,334,252,112,72,146,35,318,196,242,33,71,12,335,168,312,238,38,138,342,161,212,271,233,42,100,144,235,320,272,286,52,160,345,65,262,307,280,13,142,157,258,70,217,201,218,225,253,309,163,74,20,251,306,346,98,59,90,110,300,152,49,330,234,48,221,45,115,223,165,77,40,336,137,250,7,119,130,84,202,205,113,283,241,216,129,8,231,66,86,332,227,288,170,64,222,291,43,2,275,199,28,292,269,99,299,169,190,327,192,229,9,302,219,237,73,215,174,175,210,120,81,263,325,317,257,6,191,178,46,122,101,68,338,61,159,44,198,60,188,313,184,127,179,104,232,89,226,256,147,149,340,176,30,131,167,308,282,214,148,107,328,295,116,155,145,141,136,189,183,3,297,91,124,239,4,285,47,76,67,140,254,55,36,108,24,211,97,85,324,281","comment":"Linear magma over Z/349Z (the prime field F_349): x ◇ y = 122x + 59y (mod 349).","submitted_at":"2026-04-28 16:23:04","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/349/f7c7ee5aad567c86fe39f6c95e00a98dfce77d47db410dc45b2b955c91068539.txt"},{"canonical_hash":"54561e28b834788d4dcc0e3511b0240210e20b0fbe22b93d1e2d8afe7c68cea0","size":349,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"348,0,107,212,272,304,45,145,347,110,21,31,170,157,310,202,114,336,275,242,146,83,156,186,219,178,206,48,27,260,251,330,279,261,129,59,324,44,75,12,311,18,92,239,321,24,235,41,52,232,227,234,39,325,173,237,152,140,10,241,84,57,123,313,328,71,11,46,294,340,184,131,117,240,169,332,200,194,104,29,28,278,143,180,257,210,72,158,38,303,149,244,68,228,166,116,177,97,65,159,60,63,67,23,164,289,118,147,222,316,70,274,317,141,305,3,102,209,74,167,93,80,182,248,288,9,30,49,121,137,196,8,103,329,171,254,343,225,133,64,233,271,296,90,282,134,73,130,218,127,125,266,249,132,243,320,269,284,154,223,153,273,327,335,308,135,229,19,7,256,43,78,197,105,207,265,163,139,20,4,314,32,77,287,193,250,61,53,215,95,281,96,226,211,262,301,190,307,208,183,185,276,188,15,192,224,148,238,213,291,338,191,283,69,312,113,55,161,33,138,195,179,323,88,34,230,306,124,22,151,109,16,267,160,42,247,199,259,216,344,258,280,205,176,231,106,81,341,337,334,101,339,155,119,174,108,286,342,302,91,245,13,100,346,268,315,122,201,220,86,87,162,136,142,58,111,298,175,189,126,66,236,1,36,345,54,255,181,331,26,299,35,198,94,295,115,51,14,292,285,290,326,2,293,82,263,297,150,76,253,37,17,5,50,333,187,319,221,56,309,318,85,322,264,120,277,128,98,25,204,300,217,62,172,144,252,99,112,89,79,168,47,203,6,246,214,270,165,40","comment":"Linear magma over Z/349Z (the prime field F_349): x ◇ y = 122x + 63y (mod 349).","submitted_at":"2026-04-28 16:23:08","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/349/54561e28b834788d4dcc0e3511b0240210e20b0fbe22b93d1e2d8afe7c68cea0.txt"},{"canonical_hash":"912245748a558eb0d80681e08e668728434e04d85a0a67ac400835fdf7428c73","size":361,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,296,277,169,103,97,358,359,269,231,51,247,90,48,243,126,34,210,1,42,181,40,219,250,309,74,308,166,137,193,143,88,119,130,317,197,336,158,57,91,212,324,134,55,208,16,323,332,265,13,196,152,351,89,145,234,120,32,299,183,307,261,64,133,187,30,298,78,326,209,156,109,81,240,127,344,77,165,172,195,36,154,111,254,281,33,343,75,232,178,19,216,352,228,136,12,113,189,100,44,306,107,241,58,220,287,278,61,253,10,179,279,257,226,87,46,291,242,272,175,164,43,98,238,92,121,353,29,354,205,264,85,341,47,45,255,79,171,198,3,135,202,6,186,224,314,313,142,148,124,322,132,37,188,266,138,35,83,214,114,245,125,304,312,69,192,303,331,161,86,262,17,194,49,112,63,292,66,15,284,141,118,105,311,246,225,283,258,94,327,52,260,176,8,207,191,319,147,129,346,50,84,203,140,11,229,318,153,99,22,54,68,71,289,123,316,230,263,267,199,117,297,20,146,110,251,288,293,27,73,294,321,268,204,302,151,256,104,59,76,128,235,182,122,25,115,295,360,340,335,275,330,350,270,310,325,300,345,280,355,315,305,285,320,290,28,72,338,160,70,167,227,190,173,31,14,149,211,106,347,249,223,276,339,9,67,144,333,206,155,101,65,342,162,244,222,218,185,271,168,334,26,23,215,7,282,108,273,184,56,95,248,39,5,301,174,102,274,236,252,53,131,239,62,217,139,213,328,180,201,356,150,163,96,329,60,21,337,18,157,4,233,82,177,41,116,286,348,237,24,357,349,170,200,159,259,38,80,93,221","comment":"Size-361 = 19² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group of F_361 = GF(19²), which is (Z/19)² as an elementary abelian 19²-group; the magma is fully (Z/19)²-translation-invariant under two commuting order-19 fix-free magma automorphisms τ_1, τ_2.\n\nDistinguishing features:\n  • Both L_0 = T[0, ·] and R_0 = T[·, 0] have cycle structure (1, 36¹⁰) — order 36, with 10 orbits of length 36 covering F_361* (order 360 = 36 · 10). So 10 cosets of an order-36 subgroup of F_361* partition the non-zero elements.\n  • 2-generated: <0, 1> = the full 361 elements.\n  • L_0 is axis-additive on each F_19-axis but NOT globally F_19-linear (only ~10% of cells match the F_19-linear prediction f(a, b) = a·f(e_1) + b·f(e_2)), the structural fingerprint of near-field multiplication.\n\nWhy neither simple-linear nor AG(2, 19) line magmas exist at this size with the standard α: F_19 has |F_19*| = 18 and 10 ∤ 18, so F_19 contains no primitive 10th roots of unity — Φ_10 has no roots in F_19, ruling out per-line F_19-linear magmas. F_361 = F_19² DOES have primitive 10th roots (since 10 | 360), so simple-linear F_361 magmas exist, but their L_0 would have order 10 (not 36); ours has order 36, so this is NOT simple-linear F_361.\n\nSince 19 is NOT in the Zassenhaus exceptional near-field list {5, 7, 11, 23, 29, 59}, this is most likely a 10-coset Tao Type II piecewise-linear construction on F_361, equivalently a Dickson near-field of order 19² with the order-2 Frobenius x ↦ x^19. The 'axis-additive but globally non-linear' L_0 is the fingerprint of this non-distributive multiplication.\n\nSibling magmas (other b-reinke size-361 entries with the same template, presumably differing in which 10 multipliers are assigned to which cosets): magma#c5c647a9, magma#f304c339.\n\nDisplay reorder lays out elements as (i, j) ↦ τ_1^i τ_2^j(0) at new index 19·i + j. Under this reorder the table is fully (Z/19)²-translation-invariant; the rendered image shows clean diagonal banding from the translation symmetry, with finer within-block structure reflecting the near-field's non-distributive multiplication.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:11:17","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/361/912245748a558eb0d80681e08e668728434e04d85a0a67ac400835fdf7428c73.txt"},{"canonical_hash":"c5c647a9945ac8851b4e26d835994e0f1dfb2aa550903b7f9521a375da75c5aa","size":361,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,165,128,219,85,25,310,350,67,44,64,351,318,36,89,205,123,172,1,81,307,298,119,130,321,31,226,259,252,222,30,338,121,114,280,301,93,249,236,21,331,120,109,288,317,91,11,83,311,290,104,131,328,20,232,242,77,340,300,35,95,209,138,175,12,10,162,133,215,99,26,308,341,74,54,39,69,173,189,98,266,158,258,314,253,154,267,96,181,164,62,22,282,296,213,334,244,47,132,7,66,274,279,65,15,139,41,247,325,211,297,156,281,355,246,270,312,115,28,153,234,159,33,118,316,263,245,346,55,218,206,53,182,326,223,358,204,140,134,137,152,200,343,225,333,188,241,169,87,168,250,220,63,125,344,278,184,289,186,275,357,126,68,228,94,102,52,56,111,80,293,342,193,315,4,320,339,18,313,197,359,285,171,110,272,212,261,103,166,117,231,13,40,24,185,37,48,9,237,116,145,167,322,61,70,337,170,147,284,92,49,180,141,151,190,59,82,294,6,207,239,309,360,319,229,217,16,227,19,58,27,195,34,50,3,221,107,157,160,327,60,71,332,177,155,106,187,303,8,329,330,14,305,183,352,283,176,113,271,202,262,100,161,295,349,347,265,196,299,194,268,354,135,73,230,90,101,46,42,112,84,238,78,136,210,142,127,124,150,214,348,233,336,192,240,178,97,179,251,198,323,235,353,23,149,224,143,38,105,302,260,256,345,43,216,208,45,356,255,273,306,108,75,269,264,76,17,122,57,254,324,203,291,146,287,201,335,257,51,129,5,243,304,248,148,276,88,199,163,79,29,286,292,32,72,174,191,86,277,144","comment":"Size-361 = 19² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group of F_361 = GF(19²), which is (Z/19)² as an elementary abelian 19²-group; the magma is fully (Z/19)²-translation-invariant under two commuting order-19 fix-free magma automorphisms τ_1, τ_2.\n\nDistinguishing features:\n  • Both L_0 = T[0, ·] and R_0 = T[·, 0] have cycle structure (1, 36¹⁰) — order 36, with 10 orbits of length 36 covering F_361* (order 360 = 36 · 10). So 10 cosets of an order-36 subgroup of F_361* partition the non-zero elements.\n  • 2-generated: <0, 1> = the full 361 elements.\n  • L_0 is axis-additive on each F_19-axis but NOT globally F_19-linear (only ~10% of cells match the F_19-linear prediction f(a, b) = a·f(e_1) + b·f(e_2)), the structural fingerprint of near-field multiplication.\n\nWhy neither simple-linear nor AG(2, 19) line magmas exist at this size with the standard α: F_19 has |F_19*| = 18 and 10 ∤ 18, so F_19 contains no primitive 10th roots of unity — Φ_10 has no roots in F_19, ruling out per-line F_19-linear magmas. F_361 = F_19² DOES have primitive 10th roots (since 10 | 360), so simple-linear F_361 magmas exist, but their L_0 would have order 10 (not 36); ours has order 36, so this is NOT simple-linear F_361.\n\nSince 19 is NOT in the Zassenhaus exceptional near-field list {5, 7, 11, 23, 29, 59}, this is most likely a 10-coset Tao Type II piecewise-linear construction on F_361, equivalently a Dickson near-field of order 19² with the order-2 Frobenius x ↦ x^19. The 'axis-additive but globally non-linear' L_0 is the fingerprint of this non-distributive multiplication.\n\nSibling magmas (other b-reinke size-361 entries with the same template, presumably differing in which 10 multipliers are assigned to which cosets): magma#91224574, magma#f304c339.\n\nDisplay reorder lays out elements as (i, j) ↦ τ_1^i τ_2^j(0) at new index 19·i + j. Under this reorder the table is fully (Z/19)²-translation-invariant; the rendered image shows clean diagonal banding from the translation symmetry, with finer within-block structure reflecting the near-field's non-distributive multiplication.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:11:22","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/361/c5c647a9945ac8851b4e26d835994e0f1dfb2aa550903b7f9521a375da75c5aa.txt"},{"canonical_hash":"f304c339b7537b5ac453e87564409634d5029023fddd76b480bec37fb87d005d","size":361,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,151,68,318,179,219,294,108,16,267,86,24,138,145,134,291,282,218,1,32,9,348,119,279,203,252,136,168,164,276,93,30,71,53,175,204,312,50,342,28,62,137,228,59,340,305,106,356,319,207,105,241,269,181,278,235,122,360,215,127,97,180,205,195,200,92,210,117,185,107,102,112,132,190,220,343,27,307,170,66,133,159,176,198,114,4,41,199,48,25,271,163,247,274,324,347,316,55,111,240,310,283,345,186,64,229,233,246,142,110,67,212,33,261,317,315,125,70,79,182,255,248,339,298,157,331,201,82,126,244,3,280,281,37,169,6,173,272,141,209,257,135,208,58,284,76,124,35,353,98,14,153,17,123,104,83,237,297,149,39,15,309,160,166,31,306,333,56,188,189,46,7,227,5,21,223,113,287,299,296,224,94,139,150,323,143,73,29,156,99,12,184,51,301,161,304,34,292,78,118,148,183,328,26,155,10,144,232,120,357,275,239,77,326,293,243,222,65,355,256,43,121,196,152,334,250,74,165,22,314,158,20,194,44,193,154,61,302,338,242,311,88,36,109,171,128,57,337,230,221,236,202,351,300,54,177,23,45,273,264,100,359,101,335,268,63,42,213,286,140,19,262,103,214,358,146,40,277,129,178,81,11,289,174,91,327,192,167,254,325,265,341,13,90,258,211,290,80,349,47,226,89,308,162,322,303,266,344,285,253,8,260,249,187,131,84,87,75,206,130,336,320,216,332,263,96,95,313,18,49,346,231,225,52,330,354,259,85,172,295,197,234,352,69,329,191,38,350,217,288,72,270,115,245,147,116,251,60,238,321","comment":"Size-361 = 19² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group of F_361 = GF(19²), which is (Z/19)² as an elementary abelian 19²-group; the magma is fully (Z/19)²-translation-invariant under two commuting order-19 fix-free magma automorphisms τ_1, τ_2.\n\nDistinguishing features:\n  • Both L_0 = T[0, ·] and R_0 = T[·, 0] have cycle structure (1, 36¹⁰) — order 36, with 10 orbits of length 36 covering F_361* (order 360 = 36 · 10). So 10 cosets of an order-36 subgroup of F_361* partition the non-zero elements.\n  • 2-generated: <0, 1> = the full 361 elements.\n  • L_0 is axis-additive on each F_19-axis but NOT globally F_19-linear (only ~10% of cells match the F_19-linear prediction f(a, b) = a·f(e_1) + b·f(e_2)), the structural fingerprint of near-field multiplication.\n\nWhy neither simple-linear nor AG(2, 19) line magmas exist at this size with the standard α: F_19 has |F_19*| = 18 and 10 ∤ 18, so F_19 contains no primitive 10th roots of unity — Φ_10 has no roots in F_19, ruling out per-line F_19-linear magmas. F_361 = F_19² DOES have primitive 10th roots (since 10 | 360), so simple-linear F_361 magmas exist, but their L_0 would have order 10 (not 36); ours has order 36, so this is NOT simple-linear F_361.\n\nSince 19 is NOT in the Zassenhaus exceptional near-field list {5, 7, 11, 23, 29, 59}, this is most likely a 10-coset Tao Type II piecewise-linear construction on F_361, equivalently a Dickson near-field of order 19² with the order-2 Frobenius x ↦ x^19. The 'axis-additive but globally non-linear' L_0 is the fingerprint of this non-distributive multiplication.\n\nSibling magmas (other b-reinke size-361 entries with the same template, presumably differing in which 10 multipliers are assigned to which cosets): magma#91224574, magma#c5c647a9.\n\nDisplay reorder lays out elements as (i, j) ↦ τ_1^i τ_2^j(0) at new index 19·i + j. Under this reorder the table is fully (Z/19)²-translation-invariant; the rendered image shows clean diagonal banding from the translation symmetry, with finer within-block structure reflecting the near-field's non-distributive multiplication.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:11:26","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/361/f304c339b7537b5ac453e87564409634d5029023fddd76b480bec37fb87d005d.txt"},{"canonical_hash":"69dd46a31db0c6864d87e7148720a3ed60874de8e4d355360a2de41453e248c6","size":367,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"366,0,270,33,239,153,185,217,208,336,122,149,154,288,356,286,347,182,305,97,91,132,118,242,123,223,257,81,325,135,255,1,316,282,151,69,287,212,66,20,60,222,101,43,87,18,211,259,92,303,362,302,226,310,50,219,294,230,104,6,224,295,269,265,3,140,251,355,120,157,38,193,256,296,351,138,35,65,172,85,29,214,361,240,70,252,12,268,56,307,170,204,350,32,228,337,61,194,285,14,331,274,284,80,195,202,10,357,19,36,358,127,276,301,199,94,73,323,264,98,363,215,277,137,238,75,234,53,267,346,109,124,220,13,324,321,89,342,126,59,190,174,162,136,225,205,278,48,320,4,107,280,187,47,34,152,141,62,54,55,181,328,353,144,330,134,209,21,39,275,221,145,164,272,237,309,25,27,289,88,139,11,343,40,319,64,184,248,197,180,306,304,30,128,163,273,254,112,166,318,300,100,243,51,253,74,49,8,334,333,341,250,261,313,326,5,171,216,188,41,327,169,96,116,245,271,283,2,338,235,63,198,42,45,292,111,233,218,67,158,332,125,354,129,246,168,106,84,207,155,44,352,203,90,22,167,236,79,315,298,78,183,93,86,359,175,165,52,293,176,290,340,58,119,311,71,95,279,28,335,159,291,143,349,131,82,105,308,364,281,344,314,247,72,17,147,365,317,266,229,76,142,249,189,156,160,16,115,186,213,121,15,110,329,31,117,23,83,24,201,150,102,297,196,322,210,113,339,299,345,103,178,348,260,173,37,191,146,244,46,360,148,114,232,133,227,241,200,206,26,9,68,177,77,179,263,258,231,57,99,108,7,262,130,312,161,192","comment":"Linear magma over Z/367Z (the prime field F_367): x ◇ y = 283x + 36y (mod 367).","submitted_at":"2026-04-28 16:23:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/367/69dd46a31db0c6864d87e7148720a3ed60874de8e4d355360a2de41453e248c6.txt"},{"canonical_hash":"a6f2cea3788154c5e4ee3837e5737add5c20dfc6bebd54e35f78b409db6e53ed","size":367,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"366,0,354,58,188,29,297,12,69,76,317,291,131,296,340,96,308,327,362,213,151,119,125,158,87,116,130,66,174,89,260,298,142,356,161,64,196,214,45,361,107,346,283,143,81,37,114,47,251,38,280,270,86,202,305,254,55,156,253,53,216,230,132,6,98,259,190,240,117,223,303,229,28,330,16,9,333,277,195,211,271,84,180,288,239,290,99,30,245,232,325,282,278,363,286,176,207,329,326,299,236,94,226,249,250,82,34,110,139,103,210,157,294,170,112,121,209,304,292,313,18,184,4,289,88,79,348,275,262,208,215,187,22,199,74,104,281,63,15,337,137,3,5,189,316,20,164,105,334,328,345,32,167,335,233,261,27,307,43,145,227,144,248,46,61,319,122,56,73,194,124,221,263,224,318,102,201,71,2,181,159,136,238,173,234,177,197,220,242,52,57,140,39,257,163,324,160,185,133,59,70,183,258,75,8,309,205,166,206,106,246,90,322,172,274,228,95,284,267,273,42,225,113,255,128,49,51,198,276,118,77,342,41,60,138,85,126,154,147,323,336,287,65,25,350,50,123,111,252,353,243,148,182,19,231,355,218,149,40,200,17,97,68,311,310,165,31,175,360,265,268,146,237,347,302,339,343,264,171,306,93,36,351,178,349,241,21,332,150,134,338,272,120,109,269,91,168,364,162,14,179,129,320,35,48,193,169,155,1,314,217,365,315,244,141,23,331,341,101,312,7,11,100,67,204,344,285,44,300,108,153,135,78,222,295,203,359,321,26,235,80,191,13,24,219,186,10,212,152,301,266,247,33,279,357,192,352,256,62,83,115,358,92,127,72,293,54","comment":"Linear magma over Z/367Z (the prime field F_367): x ◇ y = 83x + 127y (mod 367).","submitted_at":"2026-04-28 16:23:18","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/367/a6f2cea3788154c5e4ee3837e5737add5c20dfc6bebd54e35f78b409db6e53ed.txt"},{"canonical_hash":"c30b026ff86a9148938c43d97c70060a68eaf112616d6f3578deb16df42f4868","size":367,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"366,0,140,199,328,216,54,23,8,174,71,55,303,109,122,16,107,49,98,269,259,242,243,333,227,33,358,218,310,186,115,129,356,99,298,198,347,344,193,84,183,121,36,301,228,235,13,32,82,180,132,154,3,346,73,116,165,313,41,31,364,321,317,365,6,40,348,360,222,247,53,246,27,144,24,191,48,37,272,249,38,18,309,151,285,110,225,161,83,341,90,152,112,43,131,330,270,69,104,74,320,171,342,62,137,173,26,34,261,204,304,258,150,331,168,264,290,128,130,92,158,349,176,35,172,208,141,78,135,345,289,253,28,251,1,5,77,9,232,88,302,190,231,273,126,178,332,224,123,124,46,181,297,68,286,60,196,93,234,260,287,315,117,201,164,91,339,240,209,327,359,288,80,322,146,15,271,189,21,254,278,357,340,296,361,275,292,343,319,200,10,336,194,81,257,145,353,294,262,30,175,274,156,229,22,52,250,352,325,169,97,17,125,351,133,362,185,111,59,58,159,267,182,61,338,166,11,306,153,167,188,142,214,219,316,207,318,354,280,70,143,76,29,237,100,241,284,223,96,65,63,355,329,233,266,85,323,300,25,326,213,205,238,72,127,277,236,255,139,39,134,335,265,66,108,47,87,155,276,148,226,160,45,350,86,244,197,103,314,337,102,113,12,203,79,206,311,118,312,157,295,283,105,215,221,252,256,299,210,106,248,230,51,138,281,217,89,67,184,147,211,192,170,163,305,101,56,179,149,14,279,282,19,363,95,291,64,50,7,245,2,293,212,162,268,308,177,324,334,94,114,42,195,57,44,307,120,136,239,187,202,119,4,263,20,75,220","comment":"Linear magma over Z/367Z (the prime field F_367): x ◇ y = 283x + 247y (mod 367).","submitted_at":"2026-04-28 16:23:23","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/367/c30b026ff86a9148938c43d97c70060a68eaf112616d6f3578deb16df42f4868.txt"},{"canonical_hash":"c802e7528a4c0fdcdd89dfa1fcb7cdfca1dbbf3dca92cf14b8f512019e95d4e3","size":367,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"366,0,341,118,297,64,74,313,253,217,365,200,30,95,269,163,209,176,173,138,342,46,156,195,352,109,51,316,225,310,119,53,165,299,132,358,129,117,94,194,298,143,14,144,112,262,151,349,308,241,65,275,19,15,272,245,181,237,266,223,75,147,7,145,121,140,255,303,88,294,314,168,85,113,73,208,50,128,150,180,254,49,99,263,324,221,100,43,68,105,218,23,107,152,305,183,264,134,197,32,21,205,231,350,329,91,325,235,228,3,201,216,137,309,193,240,222,293,179,104,31,4,103,242,331,154,101,170,77,243,96,318,211,66,259,361,44,6,250,332,270,82,124,276,41,355,69,340,29,155,164,13,18,20,84,98,106,230,136,102,210,123,17,16,55,344,219,160,280,171,177,336,56,273,11,37,24,322,61,78,174,291,345,246,63,162,108,357,261,244,139,207,220,182,90,239,153,360,354,97,343,36,161,238,187,188,306,27,285,319,47,289,281,267,191,189,184,347,338,212,157,252,172,224,93,307,265,87,149,67,196,227,178,76,249,28,135,279,60,260,353,284,337,148,59,286,198,214,287,362,110,39,57,8,126,320,33,1,199,45,52,142,274,146,167,48,22,204,215,5,317,81,12,122,335,290,206,35,288,251,226,283,38,141,80,282,232,71,363,333,311,233,25,256,296,268,351,131,111,271,120,72,323,304,328,192,330,258,40,83,54,364,62,89,186,190,92,248,58,125,166,334,79,295,327,185,326,115,9,277,300,312,175,315,116,348,236,302,127,42,133,234,292,169,10,339,229,159,321,356,359,26,346,86,278,213,2,203,34,70,130,257,247,114,301,158,202","comment":"Linear magma over Z/367Z (the prime field F_367): x ◇ y = 83x + 323y (mod 367).","submitted_at":"2026-04-28 16:23:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/367/c802e7528a4c0fdcdd89dfa1fcb7cdfca1dbbf3dca92cf14b8f512019e95d4e3.txt"},{"canonical_hash":"6120cafe405291d887a387cc44af8e4143efe7517d805f9831c4309334afd5f1","size":379,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"378,0,316,201,264,206,149,318,212,349,100,7,97,112,266,354,160,238,297,319,48,151,363,227,45,359,60,128,214,230,302,301,108,194,186,102,245,221,267,314,3,200,99,285,311,133,175,330,362,268,307,17,8,289,76,199,162,152,178,236,250,43,249,299,56,265,142,131,134,375,50,234,193,140,169,138,215,365,208,376,367,276,148,92,6,22,233,9,259,358,81,62,123,80,278,103,310,84,216,342,255,94,334,298,325,304,237,372,24,256,147,377,110,244,46,11,126,93,184,188,198,39,360,348,197,143,247,168,373,64,213,118,90,269,79,281,82,329,323,119,1,109,182,105,141,14,88,47,117,355,86,21,163,165,313,85,156,344,324,68,315,177,224,368,96,347,40,158,364,225,339,300,181,219,326,309,207,15,306,176,29,263,10,191,71,374,28,231,226,78,51,253,258,370,32,98,164,37,290,371,203,279,42,180,282,353,246,154,273,366,252,337,185,13,320,69,341,251,204,288,95,351,317,183,58,286,192,190,5,59,328,144,74,61,41,114,132,155,136,25,146,350,356,55,308,52,296,63,145,240,91,31,195,220,116,170,321,333,12,171,161,157,66,153,38,73,217,137,27,120,229,2,30,210,277,352,271,361,67,228,369,243,57,283,130,305,53,150,89,54,331,232,36,260,4,20,65,121,303,340,34,235,338,242,111,196,113,166,261,77,33,107,104,115,292,83,272,222,16,223,209,205,125,189,172,49,262,35,44,280,295,335,357,202,106,284,312,72,173,23,287,294,248,218,129,159,167,135,274,275,257,241,101,87,332,18,254,336,124,75,346,270,211,187,327,293,139,70,19,127,322,239,345,122,179,291,174,343,26","comment":"Linear magma over Z/379Z (the prime field F_379): x ◇ y = 327x + 80y (mod 379).","submitted_at":"2026-04-28 16:23:33","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/379/6120cafe405291d887a387cc44af8e4143efe7517d805f9831c4309334afd5f1.txt"},{"canonical_hash":"25210e8795f71b7e0a445a60a50e5478ec28721432a674ee28ee30e0479a3749","size":379,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"378,0,78,374,347,13,269,358,284,191,76,96,206,302,253,372,179,310,128,311,345,175,365,37,101,11,239,50,190,270,267,314,116,287,247,356,23,277,248,161,282,47,112,234,260,189,306,210,38,201,74,16,8,88,319,94,127,2,207,30,204,195,209,34,53,300,182,283,377,228,251,124,334,276,172,370,143,271,98,181,177,241,316,25,49,308,3,129,197,184,126,145,243,5,147,309,307,359,138,104,343,305,64,81,71,173,357,369,214,296,363,136,22,70,65,35,102,352,299,153,141,341,132,238,146,9,303,219,322,93,237,62,119,154,178,48,79,257,165,57,188,69,19,215,229,268,171,18,109,325,265,355,80,360,208,312,367,52,118,279,114,212,10,4,211,285,294,273,318,131,245,361,66,371,24,354,134,221,121,259,21,20,82,54,12,275,68,223,84,225,246,63,244,89,254,159,33,61,41,42,280,142,242,113,375,45,350,87,340,224,110,297,252,315,264,232,151,157,233,135,258,139,31,346,333,187,339,59,376,286,304,130,39,192,289,250,236,40,90,167,36,144,278,100,27,199,7,140,83,216,72,301,240,324,156,14,217,111,362,120,6,320,373,123,56,86,91,43,115,342,317,235,348,336,194,92,60,85,326,364,125,117,338,328,330,15,152,222,166,105,205,176,108,150,329,28,46,295,220,198,202,77,292,164,349,193,255,313,103,272,249,163,262,203,321,32,55,230,174,183,51,186,149,106,73,298,67,155,148,95,180,17,231,327,168,281,213,133,26,261,1,227,256,44,335,226,266,137,293,288,291,169,29,218,158,122,58,344,196,366,332,107,331,200,351,274,323,185,75,97,170,263,337,290,160,368,353,99,162","comment":"Linear magma over Z/379Z (the prime field F_379): x ◇ y = 327x + 247y (mod 379).","submitted_at":"2026-04-28 16:23:38","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/379/25210e8795f71b7e0a445a60a50e5478ec28721432a674ee28ee30e0479a3749.txt"},{"canonical_hash":"3a1cbb96c3d26b4336a8ecfca520d9eaa711b936440da92becceeb0f9fb89f98","size":385,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"330,331,333,339,337,332,334,338,335,336,384,0,1,3,8,6,2,4,7,53,5,328,108,109,111,117,115,110,112,116,113,114,327,217,216,219,225,223,218,220,224,221,222,329,54,55,57,63,61,56,58,62,59,60,326,271,272,274,280,278,273,275,279,276,277,324,162,163,165,171,169,164,166,170,167,168,325,349,368,351,347,345,370,372,366,353,364,343,48,37,50,46,44,39,41,35,52,33,9,157,146,159,155,153,148,150,144,161,142,118,245,234,247,243,241,236,238,232,249,230,226,103,92,105,101,99,94,96,90,107,88,64,300,289,302,298,296,291,293,287,304,285,284,191,180,193,189,187,182,184,178,195,176,174,379,358,381,377,375,360,362,356,383,354,341,18,27,20,16,14,29,31,25,22,23,12,127,136,129,125,123,138,140,134,131,132,121,265,254,267,263,261,256,258,252,269,250,227,73,82,75,71,69,84,86,80,77,78,67,320,309,322,318,316,311,313,307,270,305,281,211,200,213,209,207,202,204,198,215,196,172,359,378,361,357,355,380,382,376,363,374,340,28,17,30,26,24,19,21,15,32,13,11,137,126,139,135,133,128,130,124,141,122,120,255,264,257,253,251,266,268,262,259,260,228,83,72,85,81,79,74,76,70,87,68,66,310,319,312,308,306,321,323,317,314,315,282,201,210,203,199,197,212,214,208,205,206,173,369,348,371,367,365,350,352,346,373,344,342,38,47,40,36,34,49,51,45,42,43,10,147,156,149,145,143,158,160,154,151,152,119,235,244,237,233,231,246,248,242,239,240,229,93,102,95,91,89,104,106,100,97,98,65,290,299,292,288,286,301,303,297,294,295,283,181,190,183,179,177,192,194,188,185,186,175","comment":"Direct product of two linear magmas: F_5(2,4) × F_7(4,1) × F_11(10,2).","submitted_at":"2026-04-28 16:31:24","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/385/3a1cbb96c3d26b4336a8ecfca520d9eaa711b936440da92becceeb0f9fb89f98.txt"},{"canonical_hash":"2198a92ab6a2a00dd4f49ed582fb96197c4a2f694020cb07786ef09fdcd5750a","size":397,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"396,0,142,236,343,65,213,45,151,307,295,311,245,141,275,136,352,199,86,360,74,116,90,278,222,387,342,349,54,366,337,237,160,353,231,367,316,14,168,212,304,209,17,252,320,207,57,229,254,347,195,72,150,139,157,211,284,262,174,50,145,35,214,187,361,294,161,384,208,16,175,94,95,2,126,289,369,191,244,27,83,251,241,355,125,11,31,268,99,101,239,274,287,308,206,91,33,368,155,255,227,36,302,127,351,269,340,228,358,203,243,389,63,202,41,178,375,85,280,332,346,259,265,82,246,118,388,380,169,323,73,371,362,71,192,80,240,373,128,201,376,300,324,89,325,97,138,249,7,124,68,382,177,143,392,137,221,55,120,210,313,158,30,385,218,84,163,309,6,341,131,333,261,363,47,98,329,121,331,334,216,67,53,106,66,49,87,147,238,60,321,258,263,180,176,336,356,105,34,133,204,286,266,77,81,1,8,391,159,23,48,186,148,165,205,152,166,117,235,232,220,230,197,146,293,3,234,32,271,256,379,64,183,119,315,129,59,383,111,219,154,122,38,322,44,78,312,167,223,257,15,39,196,226,188,394,370,306,102,29,303,25,179,93,170,292,301,172,393,70,310,318,217,20,181,395,5,276,233,350,184,305,79,140,103,162,319,21,104,288,327,270,339,281,28,372,135,326,9,56,298,132,190,107,378,357,344,24,200,198,338,130,253,224,285,26,13,182,242,18,92,299,359,225,260,194,193,76,250,109,314,62,364,291,88,115,134,46,149,75,4,354,112,58,40,51,171,96,277,12,328,156,108,390,10,247,110,374,113,69,248,386,297,330,283,61,22,267,296,153,279,272,317,123,348,189,215,173,290,185,100,282,37,345,42,19,381,365,377,52,144,114,164,273,335,43,264","comment":"Linear magma over Z/397Z (the prime field F_397): x ◇ y = 362x + 30y (mod 397).","submitted_at":"2026-04-28 16:23:43","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/397/2198a92ab6a2a00dd4f49ed582fb96197c4a2f694020cb07786ef09fdcd5750a.txt"},{"canonical_hash":"ba3efc52ec044c3203bc9dfab5bb798a50d17cd0835579b9c44268b730e8da42","size":397,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"396,0,350,159,215,196,65,89,33,229,14,62,285,204,309,266,341,356,94,321,322,118,282,351,150,303,22,299,174,50,131,305,206,91,221,155,355,129,186,274,187,232,379,119,147,336,216,325,56,48,168,71,330,308,164,128,80,391,270,382,392,172,170,188,24,311,352,261,39,66,61,27,220,297,390,373,4,376,139,86,5,369,97,383,244,20,380,32,53,304,201,163,34,375,190,73,276,301,268,161,74,318,291,140,195,225,173,179,70,148,389,199,300,43,256,15,135,344,247,315,257,349,78,302,76,55,6,26,332,189,176,343,217,280,126,51,347,239,286,252,281,40,335,136,38,116,162,30,255,98,238,365,312,100,241,57,45,320,306,378,313,310,234,52,358,198,248,125,109,319,328,18,245,363,340,262,273,9,169,211,19,92,69,242,342,236,240,288,8,258,293,203,141,354,166,381,133,96,67,224,294,331,183,364,156,339,46,95,13,253,395,83,79,144,85,226,290,264,54,367,254,28,17,142,165,88,263,130,121,307,323,3,41,160,209,77,112,115,180,108,122,202,214,84,298,114,167,81,296,10,275,360,314,283,334,137,197,36,7,1,82,149,208,324,35,60,145,374,387,134,271,251,212,233,104,235,151,12,117,90,146,333,260,11,200,102,42,191,346,227,377,371,68,393,338,93,120,231,359,23,103,31,230,388,177,279,361,44,106,210,277,182,265,87,185,295,171,250,243,337,178,249,175,192,99,63,272,218,223,284,16,154,113,269,386,368,370,194,184,25,193,237,326,362,110,132,228,366,205,213,127,59,138,345,317,181,75,385,29,384,327,157,353,64,289,49,107,329,207,372,101,267,105,348,153,37,316,124,123,292,158,143,21,111,47,2,219,259,72,278,246,222,394,58,357,152,287","comment":"Linear magma over Z/397Z (the prime field F_397): x ◇ y = 362x + 332y (mod 397).","submitted_at":"2026-04-28 16:23:48","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/397/ba3efc52ec044c3203bc9dfab5bb798a50d17cd0835579b9c44268b730e8da42.txt"},{"canonical_hash":"693eb5e22551fb96af05a14ebbb20e9c9fffd4d1819bc98f5022fc771e09bc38","size":401,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,358,381,84,252,230,90,348,110,398,42,228,136,257,32,212,283,121,141,73,167,63,314,172,198,345,29,60,400,160,129,245,98,72,214,163,67,173,41,21,383,312,132,357,36,328,142,298,10,248,190,330,352,184,281,258,101,100,326,334,5,306,297,75,111,353,267,40,179,92,217,19,159,85,299,177,321,166,153,56,250,223,227,133,70,26,69,380,295,278,303,176,174,224,275,263,266,58,44,287,80,99,322,269,236,24,9,202,148,186,61,20,386,240,188,385,128,47,54,315,268,62,146,210,290,274,135,34,122,307,25,83,219,360,392,320,396,137,102,81,39,118,195,242,38,325,349,331,264,82,247,377,272,96,145,382,143,304,393,239,244,301,232,370,235,313,27,308,13,262,256,373,49,12,68,251,291,14,238,165,205,341,193,246,178,316,371,151,117,333,155,200,30,218,189,394,355,107,209,311,157,64,354,187,97,108,16,150,23,171,284,6,237,265,31,389,115,261,379,229,259,288,243,152,104,94,3,376,91,191,276,103,194,4,52,343,388,359,329,279,361,15,289,131,365,337,106,384,71,123,50,116,8,197,87,254,164,57,211,309,7,255,294,89,318,130,300,55,233,17,51,271,216,78,346,93,241,305,65,338,114,391,351,168,112,149,273,356,362,113,208,127,213,335,270,332,201,344,339,293,204,43,282,45,196,372,277,347,182,364,231,249,225,138,342,95,18,139,181,2,37,296,220,292,260,319,183,125,207,22,134,35,374,390,310,46,162,368,215,154,147,28,285,88,340,286,120,161,86,48,302,109,124,336,369,222,199,180,387,144,158,366,363,375,324,74,76,203,378,395,280,169,126,170,33,327,323,350,156,53,66,221,77,399,185,59,119,317,192,79,140,367,253,11,175,397,206,105,234,226","comment":"Linear magma over Z/401Z (the prime field F_401): x ◇ y = 373x + 29y (mod 401).","submitted_at":"2026-04-28 16:23:52","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/401/693eb5e22551fb96af05a14ebbb20e9c9fffd4d1819bc98f5022fc771e09bc38.txt"},{"canonical_hash":"399c5c4d2c75c40c9bc3ee87e019eb4600135e642fcad0812861758c45628b61","size":401,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,126,8,304,29,44,378,291,224,119,60,389,64,118,208,325,257,246,194,116,365,340,277,362,89,166,50,193,329,285,232,196,13,106,263,77,321,65,179,39,319,192,199,20,369,215,51,55,399,248,185,356,268,80,41,320,223,4,254,312,170,310,190,360,42,390,176,259,32,214,245,161,181,33,167,23,236,172,158,227,149,140,400,40,49,327,58,72,336,123,67,133,81,61,345,314,132,359,76,290,142,260,90,210,70,212,354,104,323,220,141,180,368,256,85,348,299,155,151,315,269,120,99,92,219,139,79,165,221,177,363,6,113,96,332,385,229,93,150,66,189,262,377,240,265,16,94,346,357,225,308,18,164,289,160,19,324,391,278,144,129,204,108,26,101,100,228,322,148,267,88,47,174,397,230,62,186,292,372,396,15,154,122,309,105,43,341,242,394,202,238,137,102,121,159,78,75,244,198,207,271,373,386,82,249,379,274,136,25,384,103,226,355,361,366,343,234,252,317,275,27,270,173,264,298,335,169,12,28,293,333,134,200,45,287,383,153,288,138,358,213,191,117,295,35,282,110,380,109,316,237,107,331,353,157,184,276,187,97,68,56,30,183,11,206,46,239,347,71,311,195,303,301,351,381,250,205,152,24,14,163,218,131,31,318,63,114,124,52,305,350,281,251,201,203,95,211,171,247,339,146,306,111,83,130,156,168,197,87,376,84,57,253,231,7,337,216,9,280,10,382,135,395,17,91,313,258,38,388,53,283,387,145,300,34,233,393,128,112,69,235,398,364,73,370,127,375,217,352,334,243,266,261,255,326,3,284,125,36,374,279,349,182,286,273,371,307,98,344,175,178,59,21,2,37,338,302,294,342,241,143,5,209,22,54,115,296,272,392,86,162,330,297,74,147,188,367,48,222,328","comment":"Linear magma over Z/401Z (the prime field F_401): x ◇ y = 319x + 83y (mod 401).","submitted_at":"2026-04-28 16:23:59","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/401/399c5c4d2c75c40c9bc3ee87e019eb4600135e642fcad0812861758c45628b61.txt"},{"canonical_hash":"a083f899e07de8b50f8c7155d803e1a2ee54e09b5e720ec17b03107c20964faf","size":401,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,332,245,338,176,91,252,172,174,199,60,388,254,132,209,192,93,146,279,266,178,14,284,204,340,45,166,118,247,155,137,295,334,262,374,378,3,138,179,61,2,185,212,82,269,365,343,350,158,307,377,382,64,35,272,77,310,241,275,370,373,222,324,359,321,113,226,7,392,318,261,51,28,52,223,383,186,296,15,389,333,27,328,142,258,303,109,23,301,25,294,50,316,111,220,239,33,305,363,183,136,260,153,43,12,144,130,197,89,330,154,317,329,29,325,65,213,335,285,255,246,391,88,96,106,17,398,169,69,298,117,6,196,188,291,346,355,385,235,313,165,225,129,229,217,54,230,189,97,30,44,112,143,53,360,36,83,263,205,133,339,320,11,216,150,394,125,201,123,9,203,358,42,228,127,233,289,115,396,86,283,323,152,128,151,361,218,292,107,326,13,221,259,224,322,273,270,375,341,210,177,372,135,164,282,277,207,58,250,243,265,369,182,312,85,102,161,79,38,103,278,274,362,234,395,37,55,347,18,66,145,240,304,384,114,78,366,379,46,193,92,309,32,354,288,160,99,74,72,352,191,76,238,345,232,101,100,367,56,162,208,271,219,290,126,84,231,356,399,214,131,34,110,187,227,311,344,4,167,94,253,63,315,195,41,181,237,48,21,140,387,381,49,5,357,368,75,380,348,80,59,376,293,116,202,264,190,386,170,336,198,306,24,297,8,242,351,139,119,147,173,157,300,68,122,249,71,20,400,120,171,349,22,168,200,57,73,47,19,39,251,342,108,397,124,206,98,236,70,286,90,364,302,16,393,276,159,180,248,280,175,268,257,105,149,281,287,40,121,148,337,81,141,95,215,163,353,194,67,104,244,211,327,87,10,134,31,314,299,256,331,184,26,390,319,371,308,62,156,267","comment":"Linear magma over Z/401Z (the prime field F_401): x ◇ y = 73x + 329y (mod 401).","submitted_at":"2026-04-28 16:24:03","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/401/a083f899e07de8b50f8c7155d803e1a2ee54e09b5e720ec17b03107c20964faf.txt"},{"canonical_hash":"8ac4073f8c5bec4d127135dd17a031a22f3a5fce97515e374666bb8173a2ff34","size":401,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,68,266,161,21,55,304,83,202,34,67,144,213,220,256,87,170,174,111,283,268,265,340,24,106,279,288,380,357,62,36,396,160,81,261,334,387,56,171,381,172,14,39,20,237,223,132,378,192,13,26,248,275,98,54,253,373,229,5,46,38,376,115,137,384,303,391,343,227,123,58,19,141,2,145,341,82,238,254,392,239,78,236,306,311,104,195,201,77,399,250,364,259,222,351,293,328,330,33,235,7,321,367,270,131,148,52,272,232,66,305,175,358,382,27,377,142,307,352,149,143,310,185,263,10,325,191,309,208,153,394,212,103,16,349,73,163,12,184,90,197,129,219,194,246,298,69,214,25,262,224,374,344,255,200,8,176,186,17,247,9,109,347,117,86,76,108,300,355,244,274,324,362,125,314,169,398,346,94,319,29,97,190,84,112,63,173,249,116,3,312,294,53,308,209,91,225,110,363,85,210,43,49,252,207,42,277,127,282,258,75,205,166,332,372,152,48,31,370,267,221,107,335,133,230,228,393,251,322,359,264,350,299,177,301,95,4,211,206,336,178,339,292,354,338,182,241,45,102,41,119,158,23,327,243,291,203,284,37,15,276,138,146,105,329,273,353,154,198,375,348,126,113,92,278,32,323,337,120,139,114,72,281,71,156,287,234,361,181,60,296,136,162,257,280,388,379,6,124,240,365,368,383,11,74,70,187,356,320,313,44,167,134,302,183,204,155,121,61,366,168,101,100,316,390,89,165,286,217,35,269,397,40,99,385,342,196,331,233,150,395,130,345,118,315,64,226,128,371,360,179,159,147,93,157,389,188,122,218,151,180,400,80,51,318,22,88,289,57,193,47,59,79,260,271,28,326,164,215,18,245,30,295,50,333,231,96,242,285,199,140,297,369,135,317,386,65,189,290,216","comment":"Linear magma over Z/401Z (the prime field F_401): x ◇ y = 40x + 362y (mod 401).","submitted_at":"2026-04-28 16:24:07","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/401/8ac4073f8c5bec4d127135dd17a031a22f3a5fce97515e374666bb8173a2ff34.txt"},{"canonical_hash":"b4ef4a1701c5870723f75e858d288768b66dcc5617774e025bdfc339c17e372f","size":409,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"408,0,54,90,300,404,328,343,142,364,246,97,178,333,193,274,388,12,206,233,88,221,335,6,20,192,175,234,35,113,124,1,230,371,250,139,48,181,83,211,334,186,63,195,185,152,252,41,258,78,34,286,17,344,84,281,273,111,351,169,362,75,61,99,72,121,407,223,100,280,377,292,294,393,15,62,321,228,53,401,176,112,28,144,309,204,37,387,27,260,398,68,94,89,279,29,108,137,324,241,272,312,128,406,255,9,194,153,322,154,131,51,123,107,357,198,201,81,11,143,212,378,313,56,299,376,337,161,318,65,359,110,55,372,73,22,338,184,130,264,219,315,134,5,136,297,235,352,261,213,308,307,171,164,70,403,291,183,243,222,18,145,358,298,266,159,390,216,151,50,38,385,275,253,229,323,265,39,102,44,232,203,306,349,340,365,327,293,129,373,267,396,346,168,375,395,166,32,91,251,122,109,162,244,374,370,240,158,105,118,247,87,36,170,391,379,172,350,392,263,369,133,289,331,361,336,345,310,199,236,40,106,43,269,319,225,249,271,389,42,46,155,220,386,163,270,302,354,149,14,218,239,187,287,399,74,160,167,303,304,209,257,356,231,301,140,214,138,311,215,268,126,188,342,26,77,368,59,114,363,69,314,165,341,380,295,60,317,382,208,147,7,85,205,202,353,103,119,47,127,150,326,157,190,13,259,402,132,316,276,245,320,141,104,25,283,93,98,64,394,256,23,383,33,200,305,148,24,116,180,405,49,224,325,66,19,397,290,288,381,284,96,227,4,125,76,95,57,71,366,173,355,115,277,285,80,348,21,282,30,82,262,45,248,156,189,191,67,182,330,207,79,177,52,135,254,367,226,2,120,117,31,238,179,196,16,10,339,217,92,237,210,8,384,278,197,329,174,101,242,360,146,347,332,400,296,86,58,3","comment":"Linear magma over Z/409Z (the prime field F_409): x ◇ y = 355x + 39y (mod 409).","submitted_at":"2026-04-28 16:24:13","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/409/b4ef4a1701c5870723f75e858d288768b66dcc5617774e025bdfc339c17e372f.txt"},{"canonical_hash":"5aa010d8a64bcb42bf41411227d9ed14b8ec1387b072edf73fd42ac163a98f86","size":409,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"408,0,127,287,65,141,225,272,189,49,79,234,11,407,396,239,313,37,359,216,203,220,20,307,137,93,148,30,31,62,363,36,251,182,347,224,297,400,340,308,327,263,344,144,146,187,245,350,75,205,217,171,86,53,121,372,122,164,186,318,151,240,346,168,375,162,306,218,285,69,10,337,235,176,1,377,278,353,246,90,265,281,387,273,282,175,82,8,84,345,311,293,369,170,288,354,199,326,329,130,341,61,109,39,210,358,177,154,59,271,160,348,60,232,102,259,310,70,256,156,89,315,364,211,284,45,106,404,163,242,100,197,244,149,342,135,223,179,193,241,136,112,275,255,21,200,300,153,126,392,165,198,402,269,291,360,370,398,214,34,389,54,405,167,22,320,397,85,406,381,299,262,206,212,134,362,208,80,283,215,249,394,231,188,157,14,108,118,226,266,292,41,323,13,264,260,267,133,68,128,279,166,185,28,47,401,349,15,334,111,296,236,301,99,92,96,183,155,395,124,98,58,286,276,184,325,18,63,40,81,383,115,248,376,194,302,380,374,94,131,213,52,253,43,152,343,335,51,222,35,355,382,44,202,4,123,101,48,366,333,38,294,321,132,368,191,87,107,280,304,73,361,9,55,303,174,317,76,365,268,74,331,50,274,399,116,379,196,147,257,324,88,238,142,91,270,64,228,27,328,103,227,322,7,2,378,393,277,229,173,298,161,158,367,33,120,338,201,125,143,24,252,178,250,5,114,105,219,113,97,258,78,32,110,209,356,6,67,169,180,237,117,386,138,330,207,336,25,72,319,150,16,332,290,204,289,221,254,339,385,373,243,29,77,17,314,312,23,95,159,140,172,46,129,56,26,12,83,390,195,230,352,351,316,261,305,139,190,388,371,384,3,391,145,71,42,192,181,66,247,403,19,104,57,309,233,119,295,357","comment":"Linear magma over Z/409Z (the prime field F_409): x ◇ y = 355x + 316y (mod 409).","submitted_at":"2026-04-28 16:24:18","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/409/5aa010d8a64bcb42bf41411227d9ed14b8ec1387b072edf73fd42ac163a98f86.txt"},{"canonical_hash":"ebcb8d0c6e6c1a60702ed4f9f2d92f865e75fb57ff4688145491b7f495083cbb","size":421,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,303,19,233,59,280,213,192,266,119,342,17,218,155,357,50,114,226,118,359,199,89,392,322,369,281,208,106,244,139,315,28,178,411,370,195,228,117,80,284,206,373,42,420,252,163,416,74,290,327,18,405,160,201,388,238,105,349,34,316,418,71,159,112,182,299,409,149,328,16,324,260,147,365,8,227,132,329,56,402,3,70,269,23,229,93,211,210,198,320,255,60,204,239,162,347,263,235,6,171,323,58,9,276,141,339,346,138,143,43,294,240,153,387,215,313,343,334,72,401,154,180,188,354,68,140,79,4,36,122,311,121,111,109,291,231,172,166,197,391,100,115,296,150,386,73,128,258,220,174,196,146,212,337,167,82,186,234,27,389,13,340,184,187,104,52,393,250,366,257,69,49,375,54,306,374,345,205,362,151,247,64,120,298,419,126,241,224,185,254,368,245,272,403,63,312,326,65,46,91,75,99,7,265,175,399,76,51,170,410,190,335,378,367,67,33,371,222,94,32,173,22,225,20,308,202,305,142,41,83,134,77,90,108,148,302,355,11,307,26,203,207,288,61,38,297,333,404,267,39,317,169,295,131,341,85,379,107,249,57,194,123,87,248,271,78,417,413,236,97,221,145,92,358,318,300,287,344,293,251,352,95,412,98,230,15,232,383,242,304,12,161,243,277,157,168,125,400,200,380,261,286,189,385,55,217,309,285,301,256,275,116,102,273,193,62,35,158,44,395,14,31,336,209,88,330,274,37,361,152,415,135,164,96,264,165,259,279,47,156,40,183,262,314,397,394,130,223,179,237,24,396,292,377,127,2,356,406,384,10,48,338,283,176,360,86,325,310,181,407,376,382,21,81,319,321,331,101,332,246,214,289,350,278,144,398,390,364,191,282,124,133,103,5,177,363,30,84,253,353,348,136,129,351,66,219,268,113,381,216,25,53,137,372,29,414,270,45,110,408","comment":"Linear magma over Z/421Z (the prime field F_421): x ◇ y = 378x + 44y (mod 421).","submitted_at":"2026-04-28 16:24:22","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/421/ebcb8d0c6e6c1a60702ed4f9f2d92f865e75fb57ff4688145491b7f495083cbb.txt"},{"canonical_hash":"94b880d003ccae6a98168ce524aee4e36222e973204235ab7b9f317227b96ee8","size":421,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,101,96,388,45,183,318,135,16,281,213,48,109,221,137,372,365,330,354,129,194,156,84,253,51,355,401,395,364,381,192,98,35,342,17,386,239,357,134,30,58,286,275,115,5,392,322,285,113,376,358,160,55,399,196,346,243,34,279,396,117,164,200,38,121,42,420,252,331,248,410,374,327,186,69,244,33,136,406,189,265,370,148,166,323,75,112,182,215,325,65,76,268,240,344,147,29,176,227,132,245,308,402,171,154,185,191,145,261,43,294,366,404,339,144,120,155,162,347,11,319,258,3,71,226,345,108,393,255,178,306,311,211,210,324,321,387,299,61,91,250,72,233,70,264,356,270,236,224,415,340,288,122,143,373,363,25,123,63,172,418,197,223,184,199,128,234,218,241,296,6,304,90,28,398,212,337,167,82,18,150,27,305,181,4,100,187,20,52,141,334,198,257,405,385,39,390,138,290,9,289,362,403,247,400,204,46,335,378,73,140,269,170,116,329,272,151,231,312,158,149,298,343,159,15,7,349,259,315,328,303,254,74,274,419,126,367,67,201,203,222,10,32,341,22,309,104,56,202,389,142,293,251,50,77,174,276,316,302,19,263,307,278,371,207,36,313,206,297,81,320,267,375,317,85,379,383,173,169,295,107,165,57,110,291,87,416,103,246,417,161,68,97,53,229,92,106,66,384,287,260,41,83,352,179,412,266,314,99,232,131,242,220,12,413,411,277,157,336,209,64,284,44,93,118,105,49,139,217,225,369,133,88,359,368,102,21,361,62,119,326,380,59,350,283,168,125,256,414,190,37,193,152,79,219,80,348,180,249,175,195,47,408,124,351,262,230,397,310,214,391,95,237,360,228,292,377,127,2,188,238,300,94,216,86,31,8,24,338,409,394,13,407,208,382,273,333,235,153,163,353,332,78,130,205,14,26,60,146,54,280,23,282,40,301,271,89,177,111,114","comment":"Linear magma over Z/421Z (the prime field F_421): x ◇ y = 355x + 67y (mod 421).","submitted_at":"2026-04-28 16:24:26","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/421/94b880d003ccae6a98168ce524aee4e36222e973204235ab7b9f317227b96ee8.txt"},{"canonical_hash":"61c98724ea43705935d672e058c78d992e4329fd1f3fb9ab343e1c9cee558489","size":421,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"420,0,168,199,265,157,296,293,362,327,254,60,393,302,390,285,37,93,61,380,351,58,100,150,10,243,399,33,7,176,382,403,136,131,190,379,101,248,55,67,26,28,98,144,197,413,247,332,167,95,340,221,76,328,132,89,164,88,273,350,12,1,80,129,233,388,228,365,287,278,54,352,198,288,345,371,154,225,107,103,125,163,127,57,195,179,241,304,294,404,90,104,344,111,66,44,264,147,192,259,74,109,318,343,173,87,62,99,229,91,186,376,261,209,185,236,370,138,25,315,156,355,171,158,177,329,226,110,330,272,5,149,325,182,40,121,384,336,375,347,153,38,27,234,295,262,385,223,20,271,46,65,251,349,322,9,204,212,200,34,222,372,260,159,224,217,97,417,292,113,276,216,338,4,401,43,391,11,81,242,187,41,201,202,19,334,208,23,106,257,143,123,361,2,244,96,289,148,356,263,114,3,206,398,415,116,18,406,270,312,184,394,102,13,196,230,326,205,188,416,283,324,51,146,358,79,306,32,282,151,333,353,45,316,235,418,124,231,412,411,253,397,30,291,268,181,255,191,274,128,63,6,323,82,207,307,64,71,369,48,162,69,246,410,59,414,279,112,139,39,218,258,14,232,70,175,50,85,22,239,250,363,137,165,126,174,331,252,392,115,359,275,15,120,320,73,119,387,368,381,145,366,105,237,348,160,24,395,56,49,166,396,301,17,309,215,297,383,133,108,319,227,47,402,357,52,256,219,321,134,314,300,194,84,94,29,389,405,210,337,373,335,313,317,72,364,161,135,78,408,142,266,8,77,155,75,178,21,339,290,284,269,140,16,298,374,299,342,118,286,68,130,305,377,122,35,203,407,354,308,240,238,220,267,36,311,169,400,341,346,193,172,386,277,245,189,31,280,360,310,211,141,170,214,303,249,419,180,92,183,213,42,117,152,83,86,367,53,409,378,281","comment":"Linear magma over Z/421Z (the prime field F_421): x ◇ y = 400x + 84y (mod 421).","submitted_at":"2026-04-28 16:24:32","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/421/61c98724ea43705935d672e058c78d992e4329fd1f3fb9ab343e1c9cee558489.txt"},{"canonical_hash":"fdb996108fcfb40a3cc021e061551b14525cc139a70b76fbd89cd590833943fc","size":421,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,164,258,146,257,185,352,383,243,256,240,156,213,371,351,247,180,128,279,242,106,317,26,38,239,31,57,396,360,212,337,167,82,400,350,36,158,204,334,179,160,228,250,53,278,365,307,380,122,105,45,311,225,215,25,172,90,206,341,238,394,276,274,198,56,355,222,296,329,359,373,117,99,138,336,209,109,324,200,81,195,270,411,404,349,165,120,353,409,157,132,181,6,318,333,58,264,168,125,159,191,229,151,308,249,312,70,91,162,277,34,223,357,118,306,110,134,271,11,121,112,182,261,265,44,230,176,71,63,224,74,135,218,183,24,177,88,136,130,89,42,420,252,299,340,346,298,387,234,393,8,345,284,14,273,281,386,20,254,55,51,392,322,331,221,61,344,320,96,328,147,13,244,67,372,301,280,102,39,98,361,19,401,369,335,378,54,268,123,108,216,391,342,367,199,143,330,375,139,194,201,60,405,291,410,114,319,419,126,348,309,327,163,149,119,86,12,145,266,408,64,66,184,28,131,416,300,382,235,5,15,101,255,315,332,170,97,155,68,263,40,18,370,389,124,414,368,246,140,190,292,377,127,2,150,186,267,241,29,248,236,107,316,32,69,338,390,37,141,161,3,366,30,46,33,173,142,395,47,356,48,374,211,210,305,196,193,166,304,133,232,59,399,192,10,313,290,35,303,111,287,113,203,231,260,75,418,178,398,43,294,347,227,9,175,282,326,52,289,62,153,148,364,302,73,362,85,379,286,217,78,144,104,202,23,115,407,310,259,87,384,65,214,417,129,16,27,171,397,41,83,415,205,293,251,187,381,237,226,339,207,4,275,174,297,49,100,197,325,233,412,314,354,288,7,76,169,295,152,283,92,154,358,363,272,79,262,116,72,385,219,17,137,84,253,188,388,208,285,50,21,413,323,77,321,93,245,80,103,220,402,189,269,22,343,94,376,403,406,95","comment":"Linear magma over Z/421Z (the prime field F_421): x ◇ y = 280x + 142y (mod 421).","submitted_at":"2026-04-28 16:24:36","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/421/fdb996108fcfb40a3cc021e061551b14525cc139a70b76fbd89cd590833943fc.txt"},{"canonical_hash":"70a5dac003a45fc6e2ea95c2420a224faf33b0319550968003369ac13a183872","size":421,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,356,136,376,369,134,273,161,71,77,153,261,329,164,271,304,402,105,185,22,91,10,208,151,238,179,84,253,80,6,398,257,269,352,131,411,88,324,408,381,203,183,247,264,296,195,242,358,317,278,206,155,283,57,228,24,212,337,167,82,64,14,288,326,120,250,95,244,396,334,221,26,29,307,44,122,189,129,143,309,299,109,172,174,38,173,406,310,108,190,366,308,19,222,128,245,275,121,117,15,306,168,125,25,240,284,333,279,354,243,320,265,249,204,101,325,157,132,13,258,66,81,226,180,336,209,75,23,145,403,56,165,312,154,343,162,277,370,391,357,286,138,194,50,103,263,373,112,182,93,349,380,314,8,323,231,140,410,219,386,351,360,177,256,388,214,5,42,420,252,215,4,178,46,387,150,141,176,9,200,350,21,113,218,104,170,139,303,392,322,163,53,313,260,404,348,76,147,181,160,67,372,133,364,102,375,266,193,355,233,285,419,126,390,16,291,276,48,223,342,367,115,311,414,39,55,110,33,144,69,123,74,30,235,335,378,96,225,327,331,65,35,338,12,229,98,156,400,318,100,196,383,248,384,382,319,89,99,353,339,399,332,254,97,239,236,11,124,186,34,305,40,330,116,78,224,274,292,377,127,2,234,18,267,73,365,416,68,107,148,32,405,86,54,37,393,413,171,198,114,298,201,341,142,59,47,188,216,290,43,294,389,28,361,418,220,301,232,395,315,192,94,61,374,119,51,363,287,281,371,63,344,159,166,346,146,211,210,347,227,345,259,282,158,52,205,62,321,316,280,302,241,362,169,295,118,217,246,60,20,202,191,199,407,394,175,87,300,149,130,417,45,268,27,3,397,293,251,79,289,41,83,187,213,237,58,255,207,340,359,90,297,385,184,197,409,401,412,230,270,36,7,328,85,379,152,31,92,70,106,111,272,415,262,368,72,49,135,17,137","comment":"Linear magma over Z/421Z (the prime field F_421): x ◇ y = 253x + 169y (mod 421).","submitted_at":"2026-04-28 16:24:40","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/421/70a5dac003a45fc6e2ea95c2420a224faf33b0319550968003369ac13a183872.txt"},{"canonical_hash":"62e639095ca019208d48cd2f7a6a50f5a7d1aeb77fc317261dd7e9a783490674","size":421,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"420,0,183,36,373,295,151,3,82,410,214,386,341,202,180,1,272,311,119,235,404,33,95,240,260,326,392,378,370,181,182,286,191,354,230,292,309,163,19,170,113,60,148,189,285,35,24,247,44,6,245,279,101,143,87,417,79,203,371,190,372,154,205,407,381,233,63,47,14,208,211,137,228,153,353,294,134,383,360,8,303,346,54,225,338,342,379,149,204,229,150,199,139,12,31,56,159,350,177,322,29,307,198,406,291,4,333,362,277,364,126,131,269,387,393,61,80,138,380,308,81,298,344,238,395,357,116,250,90,157,17,297,11,232,162,409,129,141,398,300,401,215,327,114,418,212,343,30,62,18,213,223,324,51,92,317,69,67,175,111,222,237,265,46,169,385,415,335,257,411,261,171,88,209,339,323,394,158,13,112,340,376,389,122,329,194,173,27,146,375,50,356,349,207,59,201,367,83,241,20,144,15,226,178,388,91,115,176,210,147,179,74,252,105,71,220,196,283,73,121,316,249,321,136,188,2,96,164,102,48,55,351,270,251,328,68,89,28,227,284,271,39,217,314,263,289,22,38,104,193,66,156,306,152,34,310,280,64,347,160,132,117,216,70,172,174,16,197,352,23,118,108,319,167,331,42,107,313,219,26,110,296,405,293,246,234,304,57,127,358,402,318,262,195,145,221,10,290,133,43,403,186,413,275,243,185,166,288,282,374,236,231,5,382,7,32,365,396,301,93,412,330,21,72,49,264,161,332,359,244,94,255,124,99,254,274,41,37,120,355,45,408,361,9,278,239,399,52,258,123,242,106,103,315,348,168,128,276,302,100,259,267,85,266,98,184,312,192,248,206,384,140,363,345,142,325,336,390,84,253,165,218,65,320,58,414,397,125,53,86,391,77,76,419,273,287,25,155,135,200,334,299,130,224,416,377,368,75,97,40,281,109,305,187,366,256,400,268,337,78,369","comment":"Linear magma over Z/421Z (the prime field F_421): x ◇ y = 400x + 316y (mod 421).","submitted_at":"2026-04-28 16:24:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/421/62e639095ca019208d48cd2f7a6a50f5a7d1aeb77fc317261dd7e9a783490674.txt"},{"canonical_hash":"cd61004e19819e9ad94cc62edc78a0c435e145ca78a64899dd98af6ad5c8b76b","size":431,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,109,327,163,392,385,21,149,132,339,425,192,270,379,3,225,419,179,32,219,65,19,59,289,129,430,344,74,274,234,280,4,247,394,204,10,218,164,55,407,210,124,347,364,236,170,177,378,112,324,216,215,134,137,368,370,211,284,148,77,183,94,235,396,415,330,296,337,33,108,140,272,319,54,150,376,277,375,412,294,154,297,166,98,246,100,116,371,107,14,421,308,63,237,42,343,405,254,157,395,146,126,121,145,373,60,64,26,403,67,283,193,298,268,41,300,388,2,141,49,172,214,358,310,78,106,29,7,131,105,113,142,169,24,390,314,165,27,287,326,48,258,345,406,250,260,92,276,226,101,152,267,231,174,393,151,251,38,139,223,70,397,25,202,262,73,249,135,359,414,304,317,80,125,194,306,18,286,207,281,147,305,400,103,342,220,15,224,168,186,84,133,413,227,196,13,96,353,338,28,119,428,176,201,212,30,97,118,46,162,171,301,221,209,37,332,205,374,195,88,351,40,290,238,203,266,423,189,271,167,232,291,402,265,110,273,259,302,335,329,399,184,114,120,87,44,58,325,50,187,76,17,382,56,404,208,51,418,23,75,255,136,303,410,159,420,117,252,424,6,86,386,377,261,333,312,245,427,416,391,213,334,243,123,138,311,228,411,12,198,348,299,401,383,9,230,5,127,318,185,90,362,66,422,71,233,91,409,340,295,102,89,199,144,350,34,288,47,417,240,182,285,8,354,253,36,366,178,389,16,52,367,316,11,61,307,45,35,191,130,43,263,111,72,242,380,99,175,239,384,357,328,320,346,222,244,321,293,95,143,429,387,264,356,217,173,85,256,53,83,408,68,282,188,241,279,275,158,360,336,341,361,180,372,39,190,128,257,22,278,93,206,229,322,156,331,315,31,313,381,82,369,79,197,160,62,161,365,269,104,57,355,323,248,122,81,115,200,181,20,309,398,292,363,69,426,155,153,352,349","comment":"Linear magma over Z/431Z (the prime field F_431): x ◇ y = 406x + 26y (mod 431).","submitted_at":"2026-04-28 16:24:51","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/431/cd61004e19819e9ad94cc62edc78a0c435e145ca78a64899dd98af6ad5c8b76b.txt"},{"canonical_hash":"80f68257d524951dda0cd3345c49566cace27c1e73ff5cfc63cdc9793e620e11","size":431,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,111,287,173,319,372,104,14,286,207,421,177,211,241,280,237,266,318,224,246,54,276,209,43,158,354,103,233,346,169,312,20,338,262,187,285,73,134,365,314,49,68,396,167,420,220,97,114,148,320,375,242,401,210,7,21,244,50,27,321,121,28,279,272,95,357,367,271,129,205,200,265,301,303,137,82,356,71,414,88,223,154,41,323,425,270,213,350,191,53,101,405,31,99,204,360,2,195,208,229,225,306,234,264,74,385,221,157,8,293,273,165,302,56,155,251,102,308,230,198,9,81,309,16,260,345,259,193,296,334,70,59,119,142,311,258,381,84,393,87,348,183,217,337,295,373,145,281,153,44,239,339,186,69,4,376,181,322,47,130,289,72,118,214,325,361,269,75,327,57,364,310,161,60,202,349,63,45,341,48,380,76,79,64,52,430,411,423,395,392,151,407,112,404,422,163,247,419,347,124,135,416,98,391,22,132,96,216,304,388,42,359,406,93,226,147,294,428,231,110,194,403,382,34,374,144,5,108,172,228,162,316,77,400,152,11,125,371,305,418,429,105,6,238,12,159,13,263,123,397,299,243,185,122,331,206,384,415,116,351,26,3,298,386,176,156,390,17,189,120,180,184,253,240,292,131,249,328,278,46,330,412,236,164,215,23,66,94,288,383,178,317,55,387,170,398,366,117,115,18,245,250,358,24,138,171,324,25,32,275,307,92,274,409,199,268,297,255,85,197,146,91,377,343,326,175,61,353,80,427,408,128,136,363,389,38,232,15,109,267,126,355,160,188,332,168,344,402,254,29,413,201,179,89,19,192,33,196,256,222,62,252,39,261,333,143,90,218,40,340,291,290,284,58,107,342,369,424,379,248,283,133,141,227,174,35,212,78,277,106,313,300,315,352,149,190,51,329,368,67,83,399,426,139,100,410,235,378,166,86,10,127,335,30,394,257,282,219,182,370,362,36,203,150,65,140,113,336,417,37","comment":"Linear magma over Z/431Z (the prime field F_431): x ◇ y = 246x + 186y (mod 431).","submitted_at":"2026-04-28 16:24:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/431/80f68257d524951dda0cd3345c49566cace27c1e73ff5cfc63cdc9793e620e11.txt"},{"canonical_hash":"24058100935f3cc7100d9a4180613d89d81e418775c51272fd82c35874df3a19","size":431,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,234,336,346,92,104,54,359,152,267,59,88,135,409,79,210,53,395,156,397,111,202,262,245,163,221,273,328,218,317,166,211,108,134,190,114,207,109,147,391,56,275,342,306,101,138,340,14,428,305,155,227,24,185,354,95,80,200,33,170,4,29,212,116,97,290,304,162,429,129,49,123,37,332,291,288,281,260,179,126,376,410,375,94,165,103,99,167,232,119,402,351,196,15,173,302,421,243,313,98,28,206,87,388,230,411,136,187,334,17,382,314,318,380,309,160,195,161,341,394,45,66,73,76,117,252,338,264,344,214,377,89,75,312,331,427,244,219,385,248,415,295,310,139,400,239,12,370,90,213,229,125,353,316,91,127,60,271,176,362,324,422,329,405,349,323,426,381,102,3,113,58,6,378,30,47,417,326,182,371,180,268,425,294,194,350,303,274,52,367,144,269,319,307,131,121,19,216,215,5,369,72,242,36,13,261,153,298,357,70,406,174,222,158,149,35,181,315,343,387,178,184,217,345,171,84,225,255,150,240,282,360,69,193,361,330,16,164,169,189,266,372,383,276,300,257,22,20,265,34,143,322,414,159,401,289,55,209,82,283,423,197,246,62,419,21,183,18,57,11,65,420,122,339,201,286,9,106,223,140,292,105,413,254,241,325,352,263,86,259,23,327,335,392,41,279,63,132,253,81,192,356,293,175,311,333,93,32,133,151,363,403,203,43,430,258,418,188,148,366,348,247,308,118,96,390,78,141,407,296,38,347,278,64,256,177,120,112,238,44,301,48,137,110,26,39,198,320,77,355,8,321,224,71,416,124,337,205,280,226,272,233,398,236,204,277,31,412,208,68,297,424,270,74,186,374,199,107,358,249,50,235,237,42,85,61,168,157,51,404,384,379,231,115,146,408,284,145,67,25,365,40,10,299,386,130,2,399,393,172,128,100,396,250,364,373,7,389,191,285,142,83,368,46,228,251,27,287,154,220","comment":"Linear magma over Z/431Z (the prime field F_431): x ◇ y = 117x + 315y (mod 431).","submitted_at":"2026-04-28 16:25:00","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/431/24058100935f3cc7100d9a4180613d89d81e418775c51272fd82c35874df3a19.txt"},{"canonical_hash":"f3456c2f733c88822f8d3b418fb40602e087417fe28566722d788e6a23310b40","size":431,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,158,34,8,152,217,411,373,270,219,30,292,191,169,116,425,391,346,147,38,43,245,67,94,84,80,197,32,403,20,366,273,41,369,353,253,48,322,324,59,236,350,185,125,259,427,240,317,16,126,316,49,250,21,167,68,187,426,223,271,285,159,229,45,124,360,206,133,72,131,414,349,406,62,319,162,409,178,58,342,88,82,303,175,99,321,183,212,10,333,418,283,252,381,55,385,56,395,213,368,89,54,63,344,207,339,272,233,251,155,428,200,325,19,274,417,85,255,347,277,31,101,9,331,171,28,265,79,231,182,401,5,202,26,93,238,98,309,300,335,122,244,149,302,139,301,135,6,37,172,87,256,243,429,75,345,421,57,328,334,96,304,424,163,408,73,308,160,103,168,377,318,379,237,114,370,291,198,405,39,25,192,180,218,314,413,267,4,295,70,372,262,71,209,181,13,371,216,104,205,305,78,76,294,7,107,123,287,27,120,266,157,278,228,326,330,340,313,214,289,284,393,100,145,179,362,415,222,46,276,188,24,127,165,186,398,254,280,404,247,246,166,117,416,374,290,2,279,249,108,18,105,113,263,397,315,143,199,137,378,358,164,15,422,154,173,376,150,23,239,52,232,65,102,388,275,258,234,338,90,307,382,221,184,110,343,225,407,111,361,235,224,53,50,423,260,144,323,109,367,118,95,399,392,47,220,394,35,327,129,288,352,306,384,210,420,268,312,40,337,380,195,74,297,329,365,257,282,140,242,310,227,402,387,332,430,86,141,156,196,64,211,386,36,11,119,83,51,320,226,134,91,286,66,22,174,241,138,60,106,42,375,81,281,148,189,293,146,153,341,364,121,355,77,390,14,177,296,299,193,204,115,357,161,194,97,356,215,190,136,61,336,92,203,12,29,142,348,311,201,298,208,269,396,130,419,400,176,261,410,112,132,383,230,389,69,151,17,359,351,264,354,3,33,248,44,128,170,363,412","comment":"Linear magma over Z/431Z (the prime field F_431): x ◇ y = 96x + 336y (mod 431).","submitted_at":"2026-04-28 16:25:05","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/431/f3456c2f733c88822f8d3b418fb40602e087417fe28566722d788e6a23310b40.txt"},{"canonical_hash":"233aaa51e826ab6328a1b2d206a47e696f7df84713ecb4f8facf46cd60ea086a","size":439,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"438,0,78,261,90,203,273,192,102,43,215,112,285,70,204,398,114,245,14,64,58,387,124,226,297,121,82,240,216,73,410,380,126,307,257,110,69,395,24,265,18,239,399,430,136,182,238,231,309,99,133,27,94,45,252,28,59,428,85,271,422,3,392,171,138,207,319,284,269,60,122,178,81,174,407,316,36,17,277,314,30,22,251,2,411,382,223,268,148,355,194,196,250,164,243,151,321,320,111,91,145,401,39,120,106,305,4,403,264,141,40,179,19,44,221,363,97,47,283,371,434,158,75,21,404,37,183,205,150,214,50,358,331,140,296,377,281,117,20,23,134,65,190,116,93,210,186,294,419,318,328,420,48,224,29,298,289,342,326,242,42,352,34,349,263,225,76,197,423,74,394,212,235,248,280,26,160,12,367,327,206,322,208,258,262,313,176,291,255,366,163,101,333,350,332,402,123,266,103,131,157,68,413,199,10,376,132,424,118,5,317,137,71,373,415,348,276,287,153,369,11,249,191,180,31,100,15,386,233,52,375,433,109,228,6,368,295,98,383,253,227,418,170,219,87,67,33,16,416,259,8,159,195,272,217,166,162,304,57,302,62,9,370,256,343,184,152,139,308,79,389,108,293,391,129,167,32,351,35,359,146,61,25,193,202,346,128,365,105,63,53,104,198,282,306,408,431,286,330,230,340,337,432,185,7,200,236,66,41,315,310,246,301,279,354,89,338,390,254,119,13,187,364,412,46,125,361,336,275,357,237,168,88,374,209,421,435,356,86,241,406,426,55,56,247,147,260,154,292,290,38,244,172,127,437,96,379,155,339,347,49,181,334,353,51,92,270,396,274,218,325,173,188,54,303,234,267,77,378,107,175,400,113,324,345,156,362,409,344,229,414,213,135,142,278,232,115,84,143,335,169,341,80,384,425,161,211,222,1,95,388,312,144,397,436,201,130,220,72,323,329,372,149,429,83,300,385,189,427,311,360,417,288,177,299,405,165,393,381","comment":"Linear magma over Z/439Z (the prime field F_439): x ◇ y = 171x + 34y (mod 439).","submitted_at":"2026-04-28 16:25:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/439/233aaa51e826ab6328a1b2d206a47e696f7df84713ecb4f8facf46cd60ea086a.txt"},{"canonical_hash":"2ee0bc4caba7ae0b12f93c41d8b08fc7b3da0bc8574ca6c5549603e26530268b","size":439,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"438,0,211,376,23,365,142,397,181,307,131,351,346,75,163,296,385,104,73,7,335,328,117,8,112,285,279,238,367,345,62,36,151,282,308,317,277,418,203,1,101,10,94,402,321,227,204,304,316,349,51,427,45,341,12,271,133,368,111,108,266,175,194,259,355,41,48,110,74,369,83,159,435,91,230,216,15,303,210,182,305,169,206,19,298,416,168,276,87,222,39,419,16,359,70,357,82,284,115,213,255,128,239,49,249,248,107,162,208,187,429,395,337,105,134,358,315,375,312,56,424,257,379,371,398,205,417,399,121,333,199,54,252,389,314,158,278,217,135,405,287,235,363,27,247,265,295,280,42,250,28,232,173,404,69,348,22,220,386,272,71,390,373,120,18,202,177,263,64,143,228,299,372,374,434,237,291,431,34,184,197,318,231,106,174,384,125,4,274,190,123,383,286,356,50,364,319,242,25,409,413,433,332,297,13,360,253,300,407,343,406,119,311,90,366,322,20,380,391,414,241,172,161,193,103,147,309,92,338,233,124,234,81,426,141,224,78,113,260,240,236,198,415,100,145,269,137,67,164,342,17,55,229,344,165,393,325,6,99,24,403,207,258,72,410,261,155,153,80,3,362,283,436,396,29,191,339,154,171,290,53,167,9,195,129,288,185,392,437,201,423,215,61,76,46,420,200,144,408,68,186,354,44,59,377,95,170,425,273,26,114,340,180,244,32,179,152,160,430,251,275,93,156,96,139,353,324,118,176,256,14,35,381,326,421,422,268,412,347,428,40,334,65,301,138,289,140,189,246,212,11,306,57,387,243,79,192,33,388,86,401,37,84,188,43,5,310,262,378,302,150,293,329,267,214,136,432,21,394,47,327,330,149,352,52,223,122,264,254,270,130,97,85,31,2,102,183,313,221,320,225,30,245,58,98,89,63,370,209,281,126,148,411,60,66,331,219,336,109,116,218,292,323,166,77,382,294,127,132,350,88,400,178,361,146,196,157,38,226","comment":"Linear magma over Z/439Z (the prime field F_439): x ◇ y = 267x + 124y (mod 439).","submitted_at":"2026-04-28 16:25:21","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/439/2ee0bc4caba7ae0b12f93c41d8b08fc7b3da0bc8574ca6c5549603e26530268b.txt"},{"canonical_hash":"701f39e2cea45c1c3a61b5144e604f8848011d30b760af68003b22ddfdfb125f","size":439,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"438,0,127,293,95,373,334,115,136,142,414,253,302,219,3,149,104,192,110,366,382,322,221,26,343,229,260,349,124,284,190,197,4,29,160,402,10,157,407,68,423,208,363,66,262,429,67,300,311,144,270,399,228,424,317,109,92,215,252,52,158,94,165,98,113,7,70,161,201,233,370,223,119,90,198,78,375,282,36,154,391,125,176,235,331,48,34,60,230,47,397,248,35,404,341,222,352,211,112,236,238,214,367,88,269,178,392,65,358,105,9,364,133,283,183,313,220,275,20,148,199,420,135,415,206,1,139,224,13,273,116,39,38,395,202,205,169,96,274,266,411,8,264,386,437,140,131,351,166,360,46,307,416,175,250,53,77,296,195,200,432,55,93,63,217,316,276,389,299,425,16,422,75,184,28,258,271,259,15,336,365,62,289,301,76,86,372,359,309,305,263,426,320,204,179,355,12,209,277,419,279,368,182,240,408,64,129,82,237,102,146,403,433,72,33,353,326,153,5,297,118,325,405,6,101,285,251,181,151,398,354,58,261,308,243,156,61,434,189,27,167,25,388,332,103,431,383,141,174,84,126,130,107,193,265,255,122,37,241,186,2,267,80,19,79,280,436,254,170,268,173,120,210,24,137,396,242,345,234,180,379,374,117,256,232,71,427,164,128,225,108,418,99,310,319,339,207,85,328,159,87,22,348,421,384,381,216,290,218,295,21,333,45,318,337,385,163,314,168,378,400,272,23,41,134,435,31,312,185,329,357,106,244,213,430,17,340,188,393,59,57,291,390,100,43,89,152,287,69,145,226,51,239,286,227,11,56,428,304,212,406,288,30,196,257,377,342,298,44,191,54,380,413,249,327,292,350,417,346,410,231,73,394,344,361,138,172,49,147,18,323,132,121,246,177,83,245,111,387,171,247,155,409,330,150,412,281,324,376,369,32,303,97,81,50,91,278,42,143,203,187,362,371,356,401,335,40,123,74,162,321,315,294,14,194,347,114,306,338","comment":"Linear magma over Z/439Z (the prime field F_439): x ◇ y = 171x + 137y (mod 439).","submitted_at":"2026-04-28 16:25:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/439/701f39e2cea45c1c3a61b5144e604f8848011d30b760af68003b22ddfdfb125f.txt"},{"canonical_hash":"f21daa02b4dcbe142b70e8cb35ae712b113c2791ca13c9932fcfe94490d27993","size":439,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"438,0,70,102,44,253,275,42,18,32,227,345,85,363,16,148,103,224,6,261,201,83,319,306,59,435,337,73,101,393,122,260,276,386,198,199,290,118,235,404,175,164,57,302,293,189,426,94,33,99,409,119,311,153,47,28,274,156,367,318,242,66,234,288,86,46,360,176,172,347,173,421,264,8,238,330,209,291,378,184,149,278,138,303,31,406,422,434,413,428,163,309,400,155,267,297,7,244,272,427,383,178,239,52,431,240,127,324,21,280,113,159,84,415,130,100,341,299,292,170,216,241,40,205,208,282,262,399,60,343,20,312,334,207,150,230,146,22,321,351,147,24,395,259,74,76,93,29,212,287,304,285,183,160,411,296,352,71,158,194,123,398,88,368,258,69,423,193,5,131,380,197,396,254,408,381,387,359,402,67,137,390,429,271,374,300,129,110,77,19,417,255,92,252,218,87,82,142,401,117,357,217,152,339,213,346,26,388,405,36,214,177,247,316,298,96,106,206,90,49,286,17,133,68,58,371,389,174,250,141,273,332,315,263,419,140,412,225,144,430,190,328,215,9,14,145,179,54,182,344,3,115,72,202,373,301,34,356,317,210,105,329,432,314,308,335,181,323,124,307,204,78,120,350,107,185,295,15,325,196,121,231,109,425,369,338,233,256,48,377,50,139,266,55,114,112,186,322,437,220,424,394,1,219,157,223,134,407,385,4,416,98,326,25,45,135,132,277,168,143,243,365,372,414,62,203,342,11,232,75,43,2,397,200,167,358,289,166,251,310,354,35,171,80,370,30,228,327,382,236,355,340,361,349,333,268,376,211,41,222,257,305,364,136,403,165,81,27,348,246,420,245,249,433,283,13,51,161,104,169,391,294,229,37,265,284,226,384,192,336,61,270,56,353,116,366,375,95,237,248,331,162,191,53,126,125,313,39,187,195,320,63,111,410,362,97,379,392,10,128,188,79,151,65,221,89,436,12,418,154,269,91,279,38,180,281,64,108,23","comment":"Linear magma over Z/439Z (the prime field F_439): x ◇ y = 267x + 143y (mod 439).","submitted_at":"2026-04-28 16:25:34","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/439/f21daa02b4dcbe142b70e8cb35ae712b113c2791ca13c9932fcfe94490d27993.txt"},{"canonical_hash":"731712672d9946b0193534b17dd0c18a9c4bfe01fc174ea4795962aaa582b9f2","size":441,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"336,75,63,260,278,69,272,57,266,364,201,189,258,252,195,246,183,240,338,273,261,70,64,267,58,279,76,339,59,71,268,262,53,280,65,274,340,281,269,54,72,275,66,263,60,341,67,55,276,270,61,264,73,282,337,265,277,62,56,259,74,271,68,366,203,5,45,40,1,35,209,50,367,36,46,335,6,51,210,41,204,368,2,331,52,47,205,42,7,37,369,43,33,206,332,38,8,48,3,370,101,207,104,103,102,106,333,105,371,49,39,4,208,44,334,34,0,372,309,321,92,86,327,80,315,98,373,81,93,328,322,99,316,87,310,374,317,329,100,94,311,88,323,82,375,89,77,312,330,83,324,95,318,376,325,313,84,78,319,96,307,90,377,97,85,320,314,91,308,79,326,342,107,119,232,226,125,220,113,214,343,221,233,126,120,215,114,227,108,344,115,127,216,234,109,228,121,222,345,229,217,110,128,223,122,211,116,346,123,111,224,218,117,212,129,230,347,213,225,118,112,231,130,219,124,348,149,137,294,288,143,306,131,300,349,283,295,144,138,301,132,289,150,350,133,145,302,296,151,290,139,284,351,291,303,152,146,285,140,297,134,352,141,153,286,304,135,298,147,292,353,299,287,136,154,293,148,305,142,354,167,155,26,20,161,14,173,32,355,15,27,162,156,9,174,21,168,356,175,163,10,28,169,22,157,16,357,23,11,170,164,17,158,29,176,358,159,171,18,12,177,30,165,24,359,31,19,178,172,25,166,13,160,360,185,197,242,236,179,254,191,248,361,255,243,180,198,249,192,237,186,362,193,181,250,244,187,238,199,256,363,239,251,188,182,257,200,245,194,365,247,235,196,190,241,184,253,202,426,380,384,385,383,379,381,382,378,427,404,403,408,405,406,409,402,407,428,417,411,412,413,415,414,410,416,429,389,388,387,393,391,390,386,392,430,395,401,400,396,397,394,399,398,431,423,418,425,419,420,424,422,421,440,432,437,439,438,436,434,435,433","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_9.","submitted_at":"2026-04-28 19:34:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/441/731712672d9946b0193534b17dd0c18a9c4bfe01fc174ea4795962aaa582b9f2.txt"},{"canonical_hash":"00430b478aac3fd65bf91fc54a971273bacd45abb71ff06400551a0c12e5439d","size":441,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,122,134,327,345,140,339,128,333,34,144,156,247,241,162,235,150,229,1,340,328,141,135,334,129,346,123,41,130,142,335,329,124,347,136,341,21,348,336,125,119,342,137,330,131,22,138,126,343,337,132,331,120,325,2,332,344,133,127,326,121,338,139,18,116,104,261,255,110,273,98,267,19,274,262,111,105,268,99,256,117,20,100,112,269,263,118,257,106,275,15,258,270,95,113,276,107,264,101,16,108,96,253,271,102,265,114,259,17,266,254,103,97,260,115,272,109,36,86,74,357,351,80,369,92,363,37,370,358,81,75,364,93,352,87,38,94,82,365,359,88,353,76,371,39,354,366,89,83,372,77,360,71,40,78,90,349,367,72,361,84,355,35,362,350,73,91,356,85,368,79,24,56,68,291,285,50,279,62,297,25,280,292,51,69,298,63,286,57,26,64,52,299,293,58,287,70,281,27,288,300,59,53,282,47,294,65,28,48,60,283,277,66,295,54,289,23,296,284,67,61,290,55,278,49,4,212,200,225,219,206,375,194,46,5,376,226,207,201,43,195,220,213,6,196,208,42,227,214,221,202,215,7,222,377,191,209,216,203,228,197,8,204,192,217,373,198,45,210,223,3,44,218,199,193,224,211,374,205,11,182,170,321,315,176,309,188,303,12,310,322,177,171,304,189,316,183,13,190,178,305,323,184,317,172,311,14,318,306,185,179,312,173,324,167,9,174,186,313,307,168,301,180,319,10,302,314,169,187,320,181,308,175,30,152,164,231,249,146,243,158,237,31,244,232,147,165,238,159,250,153,32,160,148,239,233,154,251,166,245,33,252,240,155,149,246,143,234,161,29,236,248,163,157,230,151,242,145,434,386,388,393,392,389,391,387,390,435,385,383,380,379,384,378,382,381,436,399,401,397,396,398,395,400,394,437,403,405,406,409,402,408,404,407,438,416,414,411,413,415,412,417,410,439,420,419,423,422,418,425,421,424,440,430,427,433,426,432,429,428,431","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 d50b3565) × F_9.","submitted_at":"2026-04-28 19:39:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/441/00430b478aac3fd65bf91fc54a971273bacd45abb71ff06400551a0c12e5439d.txt"},{"canonical_hash":"293cc60704aff77384de47d8252487ec6e191a3452e8c986d3b5075523df15f4","size":457,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"456,0,348,301,230,135,183,214,112,193,17,174,122,130,96,27,433,233,75,184,395,106,56,372,443,300,12,85,417,190,405,55,315,66,115,379,453,283,123,22,277,284,427,286,377,358,254,83,325,8,239,125,390,172,3,339,299,76,72,381,287,409,376,437,197,352,387,317,436,264,261,33,335,219,165,192,444,361,400,9,159,416,166,14,309,398,168,82,259,148,240,374,136,386,11,406,207,252,340,397,121,160,446,403,272,271,54,235,345,94,221,175,238,180,454,98,450,410,263,420,169,321,291,176,258,26,319,304,79,178,234,114,269,428,199,250,318,171,146,137,143,414,354,334,217,355,101,350,47,373,74,90,326,6,243,220,282,204,341,64,41,177,298,423,48,231,392,46,191,347,280,4,50,45,10,105,141,273,30,267,179,276,256,244,18,448,268,380,343,329,288,119,89,399,134,187,222,307,279,251,442,209,42,434,328,449,285,156,154,388,153,249,375,364,117,451,227,242,415,111,103,393,57,44,120,84,62,228,336,88,419,253,332,311,292,248,145,351,302,224,51,418,203,308,173,127,58,401,140,402,404,37,201,80,186,290,7,194,60,31,116,413,435,382,151,337,310,40,81,95,132,20,200,266,53,65,28,370,19,278,25,389,353,212,293,241,216,32,99,439,294,144,422,296,232,107,368,289,255,93,452,34,411,52,208,78,338,322,182,295,102,349,164,1,86,163,223,391,385,394,362,70,59,447,237,21,305,425,369,327,113,71,274,67,367,43,73,360,229,15,162,202,346,206,371,429,366,412,342,97,426,245,23,24,155,198,408,312,149,92,61,5,158,213,138,384,126,49,396,68,330,359,150,118,262,357,225,407,211,152,170,196,440,356,455,87,281,13,16,188,69,139,104,445,189,128,161,39,133,320,324,108,91,215,363,142,316,430,210,77,331,63,167,129,38,236,36,29,270,314,35,205,131,306,257,124,246,157,438,226,333,260,109,195,181,247,297,147,432,323,424,185,275,344,378,313,365,265,441,303,2,431,383,421,110,100,218","comment":"Linear magma over Z/457Z (the prime field F_457): x ◇ y = 323x + 356y (mod 457).","submitted_at":"2026-04-28 16:25:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/457/293cc60704aff77384de47d8252487ec6e191a3452e8c986d3b5075523df15f4.txt"},{"canonical_hash":"79f26199f3c867d0e69c87141318d0e959dceb95555e4b1767f57185e2d0a96d","size":457,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"456,0,3,438,40,121,435,62,37,335,118,301,432,285,59,246,34,391,332,2,115,364,298,231,429,334,282,55,56,74,243,194,31,198,388,275,329,280,41,182,112,156,361,136,295,143,228,75,426,393,331,21,279,93,52,19,53,436,71,255,240,203,191,84,28,48,195,11,385,128,272,186,326,36,277,54,38,227,179,47,109,357,153,262,358,199,133,376,292,105,140,211,225,91,72,119,423,248,390,95,328,213,18,263,276,172,90,371,454,79,16,177,50,241,433,444,68,307,252,317,237,61,200,281,188,142,81,27,25,261,45,17,192,60,8,268,382,217,125,101,269,377,183,450,323,287,33,23,274,107,51,29,35,413,224,407,176,339,44,218,106,157,354,401,150,411,259,170,355,434,196,333,130,294,373,83,289,152,102,212,137,236,208,100,222,43,88,151,69,386,116,348,420,303,245,395,387,378,92,144,325,403,210,405,15,369,260,253,273,299,169,164,87,311,368,349,451,120,76,428,13,135,174,190,452,356,238,327,430,316,441,124,65,338,304,288,249,394,455,367,234,337,58,77,197,201,278,283,185,159,139,146,78,396,24,96,22,439,258,206,42,6,14,131,189,39,57,230,5,360,265,202,379,108,214,94,122,251,98,216,266,175,374,82,180,244,447,310,320,64,284,145,30,264,20,63,271,220,104,380,453,290,26,110,32,416,410,342,221,160,404,414,173,437,336,297,86,155,215,239,103,46,154,389,351,306,398,381,147,406,408,372,256,302,167,314,352,123,431,138,193,359,330,319,127,341,291,397,370,340,80,204,286,162,149,399,99,442,209,9,134,4,233,363,205,111,97,254,219,178,85,247,313,67,148,267,66,223,383,293,113,419,345,163,417,440,300,158,242,49,392,309,384,409,375,305,89,126,141,362,322,344,400,343,207,165,402,445,12,1,366,114,257,181,250,70,270,226,296,422,166,443,161,7,312,412,308,129,365,347,346,168,448,315,117,184,73,229,425,446,10,415,132,350,171,318,187,232,449,418,353,321,235,421,324,424,427","comment":"Linear magma over Z/457Z (the prime field F_457): x ◇ y = 323x + 424y (mod 457).","submitted_at":"2026-04-28 16:25:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/457/79f26199f3c867d0e69c87141318d0e959dceb95555e4b1767f57185e2d0a96d.txt"},{"canonical_hash":"2e949be8964ad92aa07f91609b10f8f9e22fa5d2ece0376a0c9bef5174f20606","size":461,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,60,357,114,141,98,332,4,116,426,397,195,161,416,419,128,9,389,179,58,232,247,148,347,122,200,244,451,89,334,150,42,264,49,133,355,76,276,40,86,326,340,296,63,435,258,254,72,447,175,422,112,352,19,262,370,190,454,428,202,342,456,222,439,329,293,169,139,35,212,47,22,67,220,381,28,185,413,172,360,288,300,320,96,376,363,131,163,91,437,344,187,460,92,377,289,186,68,36,330,343,191,353,448,436,327,77,265,90,123,233,10,162,117,142,2,130,44,74,441,362,291,12,308,375,107,280,306,95,337,410,229,319,207,274,80,299,167,402,406,287,158,444,373,359,181,135,424,171,322,38,144,412,137,55,367,184,303,392,105,27,314,53,395,380,153,84,241,219,33,271,268,66,100,249,278,21,214,365,193,46,209,324,155,211,210,215,101,34,154,315,304,138,323,182,159,168,208,338,108,292,45,118,124,328,192,69,93,438,364,301,414,221,213,294,457,455,20,176,259,341,277,50,335,201,248,390,417,427,99,61,197,453,65,204,30,189,267,310,408,369,270,103,126,261,32,433,284,18,218,15,431,351,240,385,227,111,83,25,7,421,152,256,224,174,379,235,282,446,394,251,317,71,52,312,387,253,313,252,236,257,26,386,16,434,104,311,205,62,391,51,177,295,302,70,119,339,183,316,216,325,366,250,272,85,54,393,56,39,136,445,403,275,411,281,13,75,143,234,78,354,37,378,230,132,321,173,382,48,170,223,429,263,423,255,297,41,134,151,245,149,180,420,398,333,358,6,349,88,372,24,165,450,443,82,146,243,157,110,459,199,286,226,238,121,405,384,400,346,401,239,345,147,166,350,399,246,298,430,383,231,79,14,404,57,273,217,120,178,206,17,237,388,318,283,225,8,228,432,285,127,409,31,198,418,336,260,458,415,94,125,109,160,305,102,156,194,279,269,242,396,106,368,145,425,374,407,81,115,307,309,442,3,11,266,449,331,290,188,164,97,361,29,23,140,440,203,371,113,73,64,87,356,43,452,348,59,129,196,5","comment":"Linear magma over Z/461Z (the prime field F_461): x ◇ y = 369x + 93y (mod 461).","submitted_at":"2026-04-28 16:26:01","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/461/2e949be8964ad92aa07f91609b10f8f9e22fa5d2ece0376a0c9bef5174f20606.txt"},{"canonical_hash":"7ada576c98082776d002ed66b2a4e941a24c2a5d8a369a1453d756356706f082","size":461,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,288,145,426,140,180,28,212,326,210,414,242,148,173,129,156,46,114,216,394,208,69,40,363,88,209,256,354,61,49,266,240,105,198,270,123,80,233,333,85,404,157,171,359,346,118,269,221,142,339,158,215,258,154,235,6,144,415,447,445,190,408,391,349,112,304,81,444,72,284,188,433,358,181,320,392,77,353,456,57,450,389,241,133,163,126,67,22,162,2,151,416,110,71,292,107,368,361,257,237,134,306,342,79,185,24,314,259,207,460,92,374,429,139,70,194,457,421,19,352,372,246,253,222,407,186,225,301,36,117,47,137,182,11,48,18,356,274,335,172,341,238,192,277,435,66,243,318,73,399,187,329,196,419,227,234,276,293,75,330,332,300,29,121,350,39,373,100,43,454,27,106,384,3,231,244,56,42,289,200,448,348,195,8,385,83,220,355,381,164,176,239,371,94,203,248,155,184,93,279,101,229,161,41,14,58,33,357,299,95,441,97,143,65,25,311,30,403,116,115,63,321,87,138,160,382,410,325,360,219,135,309,294,388,26,149,459,285,303,226,337,9,401,338,334,324,108,54,197,252,96,213,16,113,313,247,412,290,287,150,199,365,152,272,319,120,15,146,366,446,317,458,167,4,170,136,62,376,127,255,193,13,280,437,413,236,380,375,263,44,132,383,364,281,451,443,275,323,204,296,214,340,218,315,51,122,406,64,217,377,393,206,183,379,165,425,109,347,316,307,423,76,38,312,174,168,189,398,302,397,386,345,10,86,205,369,60,420,32,442,327,147,305,175,254,90,201,125,230,271,282,417,283,74,53,59,427,153,191,308,422,431,232,224,310,50,264,68,91,278,262,102,179,291,7,166,430,103,455,99,411,89,438,390,328,336,396,249,268,17,159,378,260,265,351,298,322,395,128,78,370,12,261,177,21,55,119,52,343,432,331,251,31,130,5,434,387,37,250,84,35,402,405,297,362,428,228,131,98,211,367,82,169,223,439,449,453,286,124,452,111,418,400,344,34,141,273,409,424,20,104,245,440,295,267,45,23,202,436,178","comment":"Linear magma over Z/461Z (the prime field F_461): x ◇ y = 352x + 110y (mod 461).","submitted_at":"2026-04-28 16:26:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/461/7ada576c98082776d002ed66b2a4e941a24c2a5d8a369a1453d756356706f082.txt"},{"canonical_hash":"f72da3b421ace63004f059872bdc97bb858119c1a3fc5db997e8ba35d222970e","size":461,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,432,381,161,431,323,246,223,428,380,89,278,188,201,160,4,172,303,154,430,388,398,30,38,322,447,19,260,99,245,150,147,402,386,222,11,343,121,32,427,213,41,251,84,379,414,192,425,237,88,106,94,7,369,277,116,280,230,396,187,165,394,411,226,200,48,52,195,358,159,219,135,211,140,3,449,108,451,35,171,284,62,454,28,302,132,185,24,290,153,331,176,318,162,429,202,155,39,100,387,33,85,238,370,397,227,359,141,36,29,291,163,101,371,37,372,182,257,181,321,353,71,249,256,446,169,417,207,180,18,305,253,197,320,259,345,392,124,352,98,366,111,458,70,244,375,437,82,248,149,282,64,361,255,146,328,144,338,445,401,440,409,349,168,385,272,268,390,416,221,204,355,377,206,10,60,421,57,179,342,314,326,308,17,120,382,224,189,304,31,261,403,122,252,426,8,231,412,196,212,452,455,25,319,40,239,142,102,258,250,208,198,125,459,83,362,339,350,391,378,58,309,190,123,413,26,103,126,351,191,127,336,335,97,424,75,46,334,365,236,434,21,96,110,87,419,66,423,457,105,300,298,74,69,93,14,443,45,243,6,215,50,333,374,368,274,263,364,436,276,55,406,235,81,115,130,296,433,247,279,173,399,20,148,344,42,193,95,281,395,53,136,109,63,186,177,156,86,360,164,183,72,418,254,393,112,438,65,145,410,269,356,422,327,225,404,232,456,143,199,340,310,104,337,47,22,67,299,444,51,264,407,297,400,194,137,157,73,439,357,233,311,68,408,158,312,460,92,348,218,288,91,13,167,134,293,347,442,384,210,77,217,44,271,139,79,287,242,267,2,324,90,5,389,448,151,12,214,415,107,117,166,49,220,450,285,133,332,203,34,228,292,373,354,170,306,346,367,376,283,329,441,273,205,61,315,383,262,9,453,240,209,363,59,27,128,76,435,420,301,15,216,275,56,131,174,43,54,178,184,113,270,405,341,23,265,138,234,313,289,294,78,80,325,152,118,286,229,307,330,316,241,129,16,175,114,266,295,119,317","comment":"Linear magma over Z/461Z (the prime field F_461): x ◇ y = 115x + 347y (mod 461).","submitted_at":"2026-04-28 16:26:11","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/461/f72da3b421ace63004f059872bdc97bb858119c1a3fc5db997e8ba35d222970e.txt"},{"canonical_hash":"067e77fa1d3d32114ff3b563112ffa4ef4ffe720e7717ed9e161752e2bfadb1f","size":461,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,316,193,45,23,133,60,196,171,348,336,49,294,97,51,19,209,394,214,302,208,69,201,404,87,46,114,373,355,270,305,35,89,346,331,287,118,195,266,230,432,88,328,55,254,237,371,361,16,100,197,243,188,121,108,21,442,238,403,235,278,104,15,310,152,263,356,74,199,8,449,299,308,357,167,50,124,228,62,459,127,430,101,151,455,428,312,319,325,320,392,90,132,282,401,364,304,342,450,452,20,379,30,285,126,260,143,122,259,110,217,368,292,68,91,416,119,370,155,338,399,298,322,168,176,303,220,76,5,297,293,388,239,290,194,178,159,406,14,365,32,433,318,147,250,129,291,44,63,79,405,354,273,408,412,120,191,105,418,61,53,437,413,284,453,40,255,4,301,206,183,407,253,102,225,374,7,28,375,11,400,145,264,135,337,335,457,419,249,286,397,17,205,277,435,440,434,427,313,340,36,216,315,12,344,177,113,9,165,52,242,423,414,334,123,84,189,241,378,37,425,130,219,393,350,288,353,327,136,223,6,73,358,82,215,131,246,256,352,369,170,443,203,317,345,381,80,3,402,446,231,204,150,420,385,240,258,229,161,202,289,86,184,93,417,99,279,94,134,166,212,409,164,451,233,56,81,175,18,138,160,78,431,116,115,224,262,226,25,339,391,153,95,349,415,59,106,445,31,34,362,232,39,441,157,33,396,429,26,306,83,142,376,66,169,387,200,410,98,190,360,438,390,144,307,244,386,112,341,173,251,72,321,96,332,257,43,265,383,77,252,309,57,395,426,324,41,71,218,67,22,162,2,13,269,64,163,283,107,267,444,248,458,180,389,333,125,139,70,351,296,207,460,92,411,236,185,24,10,448,274,65,343,363,329,382,222,398,48,179,384,128,117,47,137,182,103,186,156,439,311,280,172,424,367,192,268,380,158,372,447,211,436,187,366,58,456,227,271,359,422,29,275,323,245,75,213,295,85,272,54,181,261,27,198,421,141,314,281,148,42,326,154,347,247,149,146,330,221,174,300,234,210,38,276,454,140,111,377,109","comment":"Linear magma over Z/461Z (the prime field F_461): x ◇ y = 89x + 373y (mod 461).","submitted_at":"2026-04-28 16:26:19","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/461/067e77fa1d3d32114ff3b563112ffa4ef4ffe720e7717ed9e161752e2bfadb1f.txt"},{"canonical_hash":"6d15413e6a0b041925ee96974b78af40c2e01ae5f973f0f629d7a69980b8cca1","size":463,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"462,0,148,203,77,243,363,334,413,418,172,224,292,362,263,458,166,158,6,189,332,142,384,178,221,91,291,226,192,448,46,85,95,439,87,17,100,204,349,5,261,375,71,2,313,266,338,150,381,449,427,373,220,240,386,72,352,404,36,400,140,73,421,357,431,45,27,424,423,52,111,379,436,442,364,306,278,163,99,80,190,441,304,214,407,182,96,256,242,411,195,70,267,300,79,444,310,129,37,247,15,223,302,31,380,397,169,181,315,456,408,419,281,454,157,433,130,385,153,273,69,460,409,18,9,346,286,177,19,382,139,50,121,128,12,74,11,324,146,211,447,365,308,26,24,296,30,257,293,446,235,276,207,16,92,340,435,198,416,455,350,117,29,76,233,287,374,134,160,98,342,212,432,137,185,206,171,208,164,149,355,41,406,288,196,459,229,394,415,165,32,193,239,322,58,194,131,376,176,369,109,232,383,387,231,399,125,201,309,425,326,127,329,22,341,191,244,200,44,250,161,301,7,317,210,114,42,170,86,402,21,378,59,274,314,174,82,295,202,122,405,260,48,249,162,297,112,156,103,429,275,417,215,414,337,461,113,213,311,143,68,64,144,197,457,88,57,219,106,377,410,151,105,285,253,327,75,141,371,108,35,318,294,443,237,252,120,83,118,97,225,344,124,430,186,248,222,55,34,145,395,282,205,438,367,328,110,347,428,180,269,119,23,147,358,40,4,283,43,277,279,1,453,359,123,234,412,264,393,265,216,209,303,227,63,272,89,33,434,262,271,321,372,388,20,241,66,218,345,245,366,28,331,320,368,403,93,81,78,61,284,49,135,268,159,290,217,398,356,167,47,14,389,107,323,154,3,184,94,319,126,51,353,102,168,187,251,25,53,452,354,348,60,199,305,335,336,280,298,343,445,333,392,228,312,289,316,440,391,67,152,132,54,339,361,62,238,426,13,401,255,390,56,8,258,437,116,188,270,175,351,183,173,299,360,104,138,38,179,133,90,65,230,420,101,259,246,254,370,10,450,39,136,84,330,325,422,451,155,396,115,236,307","comment":"Linear magma over Z/463Z (the prime field F_463): x ◇ y = 21x + 187y (mod 463).","submitted_at":"2026-04-28 16:26:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/463/6d15413e6a0b041925ee96974b78af40c2e01ae5f973f0f629d7a69980b8cca1.txt"},{"canonical_hash":"c18ea07eb2a9b214474a793ed2b6009e8c59185c5e00e52ac7d5248831c7642b","size":463,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"462,0,60,277,80,282,297,380,100,26,302,424,317,268,400,21,120,119,6,333,322,117,444,245,337,16,288,251,420,191,1,81,140,161,139,122,54,306,353,35,342,414,137,149,233,256,265,118,357,220,44,356,308,426,271,166,440,70,211,185,59,195,101,354,160,30,181,188,159,213,142,299,74,23,326,261,373,7,15,167,362,219,434,365,157,361,169,428,253,42,276,108,285,318,138,75,377,202,31,398,64,395,376,66,328,359,446,332,291,192,186,43,460,134,90,218,38,242,205,459,79,77,215,151,121,266,374,447,180,386,10,155,201,173,208,224,179,321,40,278,162,355,319,152,94,433,3,457,346,133,281,315,393,93,53,323,45,363,187,163,382,85,32,51,454,403,385,116,177,227,381,307,189,203,448,364,273,422,62,89,296,125,128,432,305,48,338,272,158,91,95,449,397,263,222,247,11,443,418,240,84,425,415,300,396,156,86,450,348,217,379,144,235,4,352,391,311,421,212,254,206,347,63,349,249,229,154,244,110,28,33,270,20,257,262,360,225,404,248,37,99,313,97,456,36,231,171,61,141,102,286,216,394,129,236,98,200,336,406,146,50,165,175,334,221,168,193,279,228,241,27,147,199,345,341,408,18,88,298,55,182,378,375,46,339,312,172,17,114,198,453,439,57,131,246,427,366,135,153,204,301,258,335,132,413,437,113,295,73,303,343,143,65,9,383,96,207,287,183,344,402,69,105,412,12,252,71,429,243,458,423,451,405,280,136,430,197,124,24,371,401,234,327,329,209,455,223,250,237,340,384,210,293,436,442,461,82,196,109,78,316,126,145,314,148,259,452,127,325,388,68,5,358,14,292,41,178,419,111,407,115,184,238,112,417,275,283,123,29,76,267,324,49,392,232,409,438,431,260,410,104,351,445,309,435,230,320,190,416,19,176,58,106,294,239,107,368,25,34,214,399,387,164,92,255,103,56,304,372,389,411,390,331,289,441,170,39,2,274,87,226,194,367,72,83,284,369,370,269,150,22,67,174,52,264,350,130,47,8,330,13,310,290","comment":"Linear magma over Z/463Z (the prime field F_463): x ◇ y = 21x + 297y (mod 463).","submitted_at":"2026-04-28 16:26:33","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/463/c18ea07eb2a9b214474a793ed2b6009e8c59185c5e00e52ac7d5248831c7642b.txt"},{"canonical_hash":"8b267e69c04289946687bbc5923fdfb4d6229fe69d2d30e9a3bc61531b15d994","size":475,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"450,4,109,181,53,65,17,41,157,77,169,413,121,97,145,133,89,29,193,451,10,114,186,59,71,23,47,162,83,174,419,126,102,150,138,95,35,198,468,340,266,230,386,400,352,376,206,316,218,423,278,254,302,290,328,364,242,463,341,267,231,387,401,353,377,207,317,219,424,279,255,303,291,329,365,243,459,8,108,180,57,69,21,45,156,81,168,417,120,96,144,132,93,33,192,453,5,111,183,54,66,18,42,159,78,171,414,123,99,147,135,90,30,195,454,2,116,188,50,62,14,38,164,74,176,410,128,104,152,140,86,26,200,458,11,118,190,52,64,16,40,166,76,178,412,130,106,154,142,88,28,202,465,347,270,234,395,407,359,383,210,323,222,431,282,258,306,294,335,371,246,469,337,271,235,392,397,348,374,211,313,223,421,283,259,307,295,325,362,247,457,7,113,185,56,68,20,44,161,80,173,416,125,101,149,137,92,32,197,474,438,447,444,433,434,439,432,443,436,449,435,448,446,442,441,437,440,445,455,6,112,184,55,67,19,43,160,79,172,415,124,100,148,136,91,31,196,470,344,272,236,393,404,356,380,212,320,224,425,284,260,308,296,332,368,248,464,339,264,229,385,399,351,372,205,315,217,428,276,252,301,288,327,360,240,471,346,274,238,394,406,358,382,214,322,226,427,286,262,310,298,334,370,250,472,343,275,239,389,403,355,379,215,319,227,430,287,263,311,299,331,367,251,462,336,265,228,391,396,349,373,204,312,216,420,277,253,300,289,324,361,241,466,342,268,232,388,402,354,378,208,318,220,429,280,256,304,292,330,366,244,452,0,115,187,49,60,12,36,163,72,175,408,127,103,151,139,84,24,199,461,9,110,182,58,70,22,46,158,82,170,418,122,98,146,134,94,34,194,467,338,269,233,384,398,350,375,209,314,221,422,281,257,305,293,326,363,245,460,1,119,191,48,61,13,37,167,73,179,409,131,107,155,143,85,25,203,456,3,117,189,51,63,15,39,165,75,177,411,129,105,153,141,87,27,201,473,345,273,237,390,405,357,381,213,321,225,426,285,261,309,297,333,369,249","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_19(7,3).","submitted_at":"2026-04-28 19:33:01","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/475/8b267e69c04289946687bbc5923fdfb4d6229fe69d2d30e9a3bc61531b15d994.txt"},{"canonical_hash":"35187eca3cd2e91b2139b09b58cde0f1471416d5fe41d9c61b9eea093ac6f272","size":475,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"450,0,216,360,25,194,168,72,240,96,408,145,384,264,288,336,49,121,312,451,10,227,371,35,203,179,83,251,107,419,155,395,275,299,347,59,131,323,468,15,231,375,39,207,183,87,255,111,423,159,399,279,303,351,63,135,327,466,13,229,372,37,205,181,85,252,109,421,157,396,276,300,348,61,133,324,459,7,224,368,32,200,176,80,248,104,416,152,392,272,296,344,56,128,320,453,1,217,361,26,192,170,74,241,98,409,146,385,265,289,337,50,122,313,454,2,219,363,27,195,171,75,243,99,411,147,387,267,291,339,51,123,315,458,6,223,367,31,199,175,79,247,103,415,151,391,271,295,343,55,127,319,474,17,233,377,41,209,185,89,257,113,425,161,401,281,305,353,65,137,329,470,18,234,378,42,210,186,90,258,114,426,162,402,282,306,354,66,138,330,457,5,222,366,30,198,174,78,246,102,414,150,390,270,294,342,54,126,318,462,434,443,440,435,433,449,437,444,438,442,432,441,445,446,448,436,439,447,455,3,220,364,28,196,172,76,244,100,412,148,388,268,292,340,52,124,316,464,23,239,383,47,215,191,95,263,119,431,167,407,287,311,359,71,143,335,472,14,230,374,38,206,182,86,254,110,422,158,398,278,302,350,62,134,326,465,21,237,381,45,213,189,93,261,117,429,165,405,285,309,357,69,141,333,471,22,238,382,46,214,190,94,262,118,430,166,406,286,310,358,70,142,334,467,12,228,373,36,204,180,84,253,108,420,156,397,277,301,349,60,132,325,473,19,235,379,43,211,187,91,259,115,427,163,403,283,307,355,67,139,331,452,11,218,362,24,193,169,73,242,97,410,144,386,266,290,338,48,120,314,461,9,226,370,34,202,178,82,250,106,418,154,394,274,298,346,58,130,322,469,16,232,376,40,208,184,88,256,112,424,160,400,280,304,352,64,136,328,460,8,225,369,33,201,177,81,249,105,417,153,393,273,297,345,57,129,321,456,4,221,365,29,197,173,77,245,101,413,149,389,269,293,341,53,125,317,463,20,236,380,44,212,188,92,260,116,428,164,404,284,308,356,68,140,332","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-25 d732efd1) × F_19(7,4).","submitted_at":"2026-04-28 19:33:25","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/475/35187eca3cd2e91b2139b09b58cde0f1471416d5fe41d9c61b9eea093ac6f272.txt"},{"canonical_hash":"c9fa3b2ec4b7343b240e24f9e614febaa185c6e0436027e3f9b78208c16bfe56","size":487,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"486,0,324,465,328,111,469,33,332,140,115,283,473,155,37,256,336,1,144,210,119,178,287,259,477,356,159,285,41,470,260,124,340,412,323,294,148,407,214,300,123,428,182,3,291,385,263,313,481,216,360,464,163,68,289,58,45,339,474,471,264,11,128,10,344,400,416,204,327,388,298,402,152,310,411,31,218,450,304,249,127,414,432,134,186,110,485,145,295,164,389,322,267,269,317,455,15,9,220,87,364,353,468,266,167,423,72,236,293,229,62,82,49,43,343,34,478,429,475,32,268,230,7,103,132,147,14,170,348,462,404,399,420,377,208,60,331,316,392,380,302,442,406,102,156,261,314,345,415,221,35,421,222,139,454,369,308,434,253,213,131,426,418,195,436,203,138,362,190,444,114,484,325,211,149,69,299,146,168,231,393,370,326,453,271,198,273,282,321,452,459,192,19,122,13,75,224,22,91,387,368,333,357,183,472,219,270,63,171,157,427,169,76,77,240,108,297,307,233,439,66,154,86,197,53,176,47,181,347,239,38,125,482,401,433,88,479,378,36,363,272,334,234,89,4,461,107,29,136,279,151,252,5,206,174,255,352,281,466,120,408,290,403,296,424,8,381,309,212,460,64,54,335,467,320,319,396,200,384,398,306,27,446,245,410,130,106,141,160,2,265,451,318,83,349,262,419,232,225,78,39,30,425,28,226,99,143,166,458,395,373,56,312,376,438,98,257,341,217,417,135,365,430,209,422,191,199,358,440,480,207,65,142,227,366,449,194,278,448,188,118,71,18,383,329,179,215,59,153,165,73,104,303,435,150,193,172,177,235,121,397,84,374,359,330,85,457,25,275,248,202,251,277,116,286,292,12,305,456,50,463,315,196,394,23,241,126,137,6,447,79,258,228,74,26,24,95,162,391,52,372,94,337,413,361,205,187,354,476,61,223,445,274,184,67,379,175,55,161,100,431,189,173,117,80,355,81,21,244,247,112,288,301,46,311,390,237,133,443,254,70,20,158,48,90,409,201,350,57,441,180,375,51,96,185,113,351,17,243,284,42,386,129,250,16,44,405,346,437,371,92,109,483,280,382,246,40,342,367,105,276,242,338,101,238,97,93","comment":"Linear magma over Z/487Z (the prime field F_487): x ◇ y = 254x + 66y (mod 487).","submitted_at":"2026-04-28 16:26:39","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/487/c9fa3b2ec4b7343b240e24f9e614febaa185c6e0436027e3f9b78208c16bfe56.txt"},{"canonical_hash":"cb0f1d63c062cd7fa3a0d26184513d60742779d7c7805d5ac1457e13458195af","size":487,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"486,0,363,436,318,14,221,44,103,294,418,332,24,313,466,339,355,201,97,75,203,369,269,366,428,69,98,152,233,131,276,365,292,190,156,99,331,28,479,19,158,119,306,84,72,179,321,370,213,129,473,77,350,244,404,387,36,382,383,356,79,137,320,227,95,198,127,155,408,224,351,333,286,325,432,394,264,417,423,60,410,477,371,222,109,256,336,456,476,260,134,246,106,223,307,2,150,469,381,48,258,42,481,196,287,424,29,310,189,328,172,353,440,368,167,421,168,326,293,304,483,238,389,444,105,124,12,162,329,409,153,458,379,160,407,55,193,397,9,35,288,228,270,67,71,34,280,454,217,291,161,289,49,384,202,420,208,39,464,102,195,451,262,56,308,245,25,141,343,345,59,240,273,434,241,154,261,214,45,148,386,178,31,462,358,83,8,4,110,85,364,11,402,248,254,74,166,447,452,484,61,480,446,64,266,22,133,82,90,448,209,422,433,191,113,139,126,450,283,183,6,403,290,173,225,234,305,396,122,185,206,275,123,5,281,425,96,367,89,348,268,220,41,165,174,32,229,259,357,80,376,87,416,272,117,1,284,197,194,3,405,314,243,216,164,299,412,118,192,274,459,135,130,104,182,442,413,200,439,81,91,142,13,257,73,437,471,52,475,461,438,175,65,263,239,411,20,373,94,101,116,17,92,349,453,40,169,377,157,54,205,252,145,250,443,282,249,50,354,352,132,16,236,317,47,253,460,186,111,455,30,199,429,211,393,58,298,170,300,226,463,271,43,62,76,279,219,297,26,18,406,184,46,398,151,388,449,144,400,338,171,21,485,114,435,380,247,474,295,302,335,177,430,176,359,431,344,163,337,180,319,38,415,296,187,472,33,267,57,390,478,159,121,316,232,115,237,125,251,467,465,327,265,100,231,362,468,401,51,414,426,255,385,441,334,277,324,342,215,399,146,136,207,86,218,311,128,70,347,392,391,27,378,395,235,341,68,482,138,204,361,312,188,63,93,315,7,149,10,470,37,340,108,147,181,301,374,285,140,242,143,107,78,419,375,278,360,212,66,88,210,346,330,457,322,15,323,427,303,112,53,230,23,309,445,372,120","comment":"Linear magma over Z/487Z (the prime field F_487): x ◇ y = 254x + 188y (mod 487).","submitted_at":"2026-04-28 16:26:49","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/487/cb0f1d63c062cd7fa3a0d26184513d60742779d7c7805d5ac1457e13458195af.txt"},{"canonical_hash":"3c947b3664dfab31c609e8aa9bbfa43bfe42934fd65bb9f6c8f8a361956873bd","size":491,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,403,288,305,231,166,132,244,299,309,440,158,252,6,75,356,248,34,189,102,78,43,179,134,345,29,281,58,297,352,414,60,66,118,448,99,48,145,268,375,173,388,185,182,406,395,168,235,373,246,38,323,12,418,283,39,186,449,282,190,441,289,237,317,385,326,417,312,341,233,343,401,382,428,11,24,465,31,273,127,204,54,322,85,473,170,198,207,193,271,37,64,307,314,410,337,368,453,245,152,347,195,218,89,435,478,372,114,397,490,196,315,171,32,234,290,419,396,146,353,44,7,167,136,209,113,106,265,483,70,394,408,399,371,27,286,121,255,405,328,72,477,19,470,457,227,181,200,142,434,140,111,216,125,184,116,438,88,240,391,81,3,387,485,82,217,458,122,484,45,172,436,369,194,205,383,386,187,374,174,67,346,249,300,2,319,267,261,213,151,96,259,80,475,144,335,380,489,279,303,390,480,47,155,276,452,51,359,239,108,98,445,333,367,432,104,87,202,447,446,156,336,262,175,437,486,117,201,329,409,137,291,115,153,65,86,25,313,191,324,183,100,59,103,159,306,377,91,124,293,413,431,15,63,443,211,215,17,351,366,426,36,56,229,110,223,296,332,362,270,220,460,139,221,57,444,378,192,138,263,433,52,280,97,250,206,459,241,141,20,28,107,147,197,219,411,199,274,344,238,284,169,269,415,180,76,133,358,129,472,361,462,226,162,178,50,349,84,331,149,456,468,42,451,9,321,295,164,469,163,77,275,21,53,222,224,18,294,101,154,487,203,109,481,476,320,188,46,4,126,228,256,71,8,33,479,454,272,55,429,327,450,247,389,119,30,35,310,404,41,355,302,93,464,425,423,254,467,74,278,364,23,365,94,120,455,5,488,22,10,350,130,285,148,251,379,363,427,16,160,26,330,157,334,277,381,214,68,370,83,439,143,73,400,210,420,398,348,308,474,466,342,442,13,407,49,298,79,253,232,62,339,393,177,243,258,422,340,14,421,69,161,131,95,424,311,430,257,482,225,165,150,463,416,412,242,264,461,230,212,92,325,292,176,105,360,304,260,301,384,123,392,112,471,287,266,354,316,90,338,208,128,402,318,40,236,376,61,135,357","comment":"Linear magma over Z/491Z (the prime field F_491): x ◇ y = 382x + 110y (mod 491).","submitted_at":"2026-04-28 16:26:54","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/491/3c947b3664dfab31c609e8aa9bbfa43bfe42934fd65bb9f6c8f8a361956873bd.txt"},{"canonical_hash":"75f709b077205447b4e176dd1449648308b3cfd80a7b8c42dffbc64f0bb328f9","size":491,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,460,291,356,36,303,151,166,198,41,269,155,280,417,470,84,114,52,463,37,65,189,209,412,472,242,81,177,279,346,133,377,162,376,6,415,399,314,42,135,93,235,47,13,318,299,476,367,159,327,43,277,302,451,478,68,289,471,352,254,217,184,12,89,392,244,141,11,435,14,324,456,50,343,333,55,38,439,484,72,237,51,260,350,486,118,398,360,160,395,20,67,138,149,339,473,332,424,78,341,440,148,2,31,365,268,401,452,406,187,345,28,402,171,347,158,221,86,371,261,10,304,193,409,202,397,353,106,129,355,267,29,379,7,208,201,437,309,361,234,270,275,214,271,216,90,240,369,62,71,222,488,136,248,77,306,230,139,83,85,109,421,91,5,436,99,442,468,450,305,311,319,180,49,490,294,425,74,66,60,205,223,197,344,191,250,336,176,354,330,328,384,475,61,322,3,381,243,467,316,307,124,485,335,461,26,459,30,25,479,116,64,192,446,453,252,134,274,22,110,374,351,108,152,447,164,438,59,255,16,126,331,466,403,102,416,157,273,100,432,161,207,156,23,120,276,247,393,195,96,323,179,87,228,94,394,383,312,265,150,405,115,153,363,241,105,15,296,482,317,239,194,283,300,88,98,295,211,79,259,190,256,386,489,147,334,257,429,462,9,107,226,44,313,233,206,57,32,288,82,404,122,231,54,73,258,292,480,338,380,287,69,154,170,251,131,407,132,378,101,34,422,326,487,227,167,454,434,310,282,218,297,359,329,225,172,35,400,24,286,443,411,396,58,281,111,46,215,246,245,284,183,4,104,372,168,236,196,146,320,427,340,123,53,448,113,370,373,325,212,414,308,431,410,219,477,229,264,426,18,342,293,210,17,390,137,321,56,387,40,27,445,130,173,278,266,465,224,388,366,70,178,103,144,140,449,238,430,357,117,175,8,444,290,364,458,337,174,188,408,163,433,419,92,213,119,45,199,253,420,362,112,185,483,204,385,389,348,423,315,121,143,469,220,21,33,418,375,200,272,285,142,301,76,382,145,262,455,48,97,263,181,19,474,232,464,165,186,63,169,457,80,128,125,358,203,298,368,95,182,75,391,441,481,413,127,349,249,428,39","comment":"Linear magma over Z/491Z (the prime field F_491): x ◇ y = 317x + 175y (mod 491).","submitted_at":"2026-04-28 16:26:59","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/491/75f709b077205447b4e176dd1449648308b3cfd80a7b8c42dffbc64f0bb328f9.txt"},{"canonical_hash":"00e1ed8c55af6dc18e9015af6bd016b7f18a7f302e50a9d666eff344eb5bb362","size":491,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,158,323,187,82,54,413,92,157,77,281,367,469,406,112,166,244,322,234,472,15,402,384,59,170,341,186,319,124,42,314,193,331,259,152,81,436,28,288,463,424,26,163,438,53,445,191,210,427,195,295,339,284,412,488,188,470,403,315,464,428,404,91,66,240,389,90,197,267,215,50,156,364,369,274,65,483,270,221,415,76,291,128,62,239,160,130,74,394,280,180,356,272,388,144,22,344,265,366,249,421,310,89,117,199,458,347,468,245,10,93,196,342,153,439,285,405,51,416,395,266,348,286,103,102,111,86,329,212,214,433,228,184,101,165,105,36,13,49,98,30,418,110,243,255,149,333,155,456,475,380,85,321,247,225,205,363,352,386,119,328,233,46,72,324,368,16,43,289,211,471,390,275,63,273,311,94,396,213,14,334,206,325,64,326,375,141,432,401,223,121,374,482,337,454,371,227,383,443,108,140,269,477,461,34,183,58,68,257,431,220,448,360,317,100,169,177,4,400,414,167,171,260,164,340,429,216,222,75,345,459,440,104,185,419,381,120,290,397,142,372,35,318,261,392,373,127,305,409,126,12,123,135,174,481,61,201,377,304,97,41,236,251,336,238,231,302,408,146,313,203,133,453,159,282,473,125,29,192,189,241,370,129,357,422,11,417,330,37,150,226,73,276,207,122,109,258,5,217,382,393,175,252,134,242,151,218,490,442,279,466,32,173,254,80,308,441,107,179,7,20,480,148,435,450,278,139,355,55,113,60,332,27,296,465,268,271,131,23,200,154,287,229,31,476,387,44,95,376,455,462,361,172,460,143,410,378,303,474,423,208,253,33,21,114,24,96,379,25,299,79,182,343,137,298,40,84,162,18,307,57,264,2,78,235,320,437,446,489,67,365,292,181,250,246,52,87,106,256,248,47,391,335,224,444,69,178,430,420,262,136,237,204,190,38,6,219,309,451,297,230,362,209,300,19,447,88,70,39,301,351,426,350,479,359,116,486,83,407,385,194,425,147,316,198,484,161,145,118,294,349,434,99,457,353,17,312,327,338,478,449,168,346,398,306,202,232,283,358,277,176,467,8,56,132,45,411,115,138,3,293,48,263,452,71,487,485,354,399,9","comment":"Linear magma over Z/491Z (the prime field F_491): x ◇ y = 184x + 308y (mod 491).","submitted_at":"2026-04-28 16:27:04","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/491/00e1ed8c55af6dc18e9015af6bd016b7f18a7f302e50a9d666eff344eb5bb362.txt"},{"canonical_hash":"142c970b7c245a0c1c10a0134d292e444c2334418cbb183779acd982b78a876b","size":491,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,309,373,63,386,354,484,293,147,138,257,233,462,303,107,324,338,215,135,304,57,32,190,82,208,122,329,348,465,160,292,186,240,86,287,363,448,366,349,229,407,132,280,199,328,422,424,487,227,167,258,238,16,282,120,297,163,133,421,172,231,106,318,384,345,19,4,450,379,209,144,411,344,441,88,85,298,398,372,70,334,294,244,26,427,46,25,445,350,15,76,275,31,212,218,210,39,116,23,477,33,68,34,410,342,195,406,17,96,137,419,154,387,236,27,151,326,75,180,364,171,28,290,464,266,80,5,438,336,253,140,136,357,117,371,400,248,486,168,360,337,468,90,310,65,335,223,92,115,413,241,3,155,126,362,112,381,385,8,91,193,250,325,21,219,45,273,416,119,425,320,81,396,272,481,142,399,174,382,341,262,161,440,97,165,279,313,278,232,268,361,284,455,463,457,276,30,321,260,105,200,270,291,182,271,489,49,89,315,127,153,53,330,333,196,99,166,389,454,134,205,249,264,100,139,73,351,476,417,176,378,408,52,365,37,261,483,13,412,472,242,179,177,83,444,35,377,162,474,104,121,203,118,42,331,485,431,47,405,220,103,84,367,453,327,435,277,302,59,380,460,93,79,352,58,217,478,12,383,392,48,239,109,141,308,128,64,246,245,235,251,430,243,288,72,237,149,456,56,94,20,300,66,356,101,216,67,40,443,143,375,332,228,470,439,146,50,2,129,71,170,9,452,14,187,51,420,402,269,347,60,319,184,469,359,206,108,95,213,202,397,255,204,423,61,267,323,183,7,110,299,437,113,459,38,466,471,18,369,314,286,436,173,62,169,222,390,234,150,77,404,426,433,475,281,403,29,189,201,44,393,442,370,156,11,409,123,376,343,490,98,131,368,164,256,401,125,197,148,289,446,434,274,158,36,230,188,181,159,322,395,479,145,467,414,307,418,191,41,69,124,263,226,221,283,214,358,192,54,355,252,428,78,22,306,178,449,10,152,447,458,340,353,451,114,224,429,74,305,102,24,157,175,296,432,259,207,254,415,316,374,247,295,391,194,225,473,87,130,388,198,285,312,461,346,111,311,55,265,339,301,211,394,482,317,43,488,185,6,480","comment":"Linear magma over Z/491Z (the prime field F_491): x ◇ y = 102x + 390y (mod 491).","submitted_at":"2026-04-28 16:27:09","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/491/142c970b7c245a0c1c10a0134d292e444c2334418cbb183779acd982b78a876b.txt"},{"canonical_hash":"b4376349e83f10c7ed5e0e1627c311e00f90678b7d674b88ccd57bbd48ba85e2","size":496,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,2,5,8,6,12,13,11,3,477,10,9,14,7,4,26,18,28,20,21,25,27,15,16,19,478,29,23,17,24,22,35,40,37,43,30,44,36,38,42,41,490,31,33,39,34,32,275,283,284,271,282,278,272,274,277,280,495,281,276,270,273,279,149,141,138,139,140,143,148,146,142,147,475,137,145,135,136,144,236,235,228,238,229,232,234,230,227,231,493,233,226,225,237,239,346,353,349,345,348,350,359,357,358,352,494,347,355,354,351,356,337,336,340,341,335,334,330,333,331,343,481,332,342,344,338,339,75,79,86,82,88,80,85,78,89,76,485,84,83,77,81,87,415,416,413,408,419,414,405,410,411,406,480,417,412,418,407,409,185,188,194,189,180,192,190,184,182,187,471,193,183,181,186,191,288,291,292,297,293,299,289,286,296,298,469,294,285,287,290,295,431,429,425,420,432,424,421,427,433,430,479,426,422,434,423,428,174,177,171,175,170,173,168,179,172,178,473,169,167,166,176,165,121,124,129,120,131,128,134,133,122,125,476,127,130,126,123,132,448,437,443,447,442,445,440,438,436,435,468,441,439,449,444,446,322,317,319,328,324,320,316,321,326,318,482,325,329,323,315,327,51,47,46,52,45,48,54,50,59,56,489,57,58,53,55,49,204,207,206,203,197,201,195,209,205,200,472,198,196,208,202,199,385,379,378,389,387,375,383,376,377,381,487,386,382,384,380,388,163,152,153,162,156,158,150,160,157,154,474,155,164,151,161,159,455,461,452,464,458,456,453,463,459,450,467,454,457,451,462,460,105,107,115,110,118,108,117,114,119,106,483,113,111,112,109,116,365,367,372,360,374,368,373,371,363,361,491,369,362,370,366,364,404,398,403,400,393,394,402,392,396,399,488,395,397,401,390,391,223,220,224,222,216,221,212,210,215,219,492,214,211,217,218,213,100,92,104,103,93,95,91,99,98,97,484,94,101,90,102,96,60,66,73,70,71,61,72,64,68,67,486,74,62,65,69,63,245,247,240,253,242,244,241,249,250,246,465,243,254,251,252,248,309,313,305,311,308,303,307,310,302,312,470,301,306,314,304,300,268,264,259,257,261,263,260,265,256,267,466,269,262,255,258,266","comment":"Tao(F_31,β=2) × F_16(ζ=8,ω=6). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-23 21:26:59","submitted_by":"bulk-import-memoryleak47","url":"https://eq677-magmas.icarm.cloud/magmas/496/b4376349e83f10c7ed5e0e1627c311e00f90678b7d674b88ccd57bbd48ba85e2.txt"},{"canonical_hash":"68ea78ce7ec14df8a489db520f2ea4911bc25159042b05939d7a198902b555da","size":496,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,10,14,13,3,5,2,7,4,477,8,6,12,9,11,29,22,26,17,18,28,25,20,24,23,478,27,16,21,15,19,33,30,35,39,40,37,44,43,31,32,490,36,42,34,38,41,273,281,282,283,280,276,271,272,275,278,495,279,274,284,270,277,145,148,144,149,135,142,136,143,141,147,475,138,140,137,146,139,226,235,234,227,232,231,230,228,237,239,493,233,229,238,236,225,354,352,348,357,355,353,345,347,358,359,494,350,346,351,356,349,338,335,343,341,337,339,336,331,340,332,481,333,344,330,334,342,89,87,80,77,88,84,75,81,78,86,485,83,82,76,85,79,416,409,406,405,413,415,411,419,407,410,480,408,412,417,414,418,186,185,183,189,191,187,190,188,180,184,471,181,192,193,182,194,288,297,292,296,295,298,285,293,286,299,469,287,289,290,291,294,425,424,429,427,421,423,433,430,422,434,479,431,426,432,428,420,176,171,173,166,177,175,169,172,179,170,473,167,178,165,174,168,120,121,128,130,125,124,132,127,131,133,476,123,134,122,129,126,435,438,442,449,448,437,445,441,446,444,468,447,436,440,439,443,318,315,322,324,319,317,321,327,325,326,482,320,316,329,323,328,59,57,49,48,58,46,55,50,47,52,489,53,45,54,56,51,201,198,208,203,200,202,195,209,204,199,472,206,196,205,197,207,387,383,389,379,386,388,376,380,378,375,487,384,382,385,377,381,162,150,163,157,154,153,159,164,156,160,474,161,155,158,152,151,459,454,460,453,462,456,464,458,461,451,467,452,457,463,455,450,117,114,105,112,118,110,116,107,113,115,483,109,108,119,111,106,364,369,365,374,373,372,371,363,362,370,491,361,367,366,368,360,397,391,393,401,396,395,392,403,400,390,488,399,398,394,402,404,224,220,216,210,223,218,221,215,212,219,492,222,213,211,214,217,98,93,94,91,96,104,101,103,90,97,484,95,99,100,102,92,60,74,65,69,70,61,64,72,62,63,486,66,67,73,68,71,243,250,246,240,245,249,244,252,241,251,465,242,247,254,248,253,314,303,304,309,313,311,302,305,308,310,470,300,307,301,312,306,266,265,267,260,255,261,263,268,264,262,466,269,256,258,259,257","comment":"Tao(F_31,β=2) × F_16(ζ=8,ω=7). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:55:41","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/496/68ea78ce7ec14df8a489db520f2ea4911bc25159042b05939d7a198902b555da.txt"},{"canonical_hash":"edc29ea1f0d1aed3a12953c2ab89cb51e8ac8b414b28456f7a4e205f4ebe5c9b","size":496,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,10,5,13,11,3,6,488,7,12,2,4,14,8,9,41,37,39,30,40,33,38,43,478,42,44,32,36,34,35,31,400,399,396,403,394,395,397,392,494,390,404,393,402,391,401,398,291,287,290,293,294,295,292,297,465,289,288,296,285,298,286,299,260,267,263,255,256,264,262,269,470,259,258,266,261,265,257,268,63,72,60,65,62,61,68,73,472,64,67,66,71,69,70,74,197,204,195,206,199,196,198,203,489,209,202,201,207,200,205,208,313,311,300,312,307,304,302,306,466,303,309,305,308,310,314,301,217,211,218,213,210,219,220,216,490,214,212,223,215,224,221,222,154,155,160,153,157,159,152,163,495,150,162,151,158,164,161,156,176,175,168,166,172,174,177,178,475,179,165,171,169,173,170,167,408,409,418,412,405,417,414,406,481,419,413,410,415,411,416,407,140,139,145,148,137,146,147,142,474,136,141,144,138,143,149,135,27,26,17,19,28,22,29,20,487,25,18,16,21,15,23,24,340,333,341,336,332,343,339,338,485,344,337,334,342,331,335,330,364,365,374,362,368,363,367,371,480,361,372,370,366,373,369,360,55,59,54,49,58,56,47,50,477,53,57,45,48,46,51,52,98,99,104,97,101,103,96,92,493,95,90,94,102,93,91,100,127,131,128,132,121,123,122,126,473,124,130,120,133,129,125,134,379,385,382,381,389,375,384,383,491,376,386,378,380,388,377,387,424,423,422,428,425,431,420,426,482,429,433,421,427,432,430,434,317,318,315,323,324,325,322,327,486,319,316,326,321,328,320,329,113,106,111,116,112,119,105,110,492,114,118,117,109,107,108,115,242,240,250,247,241,243,245,253,483,251,254,252,248,246,249,244,227,229,226,235,231,225,233,230,484,239,228,237,232,236,234,238,282,277,276,273,272,275,270,271,469,280,281,283,284,279,278,274,446,440,447,441,435,448,442,444,468,443,438,439,436,449,445,437,353,354,350,352,351,358,359,349,479,348,357,356,345,355,347,346,82,83,88,81,85,87,80,75,471,79,76,78,86,77,89,84,450,456,452,453,451,455,454,458,467,459,460,457,464,463,461,462,184,183,189,192,190,188,185,180,476,181,191,187,182,186,193,194","comment":"Tao(F_31,β=16) × F_16(ζ=8,ω=6). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:57:09","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/496/edc29ea1f0d1aed3a12953c2ab89cb51e8ac8b414b28456f7a4e205f4ebe5c9b.txt"},{"canonical_hash":"70073cc2c0251b6f462c12f82726aa0870316499053ab5106d5e8b56a58159d8","size":496,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,4,488,5,6,10,12,8,3,2,11,7,14,9,13,40,41,30,478,43,36,35,37,39,44,38,31,32,34,42,33,395,393,398,494,396,401,402,403,392,399,391,397,404,400,394,390,292,289,286,465,294,297,290,291,298,296,293,299,295,287,285,288,263,256,262,470,259,269,258,268,266,261,265,264,255,260,267,257,62,63,65,472,73,71,70,72,60,67,68,74,66,69,64,61,201,196,205,489,198,202,203,206,207,200,204,199,209,208,195,197,308,302,309,466,312,300,314,310,306,307,311,301,313,303,305,304,216,220,210,490,215,217,212,219,218,213,222,223,224,211,214,221,162,159,163,495,153,158,161,155,151,157,152,150,160,164,156,154,165,173,176,475,166,167,171,179,170,168,174,172,177,169,178,175,408,417,413,481,407,406,419,410,412,414,418,411,409,415,405,416,145,142,146,474,135,141,144,138,148,140,136,149,143,147,139,137,19,29,22,487,20,21,25,24,23,18,15,26,28,17,27,16,341,330,342,485,331,339,333,343,340,338,337,334,336,335,344,332,374,362,368,480,371,361,373,364,363,367,372,366,370,360,369,365,48,57,51,477,49,50,54,59,53,47,45,55,52,46,56,58,101,98,102,493,92,97,100,94,104,96,90,91,99,103,95,93,122,123,121,473,128,126,125,133,130,129,131,127,132,124,134,120,382,378,387,491,385,383,381,380,389,376,375,379,388,377,384,386,421,422,425,482,426,427,430,428,420,424,423,431,429,433,434,432,322,320,317,486,324,327,319,321,328,326,323,329,325,316,318,315,112,113,116,492,110,109,108,106,111,118,105,115,117,107,114,119,254,241,249,483,250,245,246,240,251,243,242,244,253,248,247,252,229,227,234,484,232,230,226,236,233,235,225,238,239,231,228,237,279,273,277,469,278,275,283,272,271,282,280,274,284,270,281,276,443,445,440,468,438,444,441,439,442,437,435,436,446,449,447,448,345,355,348,479,356,358,357,353,359,351,346,350,347,352,354,349,85,82,86,471,75,81,84,78,88,80,76,89,83,87,79,77,458,459,462,467,454,451,455,461,453,464,460,456,452,463,450,457,188,180,187,476,181,190,192,191,194,185,182,193,183,189,184,186","comment":"Tao(F_31,β=16) × F_16(ζ=8,ω=7). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 17:57:20","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/496/70073cc2c0251b6f462c12f82726aa0870316499053ab5106d5e8b56a58159d8.txt"},{"canonical_hash":"8ed9291b0f34ceb9721c40998824d64b658327a7fb0b5d29a5260bdf762a7cb4","size":499,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"498,0,117,162,410,459,455,25,18,7,67,251,63,219,318,112,311,106,108,238,360,363,295,239,356,409,263,153,175,391,405,329,168,340,399,224,401,180,282,308,217,253,220,303,152,450,283,366,213,475,17,444,120,86,446,201,468,327,248,177,13,26,186,16,461,169,197,422,256,328,268,134,258,298,473,62,139,452,165,245,497,491,297,96,264,56,160,44,445,29,58,420,140,231,223,188,3,150,83,242,310,12,52,361,413,313,379,451,54,333,494,269,76,247,184,189,292,210,470,307,306,429,319,342,479,359,309,350,69,205,462,1,490,439,30,103,300,325,185,426,125,19,427,397,302,341,155,128,81,249,355,412,432,97,60,279,458,55,289,424,118,440,99,196,154,290,389,464,121,365,349,229,453,22,337,174,53,266,322,193,351,6,28,364,433,130,275,284,267,354,481,135,114,172,443,2,376,487,286,430,167,75,113,156,345,203,218,230,21,416,170,377,236,472,59,9,347,94,190,200,102,8,126,260,369,400,291,375,477,178,482,105,149,265,10,316,78,334,164,288,163,31,37,144,176,425,199,384,87,434,216,305,166,417,207,394,362,11,5,381,70,382,116,296,98,36,47,367,323,15,396,259,157,73,182,151,478,344,34,320,418,408,312,129,35,277,254,454,159,388,198,488,448,436,421,127,374,331,293,385,212,68,20,158,40,225,390,332,353,14,136,49,66,57,348,215,146,495,32,133,411,104,48,271,392,119,489,235,447,131,147,339,246,171,72,372,414,317,222,336,206,71,273,240,61,278,315,214,194,137,467,299,346,373,123,84,179,209,486,343,208,403,107,82,321,4,221,23,41,244,423,287,132,91,141,261,124,101,211,88,89,252,428,74,407,402,465,294,51,27,115,272,233,161,95,195,143,270,38,92,460,301,368,39,406,441,449,358,202,276,496,227,262,378,274,46,314,79,24,43,463,383,234,357,280,255,80,476,352,50,110,474,204,415,387,243,483,404,493,480,395,466,109,250,419,228,304,338,226,484,257,431,148,65,232,370,85,438,471,435,90,64,398,183,442,181,122,386,111,187,173,393,371,45,191,138,457,77,145,142,456,326,324,93,330,100,437,281,469,285,33,485,492,237,241,192,380,335,42","comment":"Linear magma over Z/499Z (the prime field F_499): x ◇ y = 139x + 255y (mod 499).","submitted_at":"2026-04-28 16:27:19","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/499/8ed9291b0f34ceb9721c40998824d64b658327a7fb0b5d29a5260bdf762a7cb4.txt"},{"canonical_hash":"459ce31fa61c03b6807b660639b295057b93b38b1c52e80e629c54fe7c13dfd9","size":499,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"498,0,320,422,407,39,41,366,260,143,126,34,128,50,453,228,113,450,230,384,213,87,121,40,215,283,137,302,72,73,285,323,200,223,69,172,287,194,237,5,270,486,174,117,208,387,127,429,272,31,370,171,224,460,389,278,159,105,160,290,372,256,410,480,491,294,280,401,156,229,25,436,374,463,485,238,90,167,296,490,357,257,339,2,27,22,204,28,265,364,240,183,214,44,48,190,359,428,118,382,457,497,24,307,281,331,79,43,242,321,365,353,12,36,192,284,13,398,377,115,459,273,109,441,29,89,333,437,344,276,381,139,367,49,254,108,9,325,286,399,316,150,55,289,461,317,82,220,338,488,91,187,177,330,20,129,383,132,343,181,444,173,110,186,426,467,293,161,318,305,313,264,495,258,319,416,352,245,451,282,93,253,474,211,271,438,131,17,135,435,481,92,446,198,47,249,205,259,469,397,76,122,322,206,315,58,394,388,368,185,418,299,166,157,130,361,95,456,408,184,452,471,440,154,303,193,123,81,483,414,371,326,304,355,251,235,464,445,202,15,78,144,360,212,196,275,60,201,116,395,176,335,420,279,56,415,431,141,363,297,468,421,226,11,454,470,136,85,107,152,195,30,300,342,412,84,373,221,252,233,403,189,3,314,142,349,376,385,80,199,404,149,169,175,277,96,425,103,341,295,178,16,478,424,1,266,417,227,311,262,216,354,236,350,219,52,430,255,472,312,63,232,26,133,197,100,477,42,45,94,86,99,380,74,14,207,405,329,392,225,400,124,351,164,348,239,111,396,406,310,35,119,439,301,98,8,70,274,369,97,180,67,106,462,327,473,268,148,358,162,57,125,218,114,308,482,222,328,54,6,334,158,179,466,65,411,489,465,134,146,102,23,496,298,112,62,88,243,250,4,163,337,209,140,409,267,263,433,402,21,145,46,247,423,241,246,455,120,476,138,37,77,386,309,19,32,10,155,217,244,448,375,182,61,75,38,261,191,475,153,71,379,324,378,59,170,7,443,390,151,484,53,210,346,168,427,336,393,33,51,458,18,413,68,391,288,442,419,104,66,292,291,83,356,64,434,493,340,306,432,165,449,231,332,447,234,269,347,487,345,362,479,147,494,492,188,203,101,248","comment":"Linear magma over Z/499Z (the prime field F_499): x ◇ y = 139x + 383y (mod 499).","submitted_at":"2026-04-28 16:27:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/499/459ce31fa61c03b6807b660639b295057b93b38b1c52e80e629c54fe7c13dfd9.txt"},{"canonical_hash":"b057e03ef3c74265669b8d4778793121d0598f68fef9d95ee259cfe50ed2b7b1","size":521,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,96,337,391,520,52,140,313,405,404,512,236,351,328,350,357,110,164,310,109,15,255,57,206,14,444,21,292,202,13,429,244,509,47,201,454,168,208,264,508,145,394,280,471,167,488,325,247,174,144,491,185,276,176,166,398,375,30,318,173,107,414,135,9,275,102,335,84,433,374,282,238,463,372,106,422,410,213,340,274,479,113,69,228,432,452,86,170,54,462,321,308,439,466,409,269,89,94,450,478,475,132,441,416,431,2,344,499,39,53,183,80,517,513,438,99,199,358,360,88,400,16,162,130,474,445,259,33,64,430,241,150,379,390,38,82,481,146,312,516,126,489,36,235,198,492,368,45,356,399,287,483,4,108,473,353,77,103,205,63,226,283,302,291,378,423,333,285,243,480,435,210,142,453,125,119,455,322,507,197,385,270,129,470,355,476,468,137,246,3,251,67,331,184,76,295,73,100,397,225,387,401,362,172,377,446,155,231,8,242,97,223,192,83,141,348,448,127,237,519,115,493,111,421,384,288,256,459,273,354,22,298,24,227,245,148,346,424,169,330,427,436,395,307,72,120,326,92,268,386,186,304,152,477,376,266,315,252,415,7,43,296,336,498,191,388,239,139,79,447,411,11,511,98,114,179,218,349,87,383,189,116,309,194,272,289,90,56,32,23,133,366,20,149,345,504,486,428,81,426,157,121,200,515,71,187,17,263,234,267,195,496,279,44,151,338,300,389,482,314,501,412,490,352,42,180,369,165,62,190,484,58,317,290,78,293,381,134,284,510,407,505,334,209,217,158,211,281,118,188,456,248,105,196,271,277,49,339,469,31,221,502,68,136,19,181,74,85,66,485,402,464,320,294,156,214,260,408,224,70,60,159,449,171,233,457,494,440,230,278,257,95,343,222,299,442,51,182,347,500,26,403,437,518,41,215,327,359,420,61,305,163,161,458,316,34,254,258,297,380,392,443,240,147,406,27,12,37,329,216,219,46,311,306,117,5,207,35,91,104,203,393,367,303,48,28,487,286,265,220,122,143,472,6,18,323,175,204,497,65,177,29,301,138,319,123,413,332,10,324,370,101,434,178,59,363,373,124,382,232,341,371,506,193,229,364,212,128,55,342,249,112,467,365,50,460,451,250,503,25,417,461,75,425,40,418,465,396,514,419,261,93,361,262,160,153,131,154,495,253","comment":"Linear magma over Z/521Z (the prime field F_521): x ◇ y = 517x + 5y (mod 521).","submitted_at":"2026-04-28 16:27:36","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/521/b057e03ef3c74265669b8d4778793121d0598f68fef9d95ee259cfe50ed2b7b1.txt"},{"canonical_hash":"dbf4de574ccf075c7d3a4c6a8b02865bc5ab8f1b0722a128c6fd0fdeaa68dab9","size":521,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,19,298,50,355,238,232,75,30,409,179,155,358,411,96,303,351,443,224,129,91,265,247,37,12,92,2,132,367,273,110,481,421,432,8,389,108,510,406,341,11,198,515,4,24,316,441,449,285,492,199,266,20,34,495,193,353,306,458,217,36,491,139,447,504,121,168,68,507,234,500,113,229,6,150,140,516,248,299,146,246,284,149,263,162,319,434,88,158,373,502,336,174,28,382,57,385,378,118,39,264,448,5,38,51,312,47,380,63,401,404,256,413,143,189,185,201,282,291,78,90,440,228,117,520,52,163,505,25,13,356,347,136,250,254,208,478,191,469,466,128,315,112,377,116,103,70,513,329,104,53,313,320,122,317,93,239,271,437,308,223,23,499,384,227,328,214,349,181,211,364,183,451,205,215,71,164,48,435,169,442,3,233,56,439,512,204,426,101,152,393,371,288,258,430,99,85,331,134,427,350,514,506,381,89,69,450,133,76,276,471,445,43,324,73,497,486,416,45,338,302,197,67,27,77,102,182,330,26,64,159,508,286,368,31,476,293,220,244,474,95,10,167,173,290,115,363,84,66,65,277,153,212,105,14,402,374,235,493,274,410,340,120,335,281,376,210,98,196,83,453,268,126,454,278,160,472,394,365,54,357,405,503,501,200,111,180,429,301,362,125,295,187,81,398,456,322,483,296,269,154,509,446,372,184,314,348,257,337,114,267,482,156,171,460,419,424,488,59,345,178,107,138,157,188,127,213,287,44,289,452,321,137,414,175,230,21,422,359,310,408,388,490,87,142,465,327,370,415,172,82,455,106,369,325,259,206,123,251,144,29,7,35,433,412,468,226,392,485,166,195,397,177,326,176,461,399,279,15,32,74,431,216,318,255,190,383,151,496,9,97,80,344,464,396,241,261,242,462,130,231,420,457,161,403,477,498,100,72,94,209,186,58,141,194,260,304,41,390,17,237,480,305,262,400,207,22,425,323,473,375,294,487,86,165,240,479,202,386,517,354,109,352,148,62,253,222,203,42,243,280,124,423,489,484,395,236,221,417,332,49,272,192,283,379,249,307,511,444,219,334,361,418,387,391,463,16,252,360,60,297,366,494,245,46,135,436,438,470,292,119,300,459,407,225,343,519,61,333,518,18,131,33,145,311,346,270,55,275,475,339,428,170,309,467,79,40,147,218,342","comment":"Linear magma over Z/521Z (the prime field F_521): x ◇ y = 397x + 125y (mod 521).","submitted_at":"2026-04-28 16:27:43","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/521/dbf4de574ccf075c7d3a4c6a8b02865bc5ab8f1b0722a128c6fd0fdeaa68dab9.txt"},{"canonical_hash":"201e2e4398c0ca90b4282df96d846a63c7d0729af477f3e1432c4e12369ce1c6","size":521,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,461,361,307,316,448,367,182,219,247,343,436,3,492,499,290,416,177,46,25,401,185,519,253,426,51,389,323,463,69,293,355,305,23,166,168,282,229,19,256,422,109,286,30,363,276,214,384,358,136,11,170,118,124,100,239,433,259,81,148,309,406,141,472,398,341,387,284,79,297,154,207,66,332,299,242,318,271,467,190,16,130,374,231,475,370,91,328,381,394,156,235,450,210,502,225,430,459,175,21,134,339,193,457,338,458,209,393,369,194,270,331,296,340,405,258,123,135,275,108,228,22,68,50,184,176,491,246,447,460,217,424,420,431,129,379,336,226,334,103,221,503,87,482,267,211,75,111,144,451,7,56,105,236,301,508,249,157,495,347,444,395,63,288,353,382,470,188,223,329,244,480,345,92,485,94,72,371,43,32,36,476,201,59,505,232,320,263,438,375,410,487,350,131,279,365,517,17,98,152,89,191,273,127,5,468,199,96,198,272,97,278,409,319,200,42,484,243,469,62,494,300,6,74,86,333,128,216,490,67,274,404,269,208,192,174,501,155,90,373,466,298,153,386,140,80,99,10,213,285,18,165,292,388,518,45,498,342,366,360,314,399,280,116,77,473,132,121,418,142,351,34,515,407,488,138,312,310,411,161,113,149,376,204,179,82,439,38,512,195,264,13,413,434,321,28,146,240,233,391,48,101,506,478,261,125,60,172,163,119,202,454,453,171,477,390,27,12,37,203,160,137,33,120,115,359,44,164,9,385,372,173,403,215,73,61,41,277,95,126,151,364,486,262,58,31,93,479,187,287,346,507,55,110,481,102,378,423,245,49,107,257,330,392,456,20,224,234,327,230,189,241,206,283,471,147,238,169,383,29,255,167,354,322,252,24,289,435,181,306,64,414,303,356,396,14,428,294,445,265,442,70,348,196,84,464,496,513,510,324,158,39,53,325,250,440,520,52,509,83,441,427,302,180,251,254,237,205,326,455,106,377,54,186,57,150,40,402,8,114,159,26,452,162,260,47,145,412,511,178,112,311,514,417,76,313,497,291,212,139,465,500,268,489,85,493,483,408,197,4,88,516,349,437,504,35,71,344,222,352,443,248,104,143,266,220,335,419,446,183,227,122,295,368,337,133,429,449,380,474,15,317,65,78,397,308,432,117,357,362,421,281,304,462,425,400,415,2,218,315","comment":"Linear magma over Z/521Z (the prime field F_521): x ◇ y = 105x + 417y (mod 521).","submitted_at":"2026-04-28 16:27:50","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/521/201e2e4398c0ca90b4282df96d846a63c7d0729af477f3e1432c4e12369ce1c6.txt"},{"canonical_hash":"17b729ddff3b2af66357402903f4df4451b1f58b86aa478b503c2a55c9b2678a","size":521,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,152,185,122,208,41,480,214,303,147,516,101,261,171,442,167,455,136,448,478,151,476,369,394,404,123,405,126,275,410,308,81,396,108,331,378,445,344,23,497,337,184,257,421,270,125,59,144,505,293,215,276,294,194,115,95,290,426,128,219,389,285,121,241,21,363,274,334,19,177,193,412,67,27,77,102,397,195,78,90,400,322,229,207,83,264,132,409,485,366,69,114,512,466,155,89,202,110,118,39,168,446,427,79,40,268,161,424,307,191,380,205,94,200,224,189,399,46,463,31,267,237,48,346,247,479,338,286,230,80,248,375,317,289,519,33,499,321,244,253,99,160,402,3,342,374,213,297,239,186,395,271,364,133,425,231,187,472,228,10,158,348,423,438,300,311,316,302,85,210,471,107,431,502,481,127,506,178,70,206,318,134,482,306,494,419,73,288,146,175,352,227,330,87,487,305,218,235,385,517,82,295,28,156,190,500,473,71,518,515,55,7,9,377,278,282,493,388,325,433,514,263,392,139,443,379,291,196,119,32,100,349,483,157,444,509,222,418,284,35,97,54,131,356,314,508,204,457,328,449,498,260,323,428,347,343,312,74,72,120,450,453,6,408,435,255,221,93,360,17,452,320,170,153,370,422,22,265,162,287,240,211,353,8,484,429,371,417,199,383,141,5,243,441,62,416,437,496,42,406,145,20,367,381,376,365,503,488,283,223,75,163,407,252,166,490,198,299,336,460,251,174,362,148,309,277,68,467,225,34,188,179,386,434,98,454,354,382,310,183,15,165,351,273,414,182,281,113,172,332,96,398,111,464,254,159,135,29,140,315,256,372,489,226,333,105,14,492,511,233,104,53,45,137,24,220,401,447,49,4,301,420,474,197,329,18,142,164,387,465,25,13,130,462,37,12,92,2,477,258,242,84,269,339,298,86,176,56,350,324,154,63,491,355,30,50,259,359,341,150,358,440,209,124,60,335,486,192,249,272,432,88,279,510,313,266,43,461,16,373,475,340,61,470,58,469,459,304,411,216,413,513,201,390,232,507,236,326,36,451,212,368,149,415,106,143,57,250,217,66,65,181,262,109,116,103,203,47,245,11,319,296,393,357,436,430,504,468,173,234,26,64,280,391,117,520,52,456,345,129,91,169,238,403,439,495,501,292,458,361,384,76,180,112,138,38,51,44,327,246","comment":"Linear magma over Z/521Z (the prime field F_521): x ◇ y = 26x + 496y (mod 521).","submitted_at":"2026-04-28 16:27:57","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/521/17b729ddff3b2af66357402903f4df4451b1f58b86aa478b503c2a55c9b2678a.txt"},{"canonical_hash":"1b624e79c4d1174b10d447cbbaa67dcf4ef2f47ea1b58ee4be2676087764334d","size":523,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"522,0,381,300,398,260,317,452,415,129,277,363,334,199,469,504,432,303,146,422,294,39,31,133,351,464,216,373,486,428,106,151,449,192,320,348,163,67,439,443,311,442,56,86,48,91,150,164,19,125,481,132,233,231,390,152,503,358,445,342,123,451,168,217,466,403,209,148,337,377,365,40,180,400,84,51,456,102,460,433,328,309,459,7,73,507,103,364,65,410,14,287,167,395,181,318,36,389,142,436,498,511,149,521,250,177,248,438,407,484,169,245,520,509,26,95,462,30,359,42,140,255,468,29,185,360,234,316,483,264,420,88,226,510,165,269,354,430,394,158,33,408,57,506,197,324,417,369,101,366,68,275,473,376,3,9,477,143,450,475,345,221,326,230,476,396,374,290,90,100,109,187,2,66,32,137,82,171,427,225,367,6,304,38,184,205,412,195,198,461,335,237,53,259,406,339,159,401,453,497,515,392,113,516,166,338,382,313,267,72,194,340,265,218,455,224,424,239,501,336,186,446,262,173,122,229,111,206,43,232,10,280,479,495,47,368,27,20,59,162,157,271,272,138,485,87,46,257,202,293,28,110,251,440,333,94,500,24,281,397,437,193,105,283,243,435,112,346,182,487,286,405,22,116,447,8,411,134,175,331,50,426,425,69,74,147,108,115,214,135,341,325,434,200,386,131,4,23,383,34,85,416,292,98,490,347,393,270,378,301,372,419,494,16,160,421,467,228,492,78,362,25,238,361,343,299,247,71,493,252,413,141,391,489,307,12,15,258,5,96,126,458,204,213,379,273,83,170,49,120,154,208,99,21,188,178,444,220,242,322,384,480,375,499,321,296,55,323,201,207,222,319,429,156,212,189,215,263,478,13,352,145,254,121,70,240,276,508,423,77,356,380,176,266,418,329,470,388,514,97,117,314,409,52,130,513,118,308,183,114,355,17,399,81,330,253,284,402,89,404,211,61,357,344,282,54,235,124,472,93,241,79,441,196,256,153,518,191,353,161,203,305,463,482,279,306,190,302,139,172,246,92,128,519,223,491,60,1,249,312,371,80,297,35,496,291,512,349,64,236,385,387,44,327,37,107,76,62,179,136,174,144,288,465,289,285,155,75,502,474,104,295,63,18,274,332,219,370,310,505,45,119,127,448,268,58,457,278,350,315,11,488,517,431,41,261,298,471,414,244,454,227,210","comment":"Linear magma over Z/523Z (the prime field F_523): x ◇ y = 462x + 159y (mod 523).","submitted_at":"2026-04-28 16:28:05","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/523/1b624e79c4d1174b10d447cbbaa67dcf4ef2f47ea1b58ee4be2676087764334d.txt"},{"canonical_hash":"2c2054c9adb46762f3d662b5d91e3bce3840d045b295254bd5a91993d8430b3e","size":523,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"522,0,332,417,154,374,63,23,225,480,20,83,310,490,270,437,464,61,395,56,267,355,242,14,132,62,405,219,509,121,352,90,379,327,308,312,41,359,303,229,506,123,89,144,481,176,321,323,203,137,309,393,51,420,458,284,163,388,192,162,86,342,249,521,25,186,149,358,130,406,134,36,288,117,93,394,125,109,468,414,160,126,194,254,248,350,215,277,396,17,9,428,143,334,145,345,442,184,208,58,131,276,39,367,298,43,335,21,373,129,106,422,10,313,34,363,431,136,69,87,245,498,76,279,488,351,333,382,272,300,425,107,220,82,92,500,201,501,52,173,205,54,283,68,110,234,188,293,252,48,40,57,196,456,180,291,383,482,60,159,67,100,197,407,433,103,493,341,487,146,84,451,454,3,516,88,42,486,264,114,330,111,343,13,214,47,156,147,216,418,79,153,357,424,423,510,447,223,305,274,202,421,515,476,286,236,101,469,120,142,290,199,157,368,268,257,19,116,200,273,177,466,337,449,317,457,135,329,281,370,97,265,346,311,207,99,316,477,246,360,484,463,413,282,235,250,518,461,403,73,85,278,155,72,28,7,511,11,122,297,340,96,178,502,459,377,241,349,251,198,415,410,440,167,416,148,299,356,6,65,444,70,301,322,105,2,315,478,181,37,473,508,427,179,115,443,491,390,295,479,287,499,304,95,435,30,371,189,419,430,113,412,29,452,397,375,307,183,66,448,314,353,259,32,436,467,53,285,348,261,262,519,408,161,75,46,402,411,217,44,243,505,366,492,369,426,324,212,170,354,247,292,289,166,401,325,503,331,185,271,152,27,182,237,77,230,320,128,453,98,294,26,227,210,218,8,455,18,64,365,238,445,224,35,91,222,339,31,338,174,164,50,362,263,462,434,127,495,513,326,441,158,336,15,169,239,391,269,108,204,475,240,260,361,384,118,191,497,213,460,112,209,438,386,228,38,102,280,507,400,496,398,266,253,187,141,439,45,512,4,1,24,381,78,71,306,364,380,139,175,372,450,206,389,151,385,520,404,16,195,256,5,504,168,80,22,133,81,446,296,258,221,138,471,392,33,485,483,94,319,399,171,378,344,59,465,104,211,474,470,489,124,172,514,376,347,49,150,232,387,244,12,517,429,226,140,231,302,275,432,328,472,165,190,318,55,193,233,119,409,74,494,255","comment":"Linear magma over Z/523Z (the prime field F_523): x ◇ y = 60x + 274y (mod 523).","submitted_at":"2026-04-28 16:28:16","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/523/2c2054c9adb46762f3d662b5d91e3bce3840d045b295254bd5a91993d8430b3e.txt"},{"canonical_hash":"d52525fc5e3b1adb5beb2af1e8b45b12aa33080c83ebd3f6ee066f06b60ad6d0","size":523,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"522,0,192,311,327,303,446,390,251,37,438,403,109,51,314,29,386,391,228,384,101,172,66,357,505,21,242,86,449,333,220,465,310,185,315,164,363,282,308,100,497,388,40,46,462,78,281,75,168,512,212,173,377,481,482,177,112,166,257,215,355,206,128,426,445,92,53,124,450,139,32,356,287,484,417,70,443,320,496,98,160,340,312,135,231,165,237,115,125,486,474,440,416,247,471,158,36,298,175,439,347,218,41,241,301,418,144,335,145,25,45,8,508,61,34,131,392,354,350,513,279,10,341,170,319,62,89,262,108,95,488,470,244,506,520,332,113,490,7,126,223,329,280,453,422,107,147,294,80,425,466,14,106,427,188,239,159,359,494,263,28,479,264,297,447,431,3,309,366,368,33,420,372,42,511,410,316,469,149,4,137,52,103,460,79,1,382,321,134,208,26,430,227,330,433,346,43,196,102,163,271,378,353,455,232,162,376,393,436,519,81,58,12,138,259,87,13,326,216,266,236,441,199,365,171,324,457,240,225,193,322,307,55,267,278,54,274,352,176,179,414,489,201,122,265,286,38,434,187,389,458,273,485,492,397,419,504,405,491,143,151,369,133,387,379,255,169,268,183,161,256,249,509,222,153,423,198,69,317,501,358,437,253,178,415,412,116,510,85,514,503,24,15,291,429,461,476,221,88,407,129,435,205,472,502,452,90,305,323,495,374,304,27,50,283,200,157,140,398,468,219,117,142,507,399,338,432,74,110,197,94,463,194,57,444,370,290,146,292,48,224,339,83,373,296,385,233,285,174,275,73,136,184,64,132,130,17,295,195,211,5,500,243,59,499,258,123,395,475,424,191,342,306,230,189,49,2,383,343,186,217,516,93,459,362,299,254,349,96,284,270,480,234,252,331,344,498,325,31,288,406,105,302,515,277,114,118,156,367,65,30,272,300,76,56,381,99,380,182,9,477,72,454,111,203,411,6,67,394,235,483,180,204,238,250,361,351,473,401,467,371,20,104,396,334,260,289,207,39,181,248,318,120,63,375,214,360,84,328,209,190,364,442,119,451,493,402,348,413,246,245,141,409,448,276,404,44,517,47,226,77,71,152,261,336,16,518,127,400,23,421,18,229,456,97,213,521,478,313,269,121,35,408,337,148,464,155,150,60,22,82,345,167,202,68,487,154,210,11,91,19,428,293","comment":"Linear magma over Z/523Z (the prime field F_523): x ◇ y = 462x + 303y (mod 523).","submitted_at":"2026-04-28 16:28:26","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/523/d52525fc5e3b1adb5beb2af1e8b45b12aa33080c83ebd3f6ee066f06b60ad6d0.txt"},{"canonical_hash":"5971661c579df9f95dfa1b11793845a40f614e715773be108a47513c12e59609","size":523,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"522,0,423,386,428,190,391,63,433,305,195,251,396,387,68,109,438,430,310,177,200,455,256,10,401,16,392,224,73,363,114,8,443,170,435,308,315,328,182,306,205,275,460,395,261,501,15,346,406,181,21,398,397,335,229,447,78,96,368,122,119,505,1,42,448,110,175,372,440,348,313,486,320,490,333,354,187,369,311,469,210,143,280,250,465,202,400,282,266,327,506,456,20,384,351,422,411,198,186,89,26,326,403,449,402,227,340,151,234,484,452,247,83,264,101,152,373,225,127,75,124,508,510,194,426,158,47,360,453,314,115,38,180,295,377,3,445,44,353,160,318,265,491,171,325,86,495,100,338,480,359,133,192,317,374,188,316,217,474,254,215,498,148,304,285,415,255,76,470,307,207,488,405,297,287,504,271,514,332,149,511,281,461,424,25,51,389,263,356,342,46,472,416,159,203,502,191,48,94,414,31,291,331,432,408,471,454,267,407,434,232,60,345,35,156,118,239,61,489,39,457,399,252,103,88,273,269,82,106,366,157,288,378,352,230,69,132,18,80,284,129,482,513,62,515,45,199,97,431,169,163,238,14,213,365,121,458,512,319,27,120,201,5,381,185,58,300,246,382,104,425,172,450,43,11,219,358,41,165,303,323,301,270,390,496,341,176,393,330,442,91,117,500,418,105,367,343,481,485,349,364,464,138,245,197,277,322,451,379,417,193,84,321,444,222,146,479,242,259,147,220,70,503,189,153,355,309,33,290,7,420,155,260,166,81,95,475,128,312,183,212,249,493,299,410,71,302,483,292,499,509,144,276,2,519,258,337,467,154,497,516,409,286,427,466,262,429,55,30,113,56,34,394,98,268,77,361,283,347,64,13,279,477,57,421,92,164,233,208,116,507,22,196,376,53,241,99,167,419,214,36,298,296,385,336,388,437,112,413,362,476,344,459,240,272,446,412,79,439,141,237,142,65,184,350,28,40,150,161,90,123,178,244,294,66,478,494,139,6,253,462,492,404,521,257,50,108,29,93,72,278,59,274,52,87,228,111,17,371,236,162,209,293,380,383,107,357,339,235,441,74,136,137,179,23,145,85,173,289,473,134,248,487,9,518,24,67,54,520,223,12,231,204,375,102,334,436,131,174,140,168,468,243,4,19,49,218,226,370,329,126,135,463,37,517,221,324,130,32,216,125,211,206","comment":"Linear magma over Z/523Z (the prime field F_523): x ◇ y = 60x + 309y (mod 523).","submitted_at":"2026-04-28 16:28:33","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/523/5971661c579df9f95dfa1b11793845a40f614e715773be108a47513c12e59609.txt"},{"canonical_hash":"576a7341bbd69c717e51bf63233e66700ce9868afc67dc42b05e376631098d15","size":529,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"528,524,476,470,494,467,488,497,512,482,485,473,506,518,515,479,464,521,500,461,503,509,491,214,48,168,117,402,301,82,188,339,22,243,480,469,221,403,107,315,358,196,65,371,317,407,232,487,66,239,186,421,69,125,420,267,319,376,100,148,140,17,357,389,40,269,261,425,498,226,351,327,60,34,370,180,255,142,129,492,11,414,481,383,313,233,329,94,415,419,134,119,250,118,505,166,18,158,257,35,138,375,439,341,87,58,77,287,438,213,285,443,271,516,394,223,412,310,8,252,57,116,91,380,489,177,324,197,326,478,126,367,348,416,230,411,139,31,244,432,369,499,279,335,12,331,52,251,388,281,198,112,207,433,160,437,81,152,510,71,29,253,216,344,161,397,441,442,21,519,290,378,169,274,80,141,508,446,61,38,121,288,90,260,202,105,70,10,523,95,184,305,36,456,176,231,209,303,53,1,156,289,393,468,457,346,359,238,154,245,363,75,275,273,504,106,6,23,427,46,426,431,382,493,146,192,395,131,201,325,241,149,430,278,328,496,26,78,204,385,9,366,68,434,109,248,332,429,507,157,195,49,276,229,266,14,373,122,236,495,37,137,316,132,63,422,386,145,330,418,484,258,354,97,417,183,262,150,450,130,387,225,517,451,297,178,353,455,30,99,283,170,4,462,203,89,340,47,299,208,309,16,162,190,474,0,365,215,76,401,101,333,42,352,237,111,59,463,295,311,527,182,205,292,234,98,362,159,179,526,349,398,459,13,460,56,39,73,471,306,308,108,396,212,187,235,392,379,424,501,360,322,189,428,20,270,242,264,143,423,3,272,151,128,490,43,103,72,220,227,123,321,88,5,28,413,475,174,113,307,136,345,323,486,54,409,408,364,194,377,249,211,62,104,477,185,114,404,193,400,240,79,165,314,355,218,19,298,45,368,312,466,336,399,256,64,172,444,263,449,381,334,93,511,293,164,291,144,522,347,124,83,24,219,41,277,445,217,361,483,304,410,318,246,405,320,110,25,120,374,406,342,171,2,224,191,51,199,472,85,259,86,167,452,448,127,296,200,280,350,514,447,44,525,96,175,222,147,337,67,27,294,384,265,465,458,228,302,7,356,390,50,173,181,133,343,286,300,453,92,102,454,153,206,33,520,247,440,284,338,32,163,391,282,74,436,254,502,513,210,55,372,155,115,268,435,84,135,15","comment":"Linear magma over the extension field F_529 = F_23[α]/⟨α² − 5⟩.\n\nOperation: x ◇ y = a·x + b·y in F_529 with a = 11 + 22α, b = 20 + 8α. Here β = 20 + 8α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_529, and α_coef = -β³ - β - 1. This is Pace Nielsen's \"Type 2\" non-fully-idempotent linear 677 magma family.\n\nNote: 10 ∤ (23² − 1) = 528, so F_529 has no primitive 10th roots of unity → no Type-1 (translation-invariant fully-idempotent) linear 677 magma exists at this size. But Φ_2_5 has 4 roots in F_529 (forming 2 Galois-conjugate orbits under Frobenius), giving 2 distinct iso classes of Type-2 magmas at this size.\n\nF_529 is the proper degree-2 extension of F_23; do NOT confuse with the ring Z/529Z (which has zero divisors and is NOT a field).\n\nSize 529, not fully idempotent, right-cancellative. This iso class is one of the two known Eq 677 magmas at size 529 in the DB.\n\n[text written by Claude]","submitted_at":"2026-05-16 12:58:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/529/576a7341bbd69c717e51bf63233e66700ce9868afc67dc42b05e376631098d15.txt"},{"canonical_hash":"98cfe7aeb6265785fd08fe2e37a1b96f3d5c4af13f721fc249ed17ddf3944bd9","size":529,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"528,524,188,140,284,116,236,308,428,24,8,164,380,476,452,212,92,500,332,68,356,404,260,296,525,143,382,243,297,150,255,434,317,48,220,132,352,251,302,409,106,319,181,210,425,283,440,228,189,496,239,395,526,446,387,73,441,38,246,463,399,277,98,306,461,89,192,427,316,392,50,505,141,413,202,27,144,415,478,268,229,339,16,258,393,448,521,34,347,379,351,398,104,390,372,127,285,63,160,421,383,30,59,450,190,125,110,21,51,288,217,91,105,460,346,368,323,369,41,120,117,374,222,234,244,215,481,327,497,204,454,178,506,355,424,315,391,389,56,483,194,324,169,402,237,57,77,112,298,185,335,342,240,491,79,523,142,495,412,62,373,128,312,474,87,370,75,83,309,484,45,5,151,129,134,407,396,115,149,445,414,29,214,184,36,286,54,3,516,42,1,329,429,195,207,432,256,313,85,23,47,37,338,124,203,490,114,488,511,64,146,94,137,121,364,294,25,325,443,509,435,475,250,276,447,287,354,494,28,489,512,471,467,161,513,300,349,118,12,274,9,170,518,499,318,88,378,459,388,55,311,53,145,416,65,253,14,422,472,292,437,375,417,502,165,403,282,439,49,371,40,168,74,2,363,11,200,479,147,486,290,384,468,155,265,223,66,187,381,238,201,159,221,76,44,206,442,517,281,248,361,269,95,271,172,31,162,304,102,235,254,386,477,58,480,334,133,84,249,377,39,43,0,527,456,230,138,71,19,60,514,7,219,245,15,109,453,78,148,337,353,310,362,280,247,464,330,226,419,340,122,465,263,451,301,97,520,216,423,411,213,113,487,470,252,485,270,70,344,400,430,457,198,17,365,331,180,191,350,345,367,482,473,4,93,299,291,154,303,46,96,272,157,278,196,231,358,259,295,227,504,126,119,401,82,328,293,273,501,186,385,108,410,6,152,173,175,99,208,139,242,394,26,420,233,111,13,431,508,498,438,158,333,336,469,153,107,320,130,32,321,307,433,72,267,449,326,341,406,22,275,458,167,205,376,279,69,343,156,174,176,182,135,163,131,462,257,20,177,522,444,123,493,52,10,199,360,455,418,197,357,241,266,224,100,211,408,305,33,90,314,61,183,35,510,466,225,289,171,18,262,179,503,232,405,492,80,67,209,426,397,103,322,193,86,515,136,348,436,264,101,218,519,366,81,507,166,359,261","comment":"Linear magma over the extension field F_529 = F_23[α]/⟨α² − 5⟩.\n\nOperation: x ◇ y = a·x + b·y in F_529 with a = 11 + α, b = 14 + 9α. Here β = 14 + 9α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_529, and α_coef = -β³ - β - 1. This is Pace Nielsen's \"Type 2\" non-fully-idempotent linear 677 magma family.\n\nNote: 10 ∤ (23² − 1) = 528, so F_529 has no primitive 10th roots of unity → no Type-1 (translation-invariant fully-idempotent) linear 677 magma exists at this size. But Φ_2_5 has 4 roots in F_529 (forming 2 Galois-conjugate orbits under Frobenius), giving 2 distinct iso classes of Type-2 magmas at this size.\n\nF_529 is the proper degree-2 extension of F_23; do NOT confuse with the ring Z/529Z (which has zero divisors and is NOT a field).\n\nSize 529, not fully idempotent, right-cancellative. This iso class is one of the two known Eq 677 magmas at size 529 in the DB.\n\n[text written by Claude]","submitted_at":"2026-05-16 12:58:34","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/529/98cfe7aeb6265785fd08fe2e37a1b96f3d5c4af13f721fc249ed17ddf3944bd9.txt"},{"canonical_hash":"5f2f644f6c72959589ec20f260ded7916b2c8bb4f64d95e9d6c6d72b384d5c88","size":539,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"7,6,9,5,4,1,8,10,2,3,55,390,382,386,385,384,388,387,389,381,383,461,62,61,65,60,59,56,64,63,57,58,66,48,46,50,45,44,42,49,47,41,43,51,18,17,20,16,15,12,19,11,13,14,52,28,27,30,26,25,21,29,22,23,24,53,38,37,40,36,35,31,39,32,33,34,54,395,394,392,396,398,397,400,393,399,391,452,405,404,402,406,408,407,410,403,409,401,453,415,414,412,416,418,417,420,413,419,411,454,425,424,422,426,428,427,430,423,429,421,455,435,434,432,436,438,437,440,433,439,431,456,445,444,442,446,448,447,450,443,449,441,451,218,210,213,211,217,212,214,209,215,216,250,228,220,223,221,227,222,224,219,225,226,251,238,230,233,231,237,232,234,229,235,236,252,208,200,203,201,207,202,204,199,205,206,253,264,256,259,257,263,258,260,255,261,262,254,248,240,243,241,247,242,244,239,245,246,249,270,271,272,273,266,274,265,269,267,268,319,326,327,328,329,322,330,321,325,323,324,320,310,311,312,313,306,314,305,309,307,308,315,280,281,282,283,276,284,275,279,277,278,316,290,291,292,293,286,294,285,289,287,288,317,300,301,302,303,296,304,295,299,297,298,318,150,152,144,148,151,149,143,145,146,147,184,160,162,154,158,161,159,153,155,156,157,185,170,172,164,168,171,169,163,165,166,167,186,140,142,134,138,141,139,133,135,136,137,187,196,198,190,194,197,195,189,191,192,193,188,180,182,174,178,181,179,173,175,176,177,183,89,90,85,91,87,88,86,83,84,92,67,99,100,95,101,97,98,96,93,94,102,68,109,110,105,111,107,108,106,103,104,112,69,119,120,115,121,117,118,116,113,114,122,70,129,130,125,131,127,128,126,123,124,132,71,79,80,75,81,77,78,76,73,74,82,72,350,342,346,345,344,348,347,349,341,343,458,360,352,356,355,354,358,357,359,351,353,459,370,362,366,365,364,368,367,369,361,363,460,380,372,376,375,374,378,377,379,371,373,0,340,332,336,335,334,338,337,339,331,333,457,480,474,473,482,478,479,475,481,476,477,483,462,463,465,471,469,464,466,470,467,468,472,484,485,487,493,491,486,488,492,489,490,494,497,495,499,496,503,498,500,504,501,502,505,508,506,510,507,514,509,511,515,512,513,516,520,518,522,519,526,521,523,527,524,525,517,528,529,531,537,535,530,532,536,533,534,538","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_11(10,2).","submitted_at":"2026-04-28 19:34:37","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/539/5f2f644f6c72959589ec20f260ded7916b2c8bb4f64d95e9d6c6d72b384d5c88.txt"},{"canonical_hash":"7ef291c040b93be120f584afc22665bcd6c61a0421f713393130f5db2a9d3ee8","size":539,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"10,1,7,55,3,5,9,2,6,8,4,381,383,389,461,390,388,385,386,384,382,387,59,56,63,66,58,61,65,57,62,64,60,44,41,48,51,43,46,50,42,47,49,45,14,11,18,52,13,16,20,12,17,19,15,24,21,28,53,23,26,30,22,27,29,25,34,31,38,54,33,36,40,32,37,39,35,399,396,391,452,397,393,392,400,394,398,395,409,406,401,453,407,403,402,410,404,408,405,419,416,411,454,417,413,412,420,414,418,415,429,426,421,455,427,423,422,430,424,428,425,439,436,431,456,437,433,432,440,434,438,435,449,446,441,451,447,443,442,450,444,448,445,216,218,210,250,215,211,213,214,212,217,209,226,228,220,251,225,221,223,224,222,227,219,236,238,230,252,235,231,233,234,232,237,229,206,208,200,253,205,201,203,204,202,207,199,262,264,256,254,261,257,259,260,258,263,255,246,248,240,249,245,241,243,244,242,247,239,267,269,272,319,268,271,266,270,274,273,265,323,325,328,320,324,327,322,326,330,329,321,307,309,312,315,308,311,306,310,314,313,305,277,279,282,316,278,281,276,280,284,283,275,287,289,292,317,288,291,286,290,294,293,285,297,299,302,318,298,301,296,300,304,303,295,149,152,146,184,148,151,145,144,143,147,150,159,162,156,185,158,161,155,154,153,157,160,169,172,166,186,168,171,165,164,163,167,170,139,142,136,187,138,141,135,134,133,137,140,195,198,192,188,194,197,191,190,189,193,196,179,182,176,183,178,181,175,174,173,177,180,91,85,89,67,86,88,90,87,84,83,92,101,95,99,68,96,98,100,97,94,93,102,111,105,109,69,106,108,110,107,104,103,112,121,115,119,70,116,118,120,117,114,113,122,131,125,129,71,126,128,130,127,124,123,132,81,75,79,72,76,78,80,77,74,73,82,341,343,349,458,350,348,345,346,344,342,347,351,353,359,459,360,358,355,356,354,352,357,361,363,369,460,370,368,365,366,364,362,367,371,373,379,0,380,378,375,376,374,372,377,331,333,339,457,340,338,335,336,334,332,337,479,478,474,483,480,473,477,482,476,481,475,465,464,469,472,466,468,462,471,463,470,467,484,485,491,494,486,489,490,492,488,493,487,501,496,504,505,495,503,498,499,497,500,502,512,507,515,516,506,514,509,510,508,511,513,524,519,527,517,518,526,521,522,520,523,525,528,529,535,538,530,533,534,536,532,537,531","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_11(4,8).","submitted_at":"2026-04-28 19:35:15","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/539/7ef291c040b93be120f584afc22665bcd6c61a0421f713393130f5db2a9d3ee8.txt"},{"canonical_hash":"93f9e7b115e3e2b73f3160d1aa17f56c16f391107cd2af8d8058c76298939d95","size":539,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"5,1,8,9,10,4,3,2,6,55,7,386,381,384,385,383,389,387,382,388,461,390,61,56,64,65,60,59,58,57,62,66,63,46,41,49,50,45,44,43,42,47,51,48,16,11,19,20,15,14,13,12,17,52,18,26,23,29,30,21,25,24,22,27,53,28,36,33,39,40,32,35,34,31,37,54,38,393,395,391,394,399,398,396,400,397,452,392,403,405,401,404,409,408,406,410,407,453,402,413,415,411,414,419,418,416,420,417,454,412,423,425,421,424,429,428,426,430,427,455,422,433,435,431,434,439,438,436,440,437,456,432,443,445,441,444,449,448,446,450,447,451,442,218,213,211,209,217,216,212,210,215,250,214,228,223,221,219,227,226,222,220,225,251,224,238,233,231,229,237,236,232,230,235,252,234,208,203,201,199,207,206,202,200,205,253,204,264,259,257,255,263,262,258,256,261,254,260,248,243,241,239,247,246,242,240,245,249,244,272,265,274,268,271,270,273,269,266,319,267,328,321,330,324,327,326,329,325,322,320,323,312,305,314,308,311,310,313,309,306,315,307,282,275,284,278,281,280,283,279,276,316,277,292,285,294,288,291,290,293,289,286,317,287,302,295,304,298,301,300,303,299,296,318,297,149,152,146,147,148,143,150,144,151,184,145,159,162,156,157,158,154,160,153,161,185,155,169,172,166,167,168,164,170,163,171,186,165,139,142,136,137,138,134,140,133,141,187,135,195,198,192,193,194,190,196,189,197,188,191,179,182,176,177,178,173,180,174,181,183,175,90,89,87,84,85,86,91,88,92,67,83,100,99,97,94,95,96,101,98,102,68,93,110,109,107,104,105,106,111,108,112,69,103,120,119,117,114,115,116,121,118,122,70,113,130,129,127,124,125,126,131,128,132,71,123,80,79,77,74,75,76,81,78,82,72,73,346,341,344,345,343,349,347,342,348,458,350,356,351,354,355,353,359,357,352,358,459,360,366,361,364,365,363,369,367,362,368,460,370,376,371,374,375,373,379,377,372,378,0,380,336,331,334,335,333,339,337,332,338,457,340,476,477,481,475,474,473,479,482,480,483,478,467,466,470,464,463,462,468,471,465,472,469,484,485,492,486,491,487,489,490,493,494,488,503,497,499,496,502,501,504,495,500,505,498,514,508,510,507,513,512,515,506,511,516,509,526,520,522,519,525,524,527,518,523,517,521,528,529,536,530,535,531,533,534,537,538,532","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_11(5,7).","submitted_at":"2026-04-28 19:35:38","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/539/93f9e7b115e3e2b73f3160d1aa17f56c16f391107cd2af8d8058c76298939d95.txt"},{"canonical_hash":"8363408a17e3fce04de69e31f0601b2c9d430980242b8d752a7971280192c097","size":539,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"3,10,55,9,4,2,5,8,7,1,6,385,382,461,390,383,387,381,388,389,386,384,59,58,66,65,60,57,61,64,63,56,62,44,43,51,50,45,42,46,49,48,41,47,14,13,52,20,15,12,16,19,18,11,17,24,23,53,30,25,22,26,29,28,21,27,34,33,54,40,35,32,36,39,38,31,37,391,400,452,394,395,398,396,399,392,393,397,401,410,453,404,405,408,406,409,402,403,407,411,420,454,414,415,418,416,419,412,413,417,421,430,455,424,425,428,426,429,422,423,427,431,440,456,434,435,438,436,439,432,433,437,441,450,451,444,445,448,446,449,442,443,447,213,209,250,211,212,216,215,218,217,214,210,223,219,251,221,222,226,225,228,227,224,220,233,229,252,231,232,236,235,238,237,234,230,203,199,253,201,202,206,205,208,207,204,200,259,255,254,257,258,262,261,264,263,260,256,243,239,249,241,242,246,245,248,247,244,240,270,274,319,269,266,265,267,268,273,271,272,326,330,320,325,322,321,323,324,329,327,328,310,314,315,309,306,305,307,308,313,311,312,280,284,316,279,276,275,277,278,283,281,282,290,294,317,289,286,285,287,288,293,291,292,300,304,318,299,296,295,297,298,303,301,302,146,152,184,151,147,148,145,150,144,143,149,156,162,185,161,157,158,155,160,154,153,159,166,172,186,171,167,168,165,170,164,163,169,136,142,187,141,137,138,135,140,134,133,139,192,198,188,197,193,194,191,196,190,189,195,176,182,183,181,177,178,175,180,174,173,179,83,87,67,86,88,91,85,84,92,89,90,93,97,68,96,98,101,95,94,102,99,100,103,107,69,106,108,111,105,104,112,109,110,113,117,70,116,118,121,115,114,122,119,120,123,127,71,126,128,131,125,124,132,129,130,73,77,72,76,78,81,75,74,82,79,80,345,342,458,350,343,347,341,348,349,346,344,355,352,459,360,353,357,351,358,359,356,354,365,362,460,370,363,367,361,368,369,366,364,375,372,0,380,373,377,371,378,379,376,374,335,332,457,340,333,337,331,338,339,336,334,477,475,483,482,476,480,479,481,473,478,474,469,468,472,471,470,465,462,467,466,463,464,484,485,494,489,490,487,491,493,488,486,492,495,503,505,504,496,500,498,502,501,497,499,506,514,516,515,507,511,509,513,512,508,510,518,526,517,527,519,523,521,525,524,520,522,528,529,538,533,534,531,535,537,532,530,536","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_11(6,6).","submitted_at":"2026-04-28 19:36:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/539/8363408a17e3fce04de69e31f0601b2c9d430980242b8d752a7971280192c097.txt"},{"canonical_hash":"98b1ba0f36efa1cd471867446637619fdd6847d6120b06c901b2b73a3491b78d","size":539,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"8,6,54,9,0,4,3,5,1,2,7,364,362,378,363,358,360,357,361,359,355,356,64,62,65,56,55,60,59,61,57,58,63,49,47,50,41,42,45,44,46,40,43,48,19,17,51,10,12,15,14,16,11,13,18,29,27,52,20,22,25,24,26,21,23,28,39,37,53,30,32,35,34,36,31,33,38,447,449,451,445,448,442,443,444,450,446,441,397,399,452,395,398,392,393,394,400,396,391,407,409,453,405,408,402,403,404,410,406,401,417,419,454,415,418,412,413,414,420,416,411,427,429,455,425,428,422,423,424,430,426,421,437,439,456,435,438,432,433,434,440,436,431,273,274,310,270,269,271,278,275,277,272,276,283,284,311,280,279,281,288,285,287,282,286,293,294,312,290,289,291,298,295,297,292,296,263,264,313,260,259,261,268,265,267,262,266,319,320,314,315,316,317,324,321,323,318,322,303,304,309,299,300,301,308,305,307,302,306,229,231,246,227,224,232,223,230,226,228,225,199,201,247,197,194,202,193,200,196,198,195,255,257,248,253,250,258,249,256,252,254,251,239,241,243,237,234,242,233,240,236,238,235,209,211,244,207,204,212,203,210,206,208,205,219,221,245,217,214,222,213,220,216,218,215,184,188,459,187,192,183,191,189,186,185,190,134,138,460,137,142,133,141,139,136,135,140,144,148,66,147,152,143,151,149,146,145,150,154,158,461,157,162,153,161,159,156,155,160,164,168,457,167,172,163,171,169,166,165,170,174,178,458,177,182,173,181,179,176,175,180,116,117,70,120,119,118,114,121,115,122,113,126,127,71,130,129,128,124,131,125,132,123,76,77,72,80,79,78,74,81,75,82,73,86,87,67,90,89,88,84,91,85,92,83,96,97,68,100,99,98,94,101,95,102,93,106,107,69,110,109,108,104,111,105,112,103,390,388,380,389,384,386,383,387,385,381,382,374,372,375,373,368,370,367,371,369,365,366,344,342,376,343,338,340,337,341,339,335,336,354,352,377,353,348,350,347,351,349,345,346,334,332,379,333,328,330,327,331,329,325,326,473,474,483,479,478,481,477,475,480,482,476,462,463,472,468,467,470,466,464,469,471,465,484,485,494,490,489,492,488,486,491,493,487,496,495,505,501,500,503,499,497,502,504,498,507,506,516,512,511,514,510,508,513,515,509,519,518,517,524,523,526,522,520,525,527,521,537,529,538,533,532,535,531,528,534,536,530","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 d50b3565) × F_11(10,2).","submitted_at":"2026-04-28 19:40:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/539/98b1ba0f36efa1cd471867446637619fdd6847d6120b06c901b2b73a3491b78d.txt"},{"canonical_hash":"d524c229a8640c47d169e874cceac57e6140bb04d6c22587b8a543acedf48a24","size":541,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"540,0,472,114,165,263,468,142,285,110,536,523,161,280,379,259,131,489,464,219,229,138,216,90,281,210,126,106,108,399,532,26,368,519,182,89,157,319,339,276,349,222,375,149,336,255,444,128,127,166,330,485,363,204,460,317,462,215,11,409,225,293,497,134,97,344,212,505,302,86,443,294,277,490,48,206,68,430,122,137,78,102,342,442,104,283,386,395,65,435,528,457,254,22,365,49,364,533,286,515,59,228,178,80,92,85,324,269,153,20,46,315,155,487,335,235,482,272,21,396,345,150,139,218,190,40,371,301,451,145,73,271,332,243,198,251,148,176,440,95,253,124,140,60,123,463,183,162,402,504,326,168,422,481,240,171,359,312,374,200,432,231,456,502,71,313,252,488,458,87,129,211,115,4,7,539,419,405,245,70,221,476,267,289,527,383,493,233,94,130,403,372,93,343,226,340,132,334,208,466,413,501,348,306,298,52,434,82,446,390,439,258,53,290,232,96,273,50,491,486,400,143,44,455,275,202,180,257,64,187,508,426,175,378,118,75,492,133,8,423,74,154,387,98,376,230,338,417,310,438,394,57,100,495,147,279,261,512,382,496,427,391,234,314,61,151,516,431,318,520,524,389,385,453,296,381,250,160,449,18,526,292,361,517,377,45,414,246,360,199,156,529,303,445,282,473,14,511,197,522,55,173,288,224,34,357,174,19,513,76,291,373,88,163,41,81,103,410,320,260,242,535,351,356,266,408,195,16,425,152,42,304,525,311,181,299,268,433,441,483,366,278,331,109,469,33,475,10,478,192,507,538,31,193,17,358,518,392,424,51,341,5,169,146,270,284,135,223,220,214,112,30,186,323,353,36,448,170,367,321,15,297,101,509,447,494,72,141,346,287,69,461,369,537,63,84,328,24,159,239,25,37,194,305,77,247,35,99,144,467,406,172,244,316,436,506,256,91,2,238,249,480,531,120,407,347,136,470,352,56,450,262,119,54,404,459,184,191,179,79,12,158,380,421,398,499,265,500,121,38,322,393,300,164,530,521,418,203,307,477,201,177,236,23,295,167,107,264,355,412,429,308,185,437,370,113,479,196,1,362,428,9,274,227,116,327,452,325,105,498,350,465,67,28,29,309,39,471,248,510,6,484,411,474,454,58,188,83,384,503,125,397,534,207,205,27,111,416,189,117,237,13,3,329,354,32,43,514,415,62,388,401,209,420,241,333,47,66,213,337,217","comment":"Linear magma over Z/541Z (the prime field F_541): x ◇ y = 129x + 134y (mod 541).","submitted_at":"2026-04-28 16:28:46","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/541/d524c229a8640c47d169e874cceac57e6140bb04d6c22587b8a543acedf48a24.txt"},{"canonical_hash":"d89164d9a199e538561709e1bf1a2b3160acdbcbb8ef3e49087b6fd0aa0449b4","size":541,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,232,101,23,99,3,271,115,88,506,174,487,84,150,533,204,495,368,140,190,169,216,349,24,132,286,168,326,364,238,254,223,199,296,412,73,10,161,445,119,210,432,387,255,164,400,116,55,28,367,341,244,268,209,193,409,281,123,331,177,69,304,261,124,235,95,413,450,249,488,105,39,532,129,461,43,160,316,48,144,68,146,187,46,45,480,305,41,416,446,452,530,205,126,380,486,179,345,31,411,503,354,246,122,395,57,417,67,257,96,154,121,388,219,75,191,336,225,87,242,328,110,222,26,35,467,192,398,404,206,315,385,489,79,502,117,422,308,25,8,64,2,319,294,373,363,320,252,515,243,136,324,90,460,437,130,442,344,342,214,439,327,435,138,100,293,322,202,285,321,513,82,27,471,361,504,38,536,317,359,379,194,6,21,224,184,420,89,63,472,77,348,137,156,313,399,419,15,396,248,475,147,33,529,332,382,108,74,454,476,85,307,537,426,189,438,181,50,386,20,463,258,94,107,481,376,415,262,522,263,120,289,333,496,501,195,498,494,343,265,228,118,378,510,389,260,528,447,52,479,414,428,290,256,478,455,170,384,185,351,149,436,142,17,9,535,158,337,176,474,127,273,186,106,103,196,56,527,538,133,403,473,233,173,323,13,302,295,360,311,329,280,14,346,407,143,462,61,266,245,509,182,365,466,157,4,114,514,310,357,253,81,540,36,208,312,355,469,159,49,112,511,410,227,464,200,221,16,507,98,362,301,59,325,284,356,405,340,347,58,278,128,188,518,448,178,493,482,11,241,148,151,231,318,172,519,131,292,113,490,54,62,97,391,104,306,230,429,125,500,523,211,335,383,369,524,7,402,483,215,434,465,423,163,183,220,298,539,453,240,456,451,288,334,165,218,477,217,370,421,526,152,139,213,508,65,431,5,226,393,234,381,492,352,40,521,499,29,153,427,287,484,78,102,520,203,441,60,374,444,358,111,92,303,32,517,18,44,375,229,269,66,51,239,424,314,272,491,83,459,406,516,72,37,468,276,330,247,277,338,145,93,390,282,394,259,297,299,397,175,392,505,135,279,91,198,470,207,275,408,418,339,274,47,19,53,70,353,377,162,457,34,534,430,270,251,449,443,237,512,80,71,267,155,283,197,42,180,291,236,30,264,433,166,109,141,212,22,372,12,440,167,201,309,458,366,76,300,134,531,425,171,250,485,497,401,371,86,350,525","comment":"Linear magma over Z/541Z (the prime field F_541): x ◇ y = 229x + 313y (mod 541).","submitted_at":"2026-04-28 16:28:53","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/541/d89164d9a199e538561709e1bf1a2b3160acdbcbb8ef3e49087b6fd0aa0449b4.txt"},{"canonical_hash":"cdcafbb0fb32a27886d0babd7d9aa5f4f6578882abf9ec931aba8f2d032b6038","size":541,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,229,123,459,85,275,370,435,261,356,280,247,295,277,166,392,447,387,205,443,164,402,418,206,81,458,62,54,170,177,11,41,528,92,367,390,327,22,38,506,342,453,158,248,61,75,23,102,192,87,445,369,89,6,469,120,161,106,300,69,405,315,398,86,4,385,12,352,332,144,176,219,126,197,465,322,489,355,410,485,203,26,143,131,189,461,207,94,194,88,412,534,323,532,118,441,527,500,308,34,52,440,222,294,213,58,448,479,321,159,162,46,333,115,264,119,235,422,290,425,289,125,389,530,104,400,357,307,481,391,382,472,316,348,409,95,539,380,116,298,416,299,431,244,110,255,124,324,37,171,150,312,470,439,67,204,303,231,449,43,25,317,491,536,432,109,523,314,525,403,79,185,103,198,452,180,140,134,35,212,476,401,346,498,313,456,188,135,228,167,153,341,343,3,394,13,77,407,306,396,60,291,97,152,111,478,15,80,360,436,78,183,93,32,84,70,239,149,462,351,515,47,31,336,381,376,101,537,50,2,168,179,63,71,467,72,215,427,411,173,434,214,378,438,383,175,286,304,238,271,347,252,444,361,284,76,450,114,220,10,9,501,139,512,531,494,279,172,250,302,181,196,296,292,350,39,538,19,5,362,338,413,363,234,236,91,138,414,211,330,526,519,276,395,258,42,516,488,107,287,30,132,297,56,160,90,128,96,224,424,318,326,493,136,345,82,33,429,446,174,365,490,495,484,223,520,375,482,430,268,68,210,242,477,217,388,16,505,249,64,455,145,221,209,442,237,474,108,319,142,325,17,49,199,254,281,397,518,328,377,147,399,253,157,195,20,227,265,57,216,417,269,373,524,282,460,344,122,178,463,36,121,384,257,27,182,155,480,517,74,349,496,340,44,320,504,457,283,419,184,540,193,428,274,466,513,311,53,331,487,358,83,508,471,146,191,18,266,393,112,45,454,169,113,353,451,273,533,364,260,426,225,66,256,218,29,186,148,262,408,156,368,337,509,406,272,263,208,40,8,334,133,310,117,483,246,433,200,230,154,464,55,240,514,7,379,226,468,251,201,59,259,421,473,366,511,232,475,486,499,374,165,437,420,24,73,354,127,502,335,309,415,233,105,137,99,151,65,288,141,21,278,98,497,507,51,267,386,285,510,535,339,202,423,129,100,245,243,372,404,329,371,14,28,529,48,359,301,305,187,190,293,241,163,270,503,522,521,130,492","comment":"Linear magma over Z/541Z (the prime field F_541): x ◇ y = 141x + 401y (mod 541).","submitted_at":"2026-04-28 16:29:00","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/541/cdcafbb0fb32a27886d0babd7d9aa5f4f6578882abf9ec931aba8f2d032b6038.txt"},{"canonical_hash":"89d6f759ee0f09f94da8ee53f6cb58ca4c46bd732241ddaca4551a738aa8bae8","size":541,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,235,439,444,33,404,429,128,149,137,302,381,280,110,182,9,400,194,151,160,412,493,143,340,338,99,172,113,409,473,480,267,355,106,306,350,455,331,63,201,407,486,117,107,485,144,390,382,366,2,489,242,511,273,11,200,104,175,426,269,248,422,213,37,384,437,330,469,417,39,45,452,61,42,69,258,525,349,326,67,14,126,24,94,327,431,470,204,105,23,145,503,307,230,341,65,281,278,236,266,13,140,286,27,364,47,321,396,359,371,472,325,20,192,508,288,6,514,314,84,271,112,524,80,334,81,475,21,496,141,532,146,98,68,79,418,424,176,131,391,17,351,255,339,60,111,232,440,518,134,530,373,35,252,492,89,83,414,448,264,462,353,457,317,377,159,416,513,415,345,233,221,419,219,335,362,193,329,287,376,504,156,15,538,40,500,427,8,383,191,456,369,100,115,183,186,445,520,109,212,324,461,379,226,299,154,51,506,260,380,247,370,447,505,528,346,92,449,398,441,136,425,395,82,153,509,57,28,393,308,87,127,103,46,491,225,295,367,223,332,121,173,403,10,26,34,460,169,228,238,170,72,296,443,510,139,529,211,227,534,101,164,157,74,234,488,265,517,519,459,177,77,476,467,289,44,365,277,231,185,25,207,453,465,249,49,3,389,64,59,114,402,401,208,360,178,357,535,484,229,254,368,120,58,291,347,386,300,167,116,502,16,190,222,388,463,283,90,434,132,406,22,130,7,294,48,498,342,312,95,240,62,203,423,499,490,464,202,292,410,209,195,454,430,78,537,102,206,239,55,224,262,29,305,93,97,155,86,184,311,539,123,420,482,354,125,531,375,392,276,497,478,515,215,322,479,66,495,328,56,43,293,214,343,243,284,408,348,474,361,152,466,129,477,450,165,31,171,257,333,218,394,76,405,275,52,245,187,337,41,523,220,135,458,433,374,540,18,53,142,451,270,344,397,516,282,124,432,180,70,411,38,313,512,91,487,387,481,179,161,250,150,468,5,158,527,73,189,122,522,309,198,399,436,507,316,446,163,501,310,336,162,318,181,36,19,352,246,533,166,85,244,315,216,279,421,471,263,259,210,385,96,274,435,118,301,268,358,413,50,138,290,304,75,197,297,148,174,320,88,298,442,119,261,217,521,319,428,199,363,251,378,71,253,54,256,188,147,32,272,285,372,323,237,483,205,30,526,196,438,241,12,133,108,168,356,536,494,4,303","comment":"Linear magma over Z/541Z (the prime field F_541): x ◇ y = 125x + 417y (mod 541).","submitted_at":"2026-04-28 16:29:06","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/541/89d6f759ee0f09f94da8ee53f6cb58ca4c46bd732241ddaca4551a738aa8bae8.txt"},{"canonical_hash":"49533d344e44546b6e7cbc52ed8e301b190631d5b6002d4d01f1d6f123881b69","size":541,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,164,120,399,431,245,91,145,517,324,482,47,119,106,520,184,291,319,460,295,328,124,161,456,255,430,326,349,235,534,315,440,412,150,266,352,494,287,90,509,360,158,471,518,180,125,195,267,109,268,130,516,448,32,335,321,198,171,102,86,515,3,365,497,481,115,12,310,285,415,177,375,88,31,357,18,10,118,473,478,24,212,463,305,432,438,320,216,316,314,519,36,199,513,416,434,464,51,435,170,141,312,428,290,488,76,65,132,140,301,333,135,85,152,241,502,459,62,303,293,70,427,189,208,201,2,83,107,395,327,20,510,272,449,487,116,104,474,496,37,192,489,160,63,469,21,250,64,257,42,238,114,373,143,147,254,41,276,6,307,139,492,55,523,309,14,419,369,325,113,162,225,353,332,110,95,4,414,358,27,217,234,142,186,153,206,84,155,38,529,374,342,15,371,359,253,343,298,381,240,173,232,60,30,380,406,362,411,275,246,248,461,458,441,281,181,17,172,93,178,265,306,97,465,384,302,378,190,8,117,59,258,261,493,491,111,74,156,69,174,203,442,477,379,485,175,134,522,453,538,165,188,521,168,350,211,361,421,33,404,13,393,479,44,200,537,77,222,304,274,511,532,470,368,277,504,163,82,187,100,344,437,247,390,98,224,112,214,454,398,394,167,278,483,215,457,446,450,194,269,445,366,244,19,210,317,229,313,280,242,67,108,331,193,506,144,271,420,220,28,35,16,45,407,129,94,444,259,323,486,403,422,386,512,92,391,296,447,413,243,126,46,103,392,376,53,433,264,52,79,334,26,209,340,105,495,43,499,56,50,96,263,39,197,233,228,282,183,191,536,204,425,169,383,78,121,101,185,279,236,318,159,221,336,423,311,377,25,500,514,205,66,337,294,468,273,467,22,289,7,339,226,364,154,330,299,123,249,531,466,401,75,58,539,355,480,528,505,48,455,256,367,288,507,131,260,498,127,11,341,270,283,429,237,503,338,396,300,490,49,148,284,370,219,218,348,372,81,363,525,179,73,262,388,176,252,34,347,533,146,99,329,451,151,68,196,408,87,297,89,80,439,40,436,122,136,501,202,227,475,356,239,128,524,149,5,389,530,409,61,476,182,540,9,231,443,72,351,138,223,400,345,292,484,535,230,472,29,322,387,286,54,213,57,417,426,133,424,71,23,405,402,251,508,308,397,354,526,207,452,382,137,462,410,385,346,157,418,166,527","comment":"Linear magma over Z/541Z (the prime field F_541): x ◇ y = 49x + 493y (mod 541).","submitted_at":"2026-04-28 16:29:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/541/49533d344e44546b6e7cbc52ed8e301b190631d5b6002d4d01f1d6f123881b69.txt"},{"canonical_hash":"b0b07ba130f35dfa870d87dcb00197872e8165077e23b48c4a4f6fbead60f187","size":541,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"540,0,116,147,76,101,9,25,36,210,61,288,103,209,506,128,517,347,170,367,21,52,284,381,63,82,169,237,502,335,88,297,477,351,307,527,130,534,327,236,538,486,48,117,244,155,341,398,23,451,42,374,129,365,197,269,462,430,295,510,84,467,257,115,437,154,311,203,267,408,487,357,90,201,494,109,287,193,196,198,498,264,446,112,529,292,77,362,204,20,4,114,301,324,394,348,504,499,411,378,523,167,334,206,89,33,325,144,157,95,229,40,422,118,390,326,255,263,470,216,44,492,463,513,217,27,75,413,397,10,3,409,271,272,163,182,227,105,368,208,447,461,317,377,86,316,161,478,454,349,69,159,283,401,153,278,156,442,158,428,458,286,224,120,406,296,72,493,489,262,252,457,37,239,358,472,164,16,537,31,111,53,74,530,261,479,320,515,354,142,308,450,500,300,459,181,371,536,338,399,483,230,127,240,294,431,166,435,85,50,514,274,321,384,140,62,6,202,55,228,189,400,521,370,382,136,78,420,350,134,322,220,215,131,223,379,466,225,212,137,525,47,452,291,423,396,473,456,213,139,508,258,35,28,373,355,393,259,104,403,110,425,369,150,231,346,232,83,123,205,178,160,187,141,65,250,328,249,168,387,407,92,421,122,277,375,337,391,46,17,276,526,1,195,438,491,414,405,309,434,29,507,8,194,243,448,361,241,2,233,238,304,5,332,402,60,7,364,388,503,418,207,246,73,184,135,80,539,366,303,256,532,32,67,453,148,449,312,222,11,248,501,417,356,518,389,199,441,318,482,432,290,124,336,533,302,497,279,512,56,71,93,49,519,34,146,490,340,221,19,439,270,280,471,475,54,314,424,102,242,268,440,410,176,460,174,260,171,419,265,177,51,331,436,496,143,298,68,359,299,443,465,190,386,87,245,200,145,254,253,427,132,126,415,395,57,45,235,531,445,474,26,234,488,281,273,344,372,100,404,22,247,113,175,162,343,15,107,188,352,149,505,360,429,481,522,330,376,342,319,96,133,38,186,380,59,310,511,94,464,282,480,180,214,211,305,91,476,183,108,339,469,426,285,185,293,172,455,97,275,485,66,528,313,412,444,251,179,383,13,392,24,433,41,416,323,173,226,99,30,468,520,218,345,516,14,509,289,333,495,315,106,353,484,219,151,64,81,363,266,70,39,385,152,329,535,12,524,191,121,306,79,192,18,43,125,119,58,165,98,138","comment":"Linear magma over Z/541Z (the prime field F_541): x ◇ y = 129x + 536y (mod 541).","submitted_at":"2026-04-28 16:29:22","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/541/b0b07ba130f35dfa870d87dcb00197872e8165077e23b48c4a4f6fbead60f187.txt"},{"canonical_hash":"536c35ab92cce47b712d173f2c5524a94e1f96d787166abb9fb3f2e56ea0e134","size":547,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"546,0,469,279,394,136,204,503,319,14,61,266,129,247,428,414,244,519,482,379,529,238,100,174,54,271,172,292,353,16,339,328,169,544,444,4,407,540,304,525,363,499,163,517,25,149,8,391,522,371,105,254,6,233,217,310,187,114,484,457,264,456,253,516,3,291,378,265,278,452,472,463,332,222,374,458,229,134,450,336,288,27,424,485,88,20,442,294,493,361,74,115,476,63,316,514,447,435,296,188,30,345,179,351,474,282,158,311,142,108,235,184,112,438,39,218,409,260,382,387,98,440,381,234,178,315,441,449,471,252,216,7,303,338,99,427,203,242,286,255,397,126,388,421,257,151,147,106,299,69,383,355,154,532,59,372,284,268,261,511,213,42,495,523,349,45,410,47,465,402,488,392,276,301,219,139,418,192,195,9,542,433,40,191,401,41,531,150,241,251,439,437,281,434,360,26,221,290,113,370,498,543,270,518,13,1,185,96,399,10,207,164,83,198,236,18,67,196,33,500,160,131,109,103,37,193,272,364,507,119,143,412,334,419,94,526,307,71,312,210,23,140,274,305,306,506,159,82,12,220,240,541,275,348,283,298,396,302,177,408,141,29,475,87,228,277,263,5,24,406,352,528,128,393,167,445,211,35,180,341,322,489,51,454,313,249,346,367,91,403,76,170,72,57,31,49,224,466,537,329,308,385,189,80,79,48,366,340,527,86,297,81,209,411,102,17,95,369,436,190,138,46,510,354,420,426,448,386,183,350,513,293,335,462,515,309,390,524,327,173,413,502,317,330,201,496,226,545,144,430,64,538,343,43,117,55,120,122,477,467,376,214,358,175,508,357,116,225,326,512,509,101,365,536,75,50,166,262,176,239,273,93,362,32,206,269,359,530,194,487,494,58,146,285,215,380,38,157,295,73,423,373,377,483,104,162,443,171,481,60,468,520,110,416,21,77,324,533,478,245,132,124,89,404,460,155,123,415,161,156,486,92,535,356,121,429,501,461,425,368,85,384,56,248,34,405,28,347,505,70,118,130,197,90,289,250,432,300,44,267,68,125,337,314,259,107,344,62,19,133,451,455,232,148,539,15,237,246,135,52,491,152,65,320,199,479,230,490,231,258,431,504,84,534,459,323,480,422,145,205,165,325,375,342,200,389,182,137,208,78,223,181,321,127,227,395,11,22,333,36,66,398,497,280,400,417,464,212,153,256,202,470,97,111,473,446,492,287,331,2,186,521,453,168,53,243,318","comment":"Linear magma over Z/547Z (the prime field F_547): x ◇ y = 506x + 201y (mod 547).","submitted_at":"2026-04-28 16:29:32","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/547/536c35ab92cce47b712d173f2c5524a94e1f96d787166abb9fb3f2e56ea0e134.txt"},{"canonical_hash":"a8f059659597b89914738eab2a0ccc6bc8513b4e85df46344945e6ba5de987b3","size":547,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"546,0,239,541,366,459,11,100,493,424,51,266,249,398,216,342,85,179,128,384,167,518,393,195,376,260,525,307,343,105,469,373,201,38,306,436,21,263,511,281,294,203,110,509,520,225,322,53,503,77,387,73,117,524,434,78,470,267,221,46,61,473,500,401,328,199,276,158,433,89,140,26,259,428,390,32,103,243,408,34,421,190,330,329,226,526,101,523,112,4,352,375,449,256,169,185,95,426,193,155,514,148,189,16,233,319,116,175,138,165,194,35,62,204,394,542,348,164,162,156,177,420,65,97,92,72,528,300,455,392,326,214,403,361,285,119,137,404,205,170,33,471,264,129,386,441,132,495,517,358,270,136,219,491,370,174,535,482,272,407,125,172,317,76,457,496,456,166,353,27,118,39,217,187,115,237,228,464,242,430,479,210,502,356,153,75,383,333,296,284,312,107,211,318,130,93,320,102,159,504,106,52,41,82,316,127,254,507,360,538,446,207,232,143,302,310,31,350,292,311,321,465,273,171,178,149,331,402,521,261,12,15,475,336,291,389,289,151,283,224,304,345,124,84,181,413,213,13,208,212,188,371,120,349,427,409,47,295,519,240,453,406,341,7,530,325,488,544,412,147,235,70,30,258,531,414,332,508,297,28,271,215,63,257,391,79,22,180,513,246,145,309,25,43,87,382,109,461,485,481,397,486,29,454,346,274,83,154,497,133,301,139,5,141,74,202,399,396,534,248,18,69,299,451,444,123,192,59,49,142,88,415,48,152,293,505,480,173,265,98,234,527,277,54,344,425,314,368,231,432,364,58,355,280,56,484,369,50,134,146,71,121,337,303,94,229,483,206,157,515,191,501,510,377,460,490,423,380,411,91,439,183,223,184,338,55,445,275,23,122,209,262,447,108,218,492,286,543,96,244,222,282,168,2,279,537,198,417,443,478,20,287,381,135,99,19,487,64,8,182,150,255,334,354,359,327,36,450,429,435,437,86,269,10,477,324,419,467,438,288,448,378,57,506,400,462,298,241,305,466,42,357,458,442,529,176,113,90,388,374,250,363,253,499,67,68,463,37,418,24,516,365,416,6,545,532,410,290,351,160,431,126,472,66,17,227,200,323,308,494,540,197,340,161,251,379,335,3,339,230,315,60,498,247,236,372,476,144,131,238,536,405,163,44,422,474,111,196,367,81,45,252,533,114,468,9,245,440,1,278,452,347,80,489,14,522,539,313,40,220,362,395,186,104,268,512,385","comment":"Linear magma over Z/547Z (the prime field F_547): x ◇ y = 40x + 214y (mod 547).","submitted_at":"2026-04-28 16:29:40","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/547/a8f059659597b89914738eab2a0ccc6bc8513b4e85df46344945e6ba5de987b3.txt"},{"canonical_hash":"8dd366301fd56b07ef73b77fb10e7cfcd6e0e74726b7170f59d21418acc262f7","size":547,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"546,0,228,500,524,158,225,191,291,497,454,323,521,501,487,155,16,99,222,383,179,188,48,373,288,342,226,494,212,73,451,33,312,320,395,417,518,68,150,498,475,468,484,523,344,152,98,81,13,450,109,96,522,169,219,507,508,380,369,43,176,234,329,185,79,156,45,514,162,370,142,400,285,280,364,339,446,11,223,537,242,491,235,136,251,325,290,70,111,187,448,189,394,30,377,80,309,124,175,317,405,279,392,107,289,414,423,316,515,23,274,65,275,38,147,28,94,495,297,358,472,143,530,465,54,39,481,456,375,520,452,331,341,113,281,149,458,440,95,434,438,78,167,321,10,257,5,447,89,387,106,359,171,93,307,217,519,428,262,166,538,61,216,351,531,504,432,122,505,499,50,419,15,236,366,72,407,40,483,436,173,506,485,231,161,294,326,490,102,182,376,229,76,315,420,153,471,347,84,112,130,511,4,332,159,165,403,367,14,245,139,293,190,397,83,178,282,292,319,277,41,97,361,533,42,378,334,284,443,441,324,8,390,174,220,265,64,534,125,53,239,410,439,488,255,105,232,381,350,133,335,406,248,193,181,322,100,3,287,327,177,67,56,442,108,353,409,184,6,180,445,412,183,186,207,204,391,424,201,27,205,388,374,87,463,77,46,198,306,266,24,121,301,202,172,227,385,314,154,371,402,253,126,276,467,460,389,218,74,104,513,85,286,241,195,411,29,303,462,422,263,313,357,21,512,340,118,20,256,298,271,261,199,62,418,211,272,160,224,35,346,382,144,138,311,25,532,151,91,63,368,492,132,399,336,55,250,355,203,123,469,305,273,140,252,464,527,194,457,1,19,386,51,345,215,36,398,71,478,526,101,453,525,510,372,237,82,517,145,283,449,540,238,328,114,192,338,127,408,110,426,26,278,31,300,146,57,459,455,116,461,437,128,260,92,362,310,431,541,354,435,502,18,75,486,509,164,493,379,318,474,115,7,168,17,254,44,295,2,536,337,444,393,268,86,413,258,384,296,196,103,330,59,356,9,415,210,427,208,90,49,269,304,230,157,214,470,221,516,244,32,425,360,343,259,264,421,163,349,141,535,66,135,58,206,308,213,197,22,348,401,529,528,240,148,543,117,88,429,34,60,119,131,365,544,545,489,496,477,129,47,539,396,416,299,333,12,430,52,233,473,247,363,267,352,69,209,200,404,243,120,37,134,466,480,542,302,433,476,270,170,246,137,503,479,249,482","comment":"Linear magma over Z/547Z (the prime field F_547): x ◇ y = 506x + 305y (mod 547).","submitted_at":"2026-04-28 16:29:51","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/547/8dd366301fd56b07ef73b77fb10e7cfcd6e0e74726b7170f59d21418acc262f7.txt"},{"canonical_hash":"57c66b7e1213ee730fc264517d99e367550d994bd1453e4d3e538b54514828b7","size":547,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"546,0,518,148,323,248,401,410,46,81,103,461,206,425,215,313,381,402,466,285,488,475,266,320,61,413,230,14,70,39,36,128,186,526,207,45,271,528,8,490,293,412,280,494,121,196,43,279,446,289,218,467,85,523,531,178,455,350,374,524,371,388,513,540,173,142,331,507,62,203,380,430,126,483,333,478,525,340,295,124,16,161,217,510,3,37,299,54,506,66,51,304,378,143,2,450,251,257,12,409,73,74,272,30,470,60,328,545,336,262,431,411,260,301,155,485,361,373,329,281,358,209,193,477,318,48,345,341,426,377,395,171,136,164,312,261,447,473,58,421,185,344,235,355,511,286,288,354,138,99,283,28,330,532,145,243,18,369,509,406,533,67,414,400,72,111,315,151,520,319,372,233,22,96,439,292,311,407,451,129,436,349,27,453,183,113,396,332,519,423,255,347,106,303,112,75,529,56,214,335,458,390,459,448,127,47,365,268,275,83,445,234,133,495,385,79,141,405,117,366,236,296,216,310,115,543,24,247,408,302,290,223,166,265,360,444,134,139,4,489,163,246,64,94,180,454,282,179,41,393,383,482,150,118,146,52,231,50,182,225,200,119,424,1,389,108,417,131,35,317,116,534,252,187,278,343,443,157,226,76,172,508,149,480,90,515,160,291,316,273,9,322,11,105,159,109,391,474,484,82,6,191,363,7,135,23,337,122,398,177,98,93,535,269,356,125,314,199,211,499,338,65,452,156,219,307,205,327,457,158,496,100,38,476,404,92,325,536,42,184,359,456,88,168,539,368,481,367,244,305,15,438,34,153,212,147,256,346,514,428,241,487,154,274,544,68,258,527,170,542,498,220,201,530,137,63,324,463,228,429,110,224,152,31,491,505,26,442,497,418,460,59,334,104,441,239,69,192,140,97,263,197,195,420,264,326,253,276,512,17,382,538,352,221,123,95,130,486,468,517,250,254,89,227,386,284,300,267,190,238,464,270,394,114,210,351,502,522,353,245,91,237,19,379,71,181,33,32,500,53,348,342,541,175,102,469,213,10,25,415,13,208,78,176,419,308,120,57,165,204,249,434,387,242,392,167,521,471,294,21,416,240,101,132,449,422,479,462,433,465,259,364,5,440,432,44,376,309,198,537,188,84,287,162,403,189,503,202,399,49,437,362,86,298,435,277,169,77,80,29,55,321,504,20,229,357,384,397,194,375,493,472,222,306,516,297,370,144,40,87,501,492,339,232,107,427,174","comment":"Linear magma over Z/547Z (the prime field F_547): x ◇ y = 40x + 373y (mod 547).","submitted_at":"2026-04-28 16:30:02","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/547/57c66b7e1213ee730fc264517d99e367550d994bd1453e4d3e538b54514828b7.txt"},{"canonical_hash":"61d841ff5c27e1d32b2d18a4cf8a9fc663ef1a5bf6998f12e2a1f9c222bccc7f","size":571,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,197,51,165,23,365,372,474,336,375,161,408,170,139,268,254,59,64,266,348,209,87,52,516,391,439,37,253,357,47,454,98,458,412,499,383,242,455,406,30,385,111,248,256,366,563,531,84,193,94,127,505,335,430,67,453,235,158,334,413,464,131,102,174,396,477,337,282,450,460,224,149,172,524,132,497,540,196,363,179,515,243,216,562,545,324,281,43,409,570,228,509,462,143,79,96,397,424,49,360,182,377,74,31,313,58,353,330,405,279,269,463,156,11,215,355,568,312,283,232,153,339,416,272,533,249,154,39,308,560,374,550,65,97,185,437,429,292,204,496,225,274,423,202,33,231,277,564,273,513,176,434,503,258,210,50,518,553,390,167,447,530,525,435,449,320,351,227,342,194,155,8,191,184,489,346,517,378,467,466,528,71,387,63,541,211,29,485,3,130,380,506,561,555,120,57,294,483,38,314,388,512,426,558,7,198,180,554,160,147,136,457,246,68,66,137,122,539,299,491,48,331,212,152,419,187,422,24,217,448,16,81,28,164,134,159,438,69,15,83,501,239,459,270,4,508,77,261,10,475,325,436,240,289,552,472,114,465,205,123,511,265,221,151,384,12,507,101,219,100,544,162,410,352,5,21,307,344,90,175,275,492,190,310,444,119,407,569,121,411,105,14,452,140,510,195,262,189,359,401,200,338,34,213,201,117,322,319,112,233,484,22,251,146,36,60,80,192,326,288,223,479,20,461,565,188,214,441,287,428,367,417,389,91,55,527,536,349,425,347,290,418,110,403,76,173,177,218,323,125,104,329,85,250,559,493,54,433,316,53,183,468,115,56,169,305,538,498,259,82,234,297,264,362,128,309,181,445,116,415,548,440,32,72,124,350,522,296,2,364,519,135,252,520,27,93,431,551,148,285,306,142,399,358,354,542,222,291,237,109,166,244,168,70,61,521,557,208,236,186,247,106,260,395,369,99,280,486,13,404,107,145,373,546,526,502,327,432,488,18,414,293,138,141,298,382,394,500,157,381,220,178,370,443,376,44,321,271,480,286,230,302,103,226,300,263,129,371,26,456,356,556,163,126,487,471,171,229,343,78,566,400,567,41,478,203,332,402,446,45,304,386,284,295,6,86,108,421,255,144,9,476,442,543,42,470,451,278,420,35,549,481,535,257,340,315,345,494,547,482,267,398,490,241,368,238,333,393,150,514,25,118,73,303,318,532,534,427,276,317,328,341,88,361,379,473,92,245,46,207,133,504,17,113,523,301,89,95,40,199,311,469,19,495,392,75,529,206,537,62","comment":"Linear magma over Z/571Z (the prime field F_571): x ◇ y = 482x + 90y (mod 571).","submitted_at":"2026-04-28 16:30:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/571/61d841ff5c27e1d32b2d18a4cf8a9fc663ef1a5bf6998f12e2a1f9c222bccc7f.txt"},{"canonical_hash":"8907ebbc8074f8e44426499d8e4185e69ce1ddbb53f5684f5e114ef68c282444","size":571,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,323,249,489,437,376,155,458,89,426,496,369,273,455,309,56,332,120,200,279,344,198,201,66,399,536,523,42,507,374,164,457,263,415,404,287,257,377,352,382,360,356,291,267,378,527,70,348,124,313,373,93,380,253,4,244,568,298,341,400,521,105,411,308,549,259,569,530,453,92,188,160,207,19,370,17,284,503,509,146,38,268,256,519,335,76,532,486,18,395,35,346,62,228,115,197,165,108,194,402,466,340,544,412,275,388,113,196,154,26,116,121,95,328,266,87,52,439,314,305,37,139,451,47,320,269,438,506,365,363,242,492,329,258,422,225,134,85,289,543,454,141,79,151,127,542,372,467,67,433,178,44,485,393,330,245,102,231,319,286,431,282,487,497,281,206,172,390,132,306,292,25,343,236,552,129,45,371,297,475,110,214,560,570,114,375,556,29,136,210,491,290,106,397,182,471,131,145,293,229,333,367,442,51,41,443,270,125,158,392,548,406,169,232,39,490,339,272,513,21,211,96,288,312,525,302,8,97,128,531,295,386,261,419,168,46,403,202,204,60,277,430,159,493,5,300,483,144,153,278,498,533,427,167,541,567,562,472,315,357,559,227,436,251,98,179,20,241,355,554,326,358,561,389,508,185,481,234,464,40,86,522,174,73,417,429,484,307,63,57,445,463,209,465,368,321,349,538,7,84,123,420,103,147,250,551,75,239,180,137,122,405,450,414,219,539,212,152,285,187,516,81,217,428,130,195,199,221,191,216,418,126,243,254,424,11,325,213,61,488,77,90,238,512,362,359,183,440,361,566,171,502,148,9,434,208,50,265,535,12,316,215,276,43,410,162,447,446,233,135,401,495,33,118,218,301,133,347,310,176,501,435,235,334,48,71,546,83,547,138,262,246,510,324,143,318,91,99,30,117,416,470,112,119,350,22,80,260,150,3,23,192,534,553,109,345,248,384,317,74,271,364,381,408,461,511,540,205,283,336,459,500,462,441,327,398,53,383,190,59,177,104,303,68,161,480,28,193,425,473,111,413,524,224,69,448,58,170,226,342,518,478,31,82,6,391,36,456,14,460,10,482,230,452,528,477,32,72,181,387,331,504,2,515,385,78,252,557,27,264,354,474,34,322,514,142,550,338,505,351,222,499,237,166,280,16,54,13,175,444,366,94,65,15,247,220,203,432,520,156,223,409,184,555,107,88,353,469,449,311,421,526,468,189,565,558,24,255,563,476,545,537,157,304,163,64,407,423,299,101,529,100,517,494,173,396,274,55,337,149,186,294,140,379,564,479,49,240,296,394","comment":"Linear magma over Z/571Z (the prime field F_571): x ◇ y = 388x + 184y (mod 571).","submitted_at":"2026-04-28 16:30:20","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/571/8907ebbc8074f8e44426499d8e4185e69ce1ddbb53f5684f5e114ef68c282444.txt"},{"canonical_hash":"adc4372ffcd198c8165def134e6f51ff257022f6bb125e3e4e099b4dffb2d2ad","size":571,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,224,392,213,164,290,246,369,525,299,296,66,158,437,489,113,283,196,262,271,409,168,140,154,257,182,99,423,52,285,355,276,199,210,100,297,118,13,120,503,96,451,209,172,494,80,416,310,477,313,377,539,396,383,515,260,308,304,198,178,459,227,544,406,445,124,149,15,384,14,169,291,518,325,275,421,306,146,279,131,347,41,231,5,528,148,486,264,342,531,354,566,190,10,367,116,122,365,510,60,456,123,348,446,478,200,284,2,47,522,562,26,569,108,281,78,273,444,387,330,21,338,51,512,83,505,465,104,59,341,143,535,389,405,180,513,3,567,422,179,173,424,67,133,509,411,474,399,321,543,205,471,62,288,98,404,188,336,203,249,364,332,268,461,234,226,71,441,72,206,181,388,349,487,170,516,121,141,247,251,317,458,440,453,482,434,256,534,253,359,23,551,115,152,394,39,560,177,70,175,240,43,153,142,333,412,228,109,366,42,125,314,211,197,225,352,328,319,139,340,56,546,380,215,9,239,242,468,426,303,233,221,156,449,167,58,57,334,254,350,189,174,84,48,191,307,460,495,53,159,408,103,166,375,129,45,565,69,37,7,373,259,267,555,548,33,270,464,448,556,496,222,353,176,454,442,472,514,331,447,265,292,261,504,155,370,135,431,530,559,184,294,501,382,363,463,402,480,195,82,220,218,86,185,455,38,85,243,126,395,248,269,475,144,282,511,232,150,378,101,263,393,217,91,236,538,202,32,418,88,112,50,302,484,76,507,485,151,219,371,557,376,335,547,413,360,488,337,425,506,523,11,147,114,81,286,438,312,187,554,193,30,436,20,467,75,17,93,527,550,194,414,419,476,403,266,549,54,157,329,241,483,73,63,4,22,479,343,519,309,97,258,526,106,65,386,238,301,35,429,230,358,401,570,344,415,287,372,92,244,295,443,8,49,469,315,40,252,462,400,536,79,61,6,16,540,298,272,214,111,492,323,346,533,362,357,137,493,470,36,74,18,524,77,379,87,136,497,130,255,381,229,24,171,204,68,466,563,368,280,545,417,356,490,278,433,500,428,162,208,542,564,19,541,245,107,55,31,361,89,145,481,293,34,160,450,320,44,435,207,289,568,339,201,532,326,305,452,183,300,28,95,398,128,29,161,163,25,138,537,345,520,420,439,558,237,127,502,473,374,192,427,212,561,318,235,322,390,274,457,529,385,397,119,410,165,553,499,391,521,327,90,491,498,324,316,430,64,94,12,508,102,186,432,223,46,351,216,110,552,517,250,134,105,27,117,132,407,311,277","comment":"Linear magma over Z/571Z (the prime field F_571): x ◇ y = 168x + 404y (mod 571).","submitted_at":"2026-04-28 16:30:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/571/adc4372ffcd198c8165def134e6f51ff257022f6bb125e3e4e099b4dffb2d2ad.txt"},{"canonical_hash":"fbef18972a1845e6730b59c86ae2fe7bbb26a7dc7726b888033cc6a63e71af0e","size":571,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,325,76,551,135,239,553,535,50,486,48,311,68,480,434,9,324,46,504,490,220,41,281,203,66,363,130,190,161,440,329,432,410,75,554,204,86,292,322,12,85,102,498,316,193,502,121,528,452,15,550,24,218,447,27,543,558,291,199,279,342,457,308,276,183,248,64,134,481,330,529,184,522,128,321,180,227,399,508,264,159,521,138,338,238,259,38,327,421,52,59,11,164,283,408,442,299,88,127,318,80,552,221,293,28,185,422,186,84,510,429,261,230,166,381,320,34,424,534,168,148,150,83,235,176,101,208,233,357,496,242,253,179,95,99,49,191,194,458,509,443,231,497,119,347,105,118,405,494,226,450,466,485,388,352,251,428,548,21,315,402,375,93,346,216,55,398,514,2,47,555,25,482,260,222,169,192,389,556,271,104,477,454,507,545,197,310,270,332,287,229,113,340,501,61,378,90,117,30,306,263,143,536,67,103,200,181,165,511,209,120,403,390,62,404,212,516,158,224,173,479,476,334,384,380,464,538,527,211,72,518,493,386,461,520,368,435,433,453,249,139,319,35,96,451,515,546,144,225,369,471,137,470,313,8,506,267,365,33,412,373,14,157,123,568,449,296,344,337,136,42,323,544,523,53,423,236,444,549,223,114,512,465,36,413,237,469,244,45,196,419,349,533,468,561,23,172,57,564,484,6,273,258,312,162,503,309,265,300,167,243,406,217,478,31,213,387,370,297,37,7,371,489,269,360,125,147,44,155,446,475,415,78,351,488,566,326,505,205,219,331,39,294,149,195,353,26,333,201,335,250,268,524,420,266,361,40,286,285,393,82,418,188,542,383,111,152,427,359,438,51,364,499,280,228,284,430,234,348,376,557,379,391,73,547,124,115,58,32,416,202,112,392,304,175,532,540,290,463,303,141,20,146,109,10,411,16,65,339,81,425,100,467,3,198,537,174,436,314,43,245,163,372,206,362,500,417,17,207,560,355,278,526,531,395,401,154,240,282,13,559,129,60,187,177,232,22,170,341,210,539,97,374,445,562,407,156,354,189,377,541,4,356,171,570,456,71,289,256,92,474,69,441,122,277,160,89,382,254,495,56,455,307,517,462,472,345,414,274,298,567,525,439,116,110,246,241,563,70,275,492,302,132,215,77,491,87,448,530,328,29,151,459,252,483,288,182,385,140,366,54,350,301,126,295,394,431,305,426,18,178,5,255,247,460,19,107,397,487,131,317,343,400,409,262,358,106,94,272,91,63,519,145,569,513,565,214,79,336,153,74,142,437,396,98,257,473,133,367,108","comment":"Linear magma over Z/571Z (the prime field F_571): x ◇ y = 107x + 465y (mod 571).","submitted_at":"2026-04-28 16:30:38","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/571/fbef18972a1845e6730b59c86ae2fe7bbb26a7dc7726b888033cc6a63e71af0e.txt"},{"canonical_hash":"3fa81d278d06a28a45bc9b33162e171d1b00f0dc2587ce7411a0ec1ec40b7542","size":577,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"576,0,247,263,104,350,23,352,203,11,472,30,219,559,474,488,60,87,235,131,306,490,226,222,76,126,393,251,308,363,322,68,159,242,186,128,92,288,133,409,428,339,324,514,83,338,79,321,175,130,4,202,515,16,108,329,430,149,485,212,444,464,167,340,281,215,99,405,43,95,6,179,191,562,410,144,255,331,531,539,550,27,461,423,446,289,348,501,182,398,460,217,178,183,443,524,129,378,132,115,250,391,59,367,349,146,240,243,207,359,451,426,552,419,271,447,319,547,69,291,566,106,298,477,121,519,462,260,13,364,72,41,198,526,527,476,142,551,194,390,252,459,36,538,48,42,396,148,532,78,266,127,112,75,453,558,365,246,373,256,384,449,223,188,295,467,545,261,568,136,411,119,470,491,335,521,39,85,520,434,294,192,74,314,35,232,40,66,565,478,358,110,575,7,500,88,254,336,214,456,107,543,513,44,158,283,489,210,471,278,268,292,97,52,100,170,64,560,481,412,573,498,548,63,386,282,541,499,31,313,569,469,441,448,381,265,168,389,413,12,400,546,205,239,420,523,311,445,21,561,353,166,296,201,117,427,237,362,486,234,171,351,140,224,55,343,360,536,361,431,310,53,264,90,385,273,51,244,512,56,109,510,293,2,135,374,372,285,147,123,141,516,518,279,270,437,366,230,177,368,26,172,5,529,211,18,174,454,287,505,392,504,487,176,103,284,495,50,113,342,506,116,571,238,80,440,45,497,417,267,301,455,379,564,118,84,402,544,258,557,533,47,19,525,304,297,325,425,457,249,355,397,138,530,184,404,354,429,556,337,416,185,49,221,173,218,436,1,134,327,89,345,139,37,165,369,399,228,312,93,480,8,209,356,253,275,231,502,334,421,187,161,111,156,458,195,71,438,290,376,206,160,377,479,347,326,143,555,280,424,15,401,323,439,67,102,305,528,10,517,28,509,414,309,196,233,151,20,199,388,124,540,163,169,394,157,315,34,534,73,407,286,332,383,382,77,162,193,508,259,14,318,375,145,333,442,227,422,435,190,403,463,303,3,563,408,570,307,503,86,25,22,122,493,511,180,535,32,236,276,522,153,380,299,62,57,96,316,542,61,357,492,433,302,567,317,245,406,395,387,475,9,120,554,418,70,58,274,216,164,549,220,94,137,484,46,320,300,91,341,125,574,473,229,262,371,81,272,154,54,465,200,482,204,370,468,483,572,553,277,432,213,152,65,24,38,189,466,507,452,33,537,150,197,101,105,346,450,155,114,208,181,344,330,415,98,248,328,257,82,496,241,494,225,17,29,269","comment":"Linear magma over Z/577Z (the prime field F_577): x ◇ y = 363x + 67y (mod 577).","submitted_at":"2026-04-28 16:30:49","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/577/3fa81d278d06a28a45bc9b33162e171d1b00f0dc2587ce7411a0ec1ec40b7542.txt"},{"canonical_hash":"05709ff85f79497e8af4b127d681af3bee22a0a9c8ecd4ca3962190cf0d3a1a3","size":577,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"576,0,257,417,469,206,53,370,105,213,418,339,265,352,32,28,317,515,425,489,54,166,551,223,477,367,564,35,218,408,214,397,529,135,151,531,61,306,125,148,266,168,378,406,187,374,435,420,113,119,29,311,200,335,221,500,430,285,1,555,426,338,12,538,165,513,347,396,363,45,167,441,273,310,518,163,337,88,360,440,478,381,380,144,40,100,3,204,399,110,36,101,71,193,56,74,325,198,331,507,215,400,523,160,412,327,547,505,433,80,136,102,66,392,497,384,256,520,191,264,62,57,550,540,245,528,174,459,377,202,149,199,559,238,13,170,25,272,231,15,379,216,77,70,485,569,522,491,154,65,375,161,549,107,300,558,572,463,76,131,114,548,43,315,42,296,356,253,226,83,312,81,254,536,416,116,10,351,322,182,222,67,313,134,283,467,405,233,268,334,286,385,537,461,410,309,543,210,143,258,427,192,9,157,159,329,372,391,48,207,539,58,183,237,141,567,69,146,292,106,348,246,314,275,278,535,17,5,133,340,46,460,468,178,156,31,403,236,476,33,274,150,269,177,186,280,176,220,457,516,164,239,386,517,95,472,39,7,414,55,361,26,411,387,195,496,450,482,244,224,382,14,211,473,484,85,443,299,242,565,41,78,428,415,289,446,282,493,121,409,205,570,158,27,127,140,366,303,277,530,37,155,373,196,185,499,319,94,512,532,194,162,208,483,99,123,288,73,343,126,326,301,184,383,229,98,527,452,228,169,508,464,568,474,465,557,438,562,295,188,524,115,293,444,466,180,172,308,52,421,328,316,247,566,563,19,534,60,394,30,434,357,279,429,525,471,346,251,495,336,103,84,4,447,445,324,480,139,546,431,498,255,22,122,173,249,97,574,575,556,521,117,179,571,422,20,355,510,470,11,63,323,404,128,248,542,369,21,371,514,541,68,34,304,18,305,260,402,419,364,175,284,270,38,395,261,449,87,353,442,203,234,281,197,358,365,504,91,318,519,560,287,458,320,526,271,487,437,490,89,171,462,240,533,252,262,345,350,552,479,232,544,96,209,104,354,390,424,368,145,217,259,6,124,448,235,112,503,219,2,486,8,362,344,481,359,389,298,398,111,492,330,388,302,432,92,93,190,152,72,376,49,451,230,23,561,153,455,307,75,108,59,225,453,250,321,50,138,267,332,573,142,212,509,47,488,24,291,407,401,132,147,86,475,118,90,456,554,436,413,44,349,243,439,423,241,109,502,120,506,297,276,79,189,511,263,454,342,201,137,227,16,290,294,64,553,51,130,501,393,82,341,494,181,129,545,333","comment":"Linear magma over Z/577Z (the prime field F_577): x ◇ y = 363x + 296y (mod 577).","submitted_at":"2026-04-28 16:31:00","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/577/05709ff85f79497e8af4b127d681af3bee22a0a9c8ecd4ca3962190cf0d3a1a3.txt"},{"canonical_hash":"79749a320b3771d165eccf54c474e78f998cbece3971583b157964896a2c907e","size":625,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"622,623,616,596,496,621,607,587,487,600,550,450,580,285,480,620,603,583,483,617,556,456,597,298,497,606,513,413,571,221,471,586,191,31,486,624,613,593,493,614,547,447,594,288,494,612,510,410,560,225,460,592,180,20,492,615,563,463,544,275,444,509,164,4,409,595,23,289,183,495,610,590,490,604,543,443,584,295,484,619,516,416,577,238,477,599,197,37,499,601,573,473,551,261,451,506,171,11,406,581,33,286,193,481,527,427,534,208,434,522,154,94,422,528,87,202,147,428,382,387,388,394,611,553,453,591,281,491,602,507,407,574,228,474,582,194,34,482,605,570,470,540,265,440,512,160,1,412,585,30,292,190,485,523,423,524,215,424,529,144,84,429,535,83,209,143,435,389,383,395,384,517,258,417,559,137,77,459,578,56,239,116,478,319,356,338,377,198,297,38,609,503,403,564,235,464,589,184,24,489,618,576,476,557,278,457,519,177,17,419,598,36,299,196,498,533,433,531,201,431,526,151,91,426,521,93,206,153,421,386,393,381,391,514,248,414,542,134,74,442,568,47,222,107,468,302,347,328,374,188,294,28,572,100,40,472,505,10,252,170,405,332,310,365,340,125,260,65,32,192,608,567,467,554,268,454,502,174,14,402,588,27,282,187,488,530,430,520,205,420,532,140,80,432,525,90,212,150,425,392,390,385,380,504,255,404,549,124,64,449,575,43,229,103,475,309,343,335,364,195,284,35,579,117,57,479,518,16,259,176,418,339,316,378,357,138,277,78,39,199,541,73,266,133,441,346,373,301,331,161,251,0,46,106,293,536,436,537,218,437,539,157,97,439,538,96,219,156,438,399,396,398,397,511,241,411,546,131,71,446,561,53,226,113,461,306,353,321,371,181,291,21,562,114,54,462,508,7,242,167,408,322,307,368,354,128,274,68,22,182,545,70,272,130,445,352,370,305,320,165,240,5,52,112,290,369,323,355,304,115,224,55,69,129,243,500,245,400,552,120,60,452,565,50,232,110,465,312,350,325,360,185,280,25,569,104,44,469,515,3,249,163,415,329,303,375,344,135,264,75,29,189,558,76,279,136,458,359,376,318,337,178,257,18,59,119,296,366,333,341,311,101,231,41,66,126,253,148,214,88,82,142,207,566,111,51,466,501,13,246,173,401,326,313,361,351,121,271,61,26,186,548,67,262,127,448,342,367,308,334,168,254,8,42,102,287,372,330,345,300,105,220,45,72,132,250,155,204,95,89,149,203,19,179,276,555,63,269,123,455,349,363,315,324,175,244,15,49,109,283,379,336,358,317,118,237,58,79,139,256,141,211,81,86,146,213,2,162,267,230,362,327,348,314,108,234,48,62,122,247,145,200,85,92,152,210,9,169,263,236,158,217,98,99,159,216,6,166,273,227,12,172,270,223,233","comment":null,"submitted_at":"2026-05-14 05:27:42","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/625/79749a320b3771d165eccf54c474e78f998cbece3971583b157964896a2c907e.txt"},{"canonical_hash":"043c031024d2a68c992593b18dd4e5a3b4662586c1a2956c0d5e6e3595cbc830","size":637,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,120,412,535,253,138,362,326,227,220,499,448,206,28,462,240,292,332,555,455,419,591,368,157,312,233,2,221,133,121,500,363,407,443,327,536,207,228,254,3,537,364,222,208,408,134,229,444,122,255,328,501,4,123,409,538,256,135,359,323,224,223,502,445,209,5,218,136,124,497,360,410,446,324,533,210,225,257,1,534,361,219,211,411,137,226,447,125,258,325,498,30,175,213,267,593,528,434,398,492,557,199,287,247,31,558,529,176,194,435,214,288,399,268,242,493,594,32,269,436,559,243,215,530,494,283,177,595,400,195,33,178,216,270,596,531,431,395,495,560,196,284,244,34,561,532,179,197,432,217,285,396,265,245,496,597,35,266,433,562,246,212,527,491,286,180,598,397,198,36,318,272,418,150,483,599,563,519,279,454,204,354,37,280,484,319,449,600,273,205,564,413,355,520,145,38,414,601,281,356,274,479,515,200,320,146,565,450,39,321,275,415,147,480,602,566,516,282,451,201,357,40,277,481,322,452,603,276,202,567,416,358,517,148,41,417,604,278,353,271,482,518,203,317,149,568,453,6,345,264,511,569,172,185,155,468,605,475,168,381,7,606,173,346,476,186,259,163,156,512,382,469,570,8,513,181,607,377,260,174,470,164,341,571,151,477,9,342,261,514,572,169,182,152,471,608,478,165,378,10,609,170,343,473,183,262,166,153,509,379,472,573,11,510,184,610,380,263,171,467,167,344,574,154,474,12,438,337,142,524,117,575,611,297,488,304,373,402,13,489,617,439,305,576,338,374,612,143,403,298,525,14,144,577,490,404,339,192,299,375,440,526,613,306,15,441,340,139,521,193,578,614,300,485,301,376,405,16,486,118,442,302,579,335,371,615,140,406,295,522,17,141,580,487,401,336,119,296,372,437,523,616,303,18,393,508,129,545,114,386,350,249,581,189,544,429,19,582,116,394,190,387,503,539,351,130,430,250,546,20,131,388,583,425,504,115,251,540,389,547,352,191,21,390,505,314,548,313,383,347,316,584,315,541,426,22,585,126,391,187,384,506,542,348,132,427,252,549,23,128,385,586,428,507,127,248,543,392,550,349,188,24,294,457,370,235,236,551,587,308,464,334,421,159,25,465,237,289,329,552,458,422,588,365,160,309,230,26,366,553,466,161,459,238,310,423,290,231,589,330,27,291,460,367,232,239,554,590,311,461,331,424,162,29,369,556,463,158,456,241,307,420,293,234,592,333,630,42,50,47,43,53,46,48,52,51,45,44,49,631,88,81,84,87,86,78,83,85,80,89,79,82,632,92,93,96,101,97,100,95,98,91,90,99,94,633,60,58,54,65,64,61,57,63,55,62,56,59,634,74,66,69,68,72,77,76,73,70,67,71,75,635,108,102,104,110,112,103,106,113,111,107,109,105,636,618,627,622,629,623,621,619,624,628,625,626,620","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_13(9,11).","submitted_at":"2026-04-28 19:36:42","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/637/043c031024d2a68c992593b18dd4e5a3b4662586c1a2956c0d5e6e3595cbc830.txt"},{"canonical_hash":"7309c3a2be51c9bd201e1595f84996341216a2132e0d111885743542df503933","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,231,143,180,62,100,223,135,172,54,92,215,127,164,46,84,207,119,156,38,76,199,111,2,30,68,546,20,11,235,147,184,66,104,227,139,176,58,96,219,131,168,50,88,211,123,160,42,80,203,115,16,34,72,195,107,23,239,151,188,8,232,144,181,63,101,224,136,173,55,93,216,128,165,47,85,208,120,157,39,77,200,112,13,31,69,192,547,12,236,148,185,6,21,228,140,177,59,97,220,132,169,51,89,212,124,161,43,81,204,116,153,35,73,196,108,24,27,152,189,17,584,593,553,573,604,582,591,562,571,602,580,589,560,569,600,578,587,558,567,598,576,667,556,565,596,574,554,669,585,594,552,549,605,583,592,563,572,603,581,590,561,570,601,579,588,559,568,599,577,586,557,566,597,575,551,555,564,595,548,550,606,462,318,466,405,470,409,474,413,478,417,482,421,486,425,490,429,493,433,497,437,501,441,505,445,509,449,513,540,517,370,521,374,525,378,529,382,533,386,537,390,328,394,332,398,336,402,340,322,344,309,348,305,352,325,356,314,360,454,364,458,307,234,146,183,65,103,226,138,175,57,95,218,130,167,49,87,210,122,159,41,79,202,114,15,33,71,194,106,545,238,150,187,3,4,230,142,179,61,99,222,134,171,53,91,214,126,163,45,83,206,118,155,37,75,198,110,26,29,67,191,19,10,260,273,246,281,269,298,247,266,288,265,279,286,250,252,262,270,287,255,254,275,240,259,244,264,248,253,242,670,272,283,278,294,274,289,271,245,284,285,257,241,292,282,280,256,249,295,258,296,277,268,299,251,276,243,290,293,297,291,261,267,263,510,450,514,367,518,371,522,375,526,379,530,383,534,387,538,391,329,395,333,399,337,403,341,304,345,310,349,541,353,326,357,315,361,455,365,459,303,463,319,467,406,471,410,475,414,479,418,483,422,487,426,491,430,494,434,498,438,502,442,506,446,186,7,22,229,141,178,60,98,221,133,170,52,90,213,125,162,44,82,205,117,154,36,74,197,109,25,28,544,190,18,9,233,145,182,64,102,225,137,174,56,94,217,129,166,48,86,209,121,158,40,78,201,113,14,32,70,193,105,5,237,149,637,653,638,654,639,655,640,656,641,657,642,658,643,659,644,660,623,661,624,662,625,663,626,664,627,665,628,666,629,614,630,615,631,616,632,617,608,618,609,619,613,620,610,621,668,622,645,612,646,611,647,607,648,633,649,634,650,635,651,636,652,385,536,389,327,393,331,397,335,401,339,321,343,308,347,312,351,324,355,313,359,453,363,457,306,461,317,465,543,469,408,473,412,477,416,481,420,485,424,489,428,492,432,496,436,500,440,504,444,508,448,512,452,516,369,520,373,524,377,528,381,532,346,311,350,323,354,302,358,316,362,456,366,460,301,464,320,468,407,472,411,476,415,480,419,484,423,488,427,542,431,495,435,499,439,503,443,507,447,511,451,515,368,519,372,523,376,527,380,531,384,535,388,539,392,330,396,334,400,338,404,342,300","comment":"Tao(F_11,β=5) × F_61(ζ=9,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 16:54:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/7309c3a2be51c9bd201e1595f84996341216a2132e0d111885743542df503933.txt"},{"canonical_hash":"011faed280146ff19846baeb5218a4e6f76d64ad5b7e48950dd0b7fff21ca3a1","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,2,20,142,85,122,223,8,203,64,184,100,164,32,15,44,134,235,114,215,76,195,56,176,39,156,24,146,89,126,227,106,207,68,188,104,168,36,19,48,138,239,118,219,80,199,60,180,96,160,28,150,93,130,231,110,211,72,546,52,172,147,90,127,228,107,208,69,189,49,169,37,11,40,139,82,119,220,81,200,61,181,97,161,29,151,41,131,232,111,212,73,192,53,173,3,153,21,143,86,123,224,1,204,65,185,101,165,33,16,45,135,236,115,216,77,196,57,177,547,157,25,568,597,563,592,571,587,555,585,558,580,605,575,600,566,595,561,590,549,667,553,583,569,578,603,550,598,564,593,572,588,556,551,559,581,606,576,601,567,596,562,591,548,586,554,584,570,579,604,574,599,565,594,573,589,557,552,560,582,669,577,602,428,436,444,452,310,458,466,474,482,490,497,505,513,521,529,537,387,342,313,326,334,304,398,350,358,366,374,306,408,416,424,432,440,448,317,454,462,470,478,486,493,501,509,517,525,533,383,391,346,322,330,338,394,402,354,362,370,378,541,412,420,234,113,214,75,194,55,175,5,155,23,145,88,125,226,105,206,67,187,103,167,35,18,47,137,238,117,218,79,198,59,179,95,159,27,149,92,129,230,109,210,71,191,51,171,9,12,14,141,84,121,222,7,202,63,183,99,163,31,544,43,133,280,296,276,291,273,247,286,287,259,242,294,284,282,258,251,297,260,298,279,270,240,253,278,245,292,295,299,293,263,269,265,262,275,248,283,271,241,249,268,290,267,281,288,252,254,264,272,289,257,256,277,243,261,246,266,250,255,244,670,274,285,467,475,483,491,498,506,514,522,530,538,388,343,314,327,335,305,399,351,359,367,375,307,409,417,425,433,441,449,318,455,463,471,479,487,494,502,510,518,526,534,384,392,347,323,331,309,395,403,355,363,371,379,405,413,421,429,437,445,540,312,459,186,102,166,34,17,46,136,237,116,217,78,197,58,178,94,158,26,148,91,128,229,108,209,70,190,50,170,38,10,13,140,83,120,221,6,201,62,182,98,162,30,152,42,132,233,112,213,74,193,54,174,4,154,22,144,87,124,225,545,205,66,612,614,616,607,631,620,622,624,626,609,634,636,638,640,642,644,611,645,647,649,651,653,655,657,659,661,663,665,628,617,619,613,615,608,630,632,621,623,625,627,633,635,637,639,641,643,610,668,646,648,650,652,654,656,658,660,662,664,666,629,618,361,369,377,300,411,419,427,435,443,451,311,457,465,473,481,489,496,504,512,520,528,536,386,341,340,325,333,303,397,349,357,365,373,381,407,415,423,431,439,447,316,453,461,469,477,485,492,500,508,516,524,532,382,390,345,321,329,337,543,401,353,515,523,531,539,389,344,320,328,336,339,400,352,360,368,376,308,410,418,426,434,442,450,319,456,464,472,480,488,495,503,511,519,527,535,385,393,348,324,332,301,396,404,356,364,372,380,406,414,422,430,438,446,315,302,460,468,476,484,542,499,507","comment":"Tao(F_11,β=5) × F_61(ζ=9,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:00:23","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/011faed280146ff19846baeb5218a4e6f76d64ad5b7e48950dd0b7fff21ca3a1.txt"},{"canonical_hash":"1be0dfe46253d45c8f67d2726e5449fe5b2e8e70ebfb19a2fff02706629e4b4f","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,222,191,159,87,55,113,30,95,210,179,147,75,133,101,2,230,198,167,4,63,121,17,8,218,187,155,83,141,109,7,238,206,175,545,71,129,97,24,226,194,163,91,59,117,34,26,214,183,151,79,137,105,53,234,202,171,47,67,125,237,205,174,12,70,128,96,22,225,193,162,90,58,116,33,25,213,182,150,78,136,104,52,233,201,170,46,66,124,15,10,221,190,158,86,544,112,14,94,209,178,146,74,132,100,29,229,197,166,11,62,120,23,13,217,186,154,82,140,108,19,343,402,442,392,472,511,300,398,438,388,468,507,337,340,434,384,464,503,341,321,430,380,460,499,539,336,426,376,456,495,535,332,422,372,452,542,531,350,418,368,448,488,527,354,414,364,444,484,523,338,410,360,349,480,519,344,406,356,345,476,515,550,565,578,548,553,603,595,587,570,562,575,556,558,600,592,584,567,580,572,557,605,597,589,559,564,577,552,667,602,594,586,569,582,574,549,669,599,591,583,566,579,571,555,604,596,588,561,563,576,554,551,601,593,585,568,581,573,560,606,598,590,287,294,297,281,275,245,251,267,264,257,290,285,273,262,271,270,272,289,263,250,274,296,286,254,291,299,258,279,265,283,268,248,252,277,246,670,276,247,282,278,298,253,295,249,288,269,261,284,256,266,244,280,293,259,242,241,240,292,243,255,260,633,622,609,651,661,614,632,621,618,650,660,612,631,641,620,649,659,668,630,640,629,648,658,610,607,639,628,647,657,617,611,638,627,646,656,666,613,637,626,645,655,665,615,636,625,644,654,664,608,635,624,643,653,663,619,634,623,642,652,662,616,142,110,50,239,207,176,144,72,130,98,43,227,195,164,92,60,118,35,36,215,184,152,80,138,106,54,235,203,172,48,68,126,39,42,223,546,160,88,56,114,31,40,211,180,148,76,134,102,37,231,199,168,44,64,122,20,49,219,188,156,84,458,497,537,334,424,374,454,493,533,315,420,370,450,490,529,320,416,366,446,486,525,352,412,362,313,482,521,330,408,358,347,478,517,323,404,540,312,474,513,311,400,440,390,470,509,314,396,436,386,466,505,326,316,432,382,462,501,394,324,428,378,506,327,301,433,383,463,502,395,318,429,379,459,498,538,335,425,375,455,494,534,331,421,371,451,491,530,308,417,367,447,487,526,353,413,363,541,483,522,303,409,359,348,479,518,325,405,355,305,475,514,302,401,441,391,471,510,309,397,437,387,467,369,449,489,528,319,415,365,445,485,524,351,411,361,306,481,520,329,407,357,346,477,516,322,403,443,317,473,512,304,399,439,389,469,508,307,543,435,385,465,504,342,339,431,381,461,500,393,328,427,377,457,496,536,333,423,373,453,492,532,310,419,189,157,85,143,111,9,93,208,177,145,73,131,99,28,228,196,165,16,61,119,27,6,216,185,153,81,139,107,18,236,204,173,5,69,127,547,21,224,192,161,89,57,115,32,41,212,181,149,77,135,103,51,232,200,169,45,65,123,38,3,220","comment":"Tao(F_11,β=5) × F_61(ζ=20,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:00:38","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/1be0dfe46253d45c8f67d2726e5449fe5b2e8e70ebfb19a2fff02706629e4b4f.txt"},{"canonical_hash":"ad050b7424969ca6f69336d52d18a03ea6c40d5bbb6e4a1b9a9d576c5c3709b1","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,9,25,233,78,213,132,193,112,174,30,154,62,41,12,90,225,544,205,124,186,104,166,17,146,69,16,237,82,217,136,197,116,178,96,158,67,60,49,37,229,74,209,128,190,108,170,39,150,35,14,94,86,221,140,201,120,182,100,162,51,143,204,123,185,103,165,20,145,22,5,236,81,216,135,196,115,177,547,157,66,59,48,4,228,73,208,127,189,107,169,1,149,34,55,93,85,220,139,200,119,181,99,161,2,3,8,24,232,77,212,131,192,111,173,29,153,21,40,11,89,224,351,370,363,353,306,397,405,413,421,429,437,371,379,387,342,307,346,541,451,459,467,475,483,491,498,506,514,522,530,538,313,310,340,368,318,335,401,409,417,425,433,441,375,383,391,330,315,361,447,455,463,471,479,487,494,502,510,518,526,534,395,239,84,219,138,199,118,180,98,160,58,56,57,23,231,76,211,130,546,110,172,28,152,46,65,33,88,223,142,203,122,184,102,164,53,144,45,27,235,80,215,134,195,114,176,32,156,64,43,47,92,227,72,207,126,188,106,168,19,148,44,54,261,248,272,294,284,252,289,297,256,277,263,281,266,246,250,275,244,670,274,245,280,276,296,251,293,247,286,267,259,282,254,264,242,278,291,257,241,298,299,290,240,253,258,285,292,295,279,273,243,249,265,262,255,288,283,271,260,269,268,270,287,406,414,422,430,438,372,380,388,326,355,347,444,452,460,468,476,484,542,499,507,515,523,531,539,348,324,321,358,319,336,402,410,418,426,434,442,376,384,392,331,365,357,448,456,464,472,480,488,495,503,511,519,527,535,337,327,323,364,354,332,398,191,109,171,6,151,36,15,95,87,222,141,202,121,183,101,163,52,545,10,26,234,79,214,133,194,113,175,31,155,63,42,13,91,226,71,206,125,187,105,167,18,147,70,7,238,83,218,137,198,117,179,97,159,68,61,50,38,230,75,210,129,453,461,469,477,485,492,500,508,516,524,532,393,349,325,322,300,301,543,403,411,419,427,435,443,377,385,304,305,344,302,449,457,465,473,481,489,496,504,512,520,528,536,311,308,338,366,320,333,399,407,415,423,431,439,373,381,389,328,356,359,445,501,509,517,525,533,394,350,369,362,352,343,396,404,412,420,428,436,540,378,386,341,316,345,303,450,458,466,474,482,490,497,505,513,521,529,537,312,309,339,367,317,334,400,408,416,424,432,440,374,382,390,329,314,360,446,454,462,470,478,486,493,626,628,618,623,610,642,644,646,648,650,652,654,656,658,660,662,664,666,622,617,615,608,609,607,631,633,635,637,639,641,625,627,629,611,621,620,643,645,647,649,651,653,655,657,659,661,663,665,612,668,616,613,614,619,630,632,634,636,638,640,624,548,586,554,551,563,570,604,565,599,578,594,573,589,550,584,557,564,669,568,602,581,597,576,592,571,587,549,561,667,559,605,566,600,579,595,574,590,560,585,556,562,553,569,603,582,598,577,593,572,588,555,583,558,552,606,567,601,580,596,575,591","comment":"Tao(F_11,β=5) × F_61(ζ=20,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:00:55","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/ad050b7424969ca6f69336d52d18a03ea6c40d5bbb6e4a1b9a9d576c5c3709b1.txt"},{"canonical_hash":"e8c028d68b6ea8514ed48c4ab3aa232f03060d7e27eef11cfcbe8e2df7161ab4","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,2,9,42,38,34,30,11,3,57,53,49,239,235,231,227,223,219,215,211,207,203,199,195,546,188,184,180,176,172,168,164,160,156,152,148,144,22,18,95,91,87,83,79,75,71,67,63,59,142,138,134,130,126,122,118,114,110,106,102,98,6,19,15,92,88,84,80,76,72,68,64,60,143,139,135,131,127,123,119,115,111,107,103,99,547,10,23,43,39,35,31,27,1,24,54,50,46,236,232,228,224,220,216,212,208,204,200,196,192,189,185,181,177,173,169,165,161,157,153,149,145,582,581,580,579,578,577,576,575,574,573,572,571,550,549,551,558,557,556,555,667,548,554,560,559,669,606,605,604,603,602,601,600,599,598,597,596,595,594,593,592,591,590,589,588,587,586,585,584,583,553,552,570,569,568,567,566,565,564,563,562,561,517,462,369,400,537,482,389,420,314,501,446,440,344,521,466,373,404,347,486,393,424,328,505,450,540,309,525,470,377,408,351,490,317,428,332,509,454,361,313,529,474,381,412,355,493,321,432,336,513,458,365,396,533,478,385,416,325,497,308,436,340,238,234,230,226,222,218,214,210,206,202,198,194,191,187,183,179,175,171,167,163,159,155,151,147,545,21,17,94,90,86,82,78,74,70,66,62,58,141,137,133,129,125,121,117,113,109,105,101,97,4,5,45,41,37,33,29,14,26,56,52,48,248,284,277,250,293,267,256,294,253,240,255,265,261,290,246,269,266,268,274,259,279,287,292,245,670,275,262,257,249,289,244,298,296,299,276,260,291,295,285,271,283,264,286,297,263,280,247,254,278,243,282,281,272,241,258,288,270,242,251,252,273,333,510,455,362,305,530,475,382,413,356,494,322,433,337,514,459,366,397,534,479,386,417,326,498,541,437,341,518,463,370,401,538,483,390,421,315,502,447,441,345,522,467,374,405,348,487,394,425,329,506,451,358,306,526,471,378,409,352,491,318,429,190,186,182,178,174,170,166,162,158,154,150,146,7,20,16,93,89,85,81,77,73,69,65,61,544,140,136,132,128,124,120,116,112,108,104,100,96,12,8,44,40,36,32,28,13,25,55,51,47,237,233,229,225,221,217,213,209,205,201,197,193,626,634,613,655,612,639,616,660,646,622,630,665,651,627,635,607,656,642,640,617,661,647,623,631,666,652,628,636,668,657,643,641,610,662,648,624,632,618,653,629,637,614,658,644,620,608,663,649,625,633,619,654,611,638,615,659,645,621,609,664,650,469,376,407,350,489,316,427,331,508,453,360,311,528,473,380,411,354,492,320,431,335,512,457,364,543,532,477,384,415,324,496,307,435,339,516,461,368,399,536,481,388,419,300,500,445,439,343,520,465,372,403,346,485,392,423,327,504,449,443,301,524,422,312,503,448,442,310,523,468,375,406,349,488,395,426,330,507,452,359,303,527,472,379,410,353,542,319,430,334,511,456,363,302,531,476,383,414,357,495,323,434,338,515,460,367,398,535,480,387,418,304,499,444,438,342,519,464,371,402,539,484,391","comment":"Tao(F_11,β=5) × F_61(ζ=34,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:01:14","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/e8c028d68b6ea8514ed48c4ab3aa232f03060d7e27eef11cfcbe8e2df7161ab4.txt"},{"canonical_hash":"54f3ca59339d004fee97bb67fa820f36b9220943362c4ba8e9bd98a02e02af1e","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,235,211,188,164,34,73,142,118,38,23,239,215,546,168,144,47,87,122,98,27,77,219,195,172,148,51,91,126,102,31,81,223,199,176,152,55,95,130,106,32,12,227,203,180,156,59,65,134,110,20,10,231,207,184,160,16,69,138,114,4,70,139,115,3,42,236,212,189,165,21,44,143,119,547,24,74,216,192,169,145,48,88,123,99,28,78,220,196,173,149,52,92,127,103,5,82,224,200,177,153,56,85,131,107,17,13,228,204,181,157,60,66,135,111,11,2,232,208,185,161,581,575,549,667,606,600,594,588,555,565,582,576,548,556,669,601,595,589,583,559,568,577,571,557,566,602,596,590,584,560,569,578,572,558,567,603,597,591,585,561,570,579,573,553,551,604,598,592,586,562,563,580,574,554,550,605,599,593,587,552,564,345,486,314,428,446,513,308,363,474,375,416,361,501,329,540,462,529,404,349,490,335,432,450,517,336,367,478,379,420,339,505,340,389,466,533,408,353,493,343,436,454,521,396,371,482,383,424,307,509,318,393,470,537,412,357,497,325,440,458,525,400,234,210,187,163,33,72,141,117,37,22,238,214,191,167,545,46,86,121,97,26,76,218,194,171,147,50,90,125,101,30,80,222,198,175,151,54,94,129,105,41,84,226,202,179,155,58,64,133,109,19,15,230,206,183,159,62,68,137,113,9,6,244,254,250,279,295,258,255,257,263,248,268,276,281,294,670,264,251,246,298,278,293,287,285,288,265,249,280,284,274,260,272,253,275,286,252,269,296,243,267,292,271,270,261,289,247,277,259,291,241,240,262,297,273,266,299,282,256,245,283,242,290,467,534,409,354,494,322,437,455,522,397,372,483,384,425,541,510,319,394,471,538,413,358,498,326,441,459,526,401,346,487,315,429,447,514,309,364,475,376,417,362,502,330,386,463,530,405,350,491,306,433,451,518,337,368,479,380,421,333,506,341,390,186,162,39,71,140,116,36,43,237,213,190,166,7,45,544,120,96,25,75,217,193,170,146,49,89,124,100,29,79,221,197,174,150,53,93,128,104,40,83,225,201,178,154,57,63,132,108,18,14,229,205,182,158,61,67,136,112,8,35,233,209,615,640,645,662,630,624,652,610,637,642,659,613,629,649,666,634,621,656,616,641,646,663,631,618,653,609,638,643,660,608,622,650,625,635,611,657,617,627,647,664,632,619,654,668,639,644,661,607,623,651,626,636,614,658,612,628,648,665,633,620,655,419,304,504,305,388,465,532,407,352,492,342,435,453,520,543,370,481,382,423,321,508,317,392,469,536,411,356,496,324,439,457,524,399,344,485,313,427,445,512,310,385,473,374,415,360,500,328,443,461,528,403,348,489,302,431,449,516,303,366,477,378,515,301,365,476,377,418,316,503,331,387,464,531,406,351,542,300,434,452,519,338,369,480,381,422,334,507,332,391,468,535,410,355,495,323,438,456,523,398,373,484,312,426,444,511,320,395,472,539,414,359,499,327,442,460,527,402,347,488,311,430,448","comment":"Tao(F_11,β=5) × F_61(ζ=34,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:01:30","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/54f3ca59339d004fee97bb67fa820f36b9220943362c4ba8e9bd98a02e02af1e.txt"},{"canonical_hash":"5530ca7ad10917bf4bf7eb954d1dd8d5a8ec23226e552db0cf393119495de146","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,5,178,124,213,90,75,146,9,182,128,217,47,79,150,94,186,132,221,51,25,154,98,190,136,225,55,29,158,102,193,140,229,59,33,162,106,197,544,233,63,37,166,110,201,116,237,16,41,170,11,205,82,67,20,45,174,120,209,86,71,143,232,62,36,165,109,200,115,236,15,40,169,14,204,81,66,19,44,173,119,208,85,70,1,4,177,123,212,89,74,145,8,181,127,216,93,78,149,547,185,131,220,50,24,153,97,189,135,224,54,28,157,101,192,139,228,58,32,161,105,196,433,441,417,387,348,356,364,321,447,455,463,471,479,487,494,502,510,518,526,534,368,376,326,334,342,306,395,403,411,421,429,437,413,383,391,352,360,317,541,451,459,467,475,483,491,498,506,514,522,530,538,372,380,330,338,346,310,399,407,312,425,239,18,43,172,13,207,84,69,22,2,176,122,211,88,73,144,7,180,126,215,92,77,148,3,184,130,219,49,23,152,96,188,134,223,53,27,156,100,546,138,227,57,31,160,104,195,142,231,61,35,164,108,199,114,235,65,39,168,112,203,118,292,260,253,245,281,243,266,256,262,272,249,287,251,259,254,298,244,268,263,242,276,288,255,285,269,271,277,264,286,295,278,258,296,293,297,246,247,267,670,273,240,241,291,299,290,252,284,289,280,270,283,265,275,279,261,294,282,248,257,274,250,365,322,448,456,464,472,480,488,495,503,511,519,527,535,369,377,327,335,343,307,396,404,412,422,430,438,414,384,392,353,361,318,444,452,460,468,476,484,542,499,507,515,523,531,539,373,323,331,339,302,303,400,408,313,426,434,442,418,388,349,357,191,137,226,56,30,159,103,194,141,230,60,34,163,107,198,113,234,64,38,167,111,202,117,238,17,42,171,12,206,83,68,21,46,175,121,210,87,72,545,6,179,125,214,91,76,147,10,183,129,218,48,80,151,95,187,133,222,52,26,155,99,528,536,370,378,328,336,344,308,397,405,314,423,431,439,415,385,393,354,362,319,445,453,461,469,477,485,492,500,508,516,524,532,366,374,324,332,340,304,543,401,409,419,427,435,443,381,389,350,358,315,300,449,457,465,473,481,489,496,504,512,520,345,309,398,406,311,424,432,440,416,386,347,355,363,320,446,454,462,470,478,486,493,501,509,517,525,533,367,375,325,333,341,305,394,402,410,420,428,436,540,382,390,351,359,316,301,450,458,466,474,482,490,497,505,513,521,529,537,371,379,329,337,651,653,655,657,659,661,663,665,624,626,614,616,618,609,631,633,623,636,638,640,635,628,630,620,622,611,642,644,646,648,650,652,654,656,658,660,662,664,666,625,613,615,617,608,607,632,634,668,637,639,641,627,629,619,621,610,612,643,645,647,649,548,593,579,602,560,554,585,572,594,580,603,561,555,586,573,595,581,604,562,556,587,574,596,582,605,563,557,588,575,597,576,606,551,558,589,564,598,568,669,552,559,590,667,599,569,565,553,549,591,577,600,570,566,583,550,592,578,601,571,567,584","comment":"Tao(F_11,β=5) × F_61(ζ=58,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:01:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/5530ca7ad10917bf4bf7eb954d1dd8d5a8ec23226e552db0cf393119495de146.txt"},{"canonical_hash":"6bf49a0e13080778d3618f7b52a9e02e92bdf880aee4d5da23f05be29fc31367","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,6,30,111,236,220,204,189,173,157,18,64,48,143,127,10,547,34,115,99,224,208,192,177,161,145,68,52,80,131,15,91,38,22,103,228,212,196,181,165,149,72,56,84,135,119,95,42,26,107,232,216,200,185,169,153,76,60,77,139,123,155,20,62,46,141,125,12,8,32,113,238,222,206,191,175,159,545,66,50,78,129,17,89,36,117,101,226,210,194,179,163,147,70,54,82,133,13,93,40,24,105,230,214,198,183,167,151,74,58,86,137,121,97,44,28,109,234,218,202,187,171,45,140,124,2,7,31,112,237,221,205,190,174,158,3,65,49,544,128,11,88,35,116,100,225,209,193,178,162,146,69,53,81,132,16,92,39,23,104,229,213,197,182,166,150,73,57,85,136,120,96,43,27,108,233,217,201,186,170,154,19,61,341,402,507,472,375,383,314,333,535,499,464,367,442,398,325,527,542,456,359,434,390,414,519,484,448,351,426,305,406,511,476,321,387,300,337,539,503,468,371,379,309,329,531,495,460,363,438,394,418,523,488,452,355,430,304,410,515,480,444,347,422,575,606,602,598,594,590,586,553,564,560,582,578,551,548,557,576,669,603,599,595,591,587,583,565,561,568,579,552,571,558,554,573,604,600,596,592,588,584,566,562,569,580,667,572,559,555,574,605,601,597,593,589,585,567,563,570,581,577,549,550,556,262,245,277,279,249,284,246,269,250,253,270,267,271,296,297,287,670,281,291,290,265,273,264,259,244,275,241,278,243,285,283,251,256,268,242,298,252,282,288,266,255,260,295,240,293,286,263,257,280,299,247,289,254,261,272,294,276,258,292,248,274,639,630,635,661,652,643,620,637,609,633,659,650,612,629,668,617,666,657,648,625,627,610,615,664,655,646,623,640,631,613,662,653,644,621,638,607,634,660,651,642,619,636,618,632,658,649,626,628,611,616,665,656,647,624,641,608,614,663,654,645,622,203,188,172,156,21,63,47,142,126,9,4,33,114,239,223,207,546,176,160,144,67,51,79,130,14,90,37,118,102,227,211,195,180,164,148,71,55,83,134,1,94,41,25,106,231,215,199,184,168,152,75,59,87,138,122,98,5,29,110,235,219,482,446,349,424,343,404,509,474,319,385,316,335,537,501,466,369,540,302,327,529,493,458,361,436,392,416,521,486,450,353,428,307,408,513,478,303,345,420,339,400,505,470,373,381,311,331,533,497,462,365,440,396,323,525,490,454,357,432,388,412,517,530,494,459,362,437,393,417,522,487,451,354,429,308,409,514,479,541,346,421,340,401,506,471,374,382,317,332,534,498,463,366,441,397,324,526,491,455,358,433,389,413,518,483,447,350,425,344,405,510,475,320,386,313,336,538,502,467,370,378,312,328,372,380,310,330,532,496,461,364,439,395,322,524,489,453,356,431,543,411,516,481,445,348,423,342,403,508,473,376,384,315,334,536,500,465,368,443,301,326,528,492,457,360,435,391,415,520,485,449,352,427,306,407,512,477,318,377,419,338,399,504,469","comment":"Tao(F_11,β=5) × F_61(ζ=58,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:02:05","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/6bf49a0e13080778d3618f7b52a9e02e92bdf880aee4d5da23f05be29fc31367.txt"},{"canonical_hash":"3adec767ec0b9ffdeb996ef7002d3392cdd3a54132ae165d3797ae4747d5da75","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,37,17,50,42,11,21,2,30,8,10,40,35,22,54,34,4,20,14,23,43,57,13,46,39,44,41,18,52,38,28,19,15,9,59,49,27,48,45,5,3,25,7,26,16,47,55,12,32,33,6,29,58,36,51,665,56,31,53,24,129,151,145,140,168,147,162,153,173,176,120,128,171,157,163,158,124,142,161,132,179,138,152,174,159,122,166,170,146,165,131,141,175,143,160,123,169,150,137,126,148,172,133,167,144,149,127,135,178,154,164,139,136,121,134,155,661,130,177,125,156,68,96,65,62,91,92,107,75,80,89,87,106,99,83,108,84,71,118,74,101,70,61,78,81,85,79,111,117,113,110,67,63,88,119,73,97,116,95,115,86,93,100,102,112,64,94,105,104,69,76,109,60,114,98,103,77,664,66,90,72,82,577,545,564,584,580,593,574,556,597,594,558,543,572,586,562,549,569,553,575,566,551,589,546,588,573,568,567,541,587,542,540,550,565,570,554,592,548,561,585,571,552,557,595,596,555,576,599,579,583,563,547,578,582,559,590,598,663,544,591,560,581,485,500,482,516,495,496,528,511,503,493,491,527,520,506,529,507,488,539,510,522,487,514,501,504,508,502,532,538,534,531,484,517,492,481,509,518,537,499,536,490,497,521,523,533,480,498,526,525,486,512,530,515,535,519,524,513,670,483,494,489,505,255,242,240,267,298,278,261,285,256,284,252,254,276,246,286,292,245,258,260,264,287,269,295,263,272,275,270,277,268,290,274,282,259,265,253,243,297,281,299,271,249,257,279,251,280,266,273,293,262,248,244,250,283,296,241,289,668,294,247,291,288,326,341,323,357,336,337,309,352,344,334,332,308,300,347,310,348,329,320,351,303,328,355,342,345,349,343,313,319,315,312,325,358,333,321,350,359,318,340,317,331,338,302,304,314,322,339,307,306,327,353,311,356,316,301,305,354,667,324,335,330,346,372,405,402,371,408,411,375,396,417,384,397,391,366,416,376,392,370,388,386,400,390,379,374,362,373,401,382,406,415,367,413,393,385,389,398,394,378,369,363,404,361,399,419,383,387,403,364,365,412,380,377,410,409,395,414,381,666,418,407,368,360,217,207,203,221,214,220,204,180,232,235,187,185,205,236,194,237,209,195,181,199,183,223,192,226,211,201,200,212,227,191,224,182,198,229,196,208,186,193,230,210,184,190,239,231,197,228,219,213,222,202,206,218,216,189,238,233,660,234,225,188,215,640,635,626,659,641,646,602,619,658,657,604,609,601,644,616,611,636,621,633,628,613,650,614,649,652,624,625,630,600,617,651,606,629,632,620,607,612,615,643,605,610,603,656,608,618,634,645,642,653,627,631,639,637,623,647,655,662,654,648,622,638,459,454,428,468,470,477,456,479,438,472,429,437,431,462,443,421,467,433,455,475,425,478,444,458,452,449,450,432,465,446,466,436,448,424,422,453,435,441,463,451,434,439,426,473,440,423,469,460,457,447,442,420,476,445,427,471,669,474,464,430,461","comment":"Tao(F_11,β=9) × F_61(ζ=9,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:02:21","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/3adec767ec0b9ffdeb996ef7002d3392cdd3a54132ae165d3797ae4747d5da75.txt"},{"canonical_hash":"5befff131d5bf56bff8bc80d9c8a80c9eff0438375737bead293545f28f3af37","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,42,50,19,46,3,37,12,33,35,27,17,4,54,16,29,45,39,5,20,57,38,23,26,21,18,43,52,25,10,44,40,34,59,49,9,48,22,30,28,7,32,8,41,24,55,47,14,15,31,11,58,2,51,665,56,13,53,6,36,168,132,155,123,172,173,175,151,176,135,179,159,146,148,147,122,129,174,161,144,153,169,152,133,150,140,128,124,139,171,156,136,130,120,157,127,167,126,134,165,160,162,141,131,166,178,164,143,137,149,154,125,158,163,138,661,170,177,121,145,142,91,116,61,86,87,102,65,75,84,72,101,94,78,103,79,69,113,82,96,68,63,73,76,80,74,106,112,108,105,118,60,83,114,81,92,111,90,110,71,88,95,97,107,115,89,100,99,67,66,104,64,109,93,98,62,664,117,85,70,77,119,549,540,576,585,574,547,582,588,568,584,561,552,577,553,559,563,558,541,596,545,591,566,594,551,579,580,546,593,567,592,599,595,543,557,564,560,554,578,550,562,583,569,587,581,565,573,586,575,597,548,542,572,555,590,570,663,598,589,556,571,544,486,528,502,480,482,514,497,489,539,537,513,506,492,515,493,534,525,496,508,533,500,487,490,494,488,518,524,520,517,530,503,538,526,495,504,523,485,522,536,483,507,509,519,527,484,512,511,532,498,516,501,521,505,510,499,670,529,481,535,491,531,240,241,294,252,265,298,261,285,260,281,283,263,277,262,246,276,287,297,291,253,266,249,290,269,272,267,264,295,244,271,258,296,292,282,242,251,257,299,268,288,286,255,280,256,293,270,247,289,274,275,279,259,250,278,243,668,248,273,245,254,284,341,323,357,336,337,309,352,344,334,332,308,300,347,310,348,329,320,351,303,328,355,342,345,349,343,313,319,315,312,325,358,333,321,350,359,318,340,317,331,338,302,304,314,322,339,307,306,327,353,311,356,316,301,305,354,667,324,335,330,346,326,391,390,408,406,410,385,400,404,375,413,384,394,379,376,369,365,361,388,381,366,403,380,417,386,419,372,399,362,412,416,398,411,395,387,392,383,371,409,370,397,382,414,373,389,360,363,364,367,401,377,407,374,396,418,402,666,415,405,393,378,368,204,235,213,211,217,189,222,238,226,206,197,188,214,194,183,185,193,190,218,199,228,220,231,201,237,236,202,230,221,229,200,219,191,186,203,239,195,215,187,198,205,227,209,223,184,216,210,212,234,181,224,180,196,233,207,660,208,232,192,182,225,600,640,637,606,635,624,626,628,658,641,659,604,634,616,622,608,615,612,657,620,654,643,649,625,655,656,609,650,644,653,619,603,611,602,613,621,610,633,601,607,642,630,629,627,623,636,605,638,639,614,631,646,617,651,648,662,647,652,618,645,632,430,465,421,470,435,451,454,467,457,445,450,442,463,447,449,452,440,453,428,448,474,455,456,477,466,437,434,475,436,459,429,476,424,446,431,433,439,432,444,423,468,426,472,469,438,461,427,462,478,443,420,422,441,464,471,669,458,473,425,460,479","comment":"Tao(F_11,β=9) × F_61(ζ=9,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:02:42","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/5befff131d5bf56bff8bc80d9c8a80c9eff0438375737bead293545f28f3af37.txt"},{"canonical_hash":"a66f42c0dbb589d2e4926b34c46ae1a8f1a1bae5b52bcb2d49bdf45acbfe2517","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,48,14,39,52,15,32,42,40,5,18,53,29,21,16,13,7,33,9,36,43,59,51,41,27,20,6,35,50,19,49,665,54,24,55,30,11,25,22,46,56,17,38,31,4,28,12,8,3,26,34,58,23,10,45,47,37,2,57,44,129,139,167,177,148,145,162,160,155,137,143,152,151,136,159,144,176,138,179,156,120,161,126,163,127,146,153,149,123,132,141,168,661,140,122,130,142,135,133,178,124,158,150,173,154,175,147,166,128,125,171,164,169,170,131,165,174,172,157,121,134,95,89,73,102,118,115,108,79,99,64,113,62,60,63,78,114,101,65,85,75,105,80,88,109,93,116,97,119,67,103,91,74,664,90,66,96,92,87,104,84,100,77,61,112,98,107,117,72,94,82,110,70,68,69,81,71,106,111,76,83,86,540,592,591,559,583,551,586,571,557,595,599,593,575,547,543,596,573,549,578,579,553,560,570,566,590,544,555,563,567,545,588,581,663,582,587,542,568,564,556,562,589,565,569,561,554,580,577,550,574,597,558,546,576,594,598,548,541,572,585,552,584,524,518,488,494,510,507,500,533,528,516,505,514,513,515,532,506,493,517,539,529,497,534,482,501,522,508,526,511,491,495,520,489,670,519,490,525,521,480,496,538,492,531,512,504,527,499,509,487,523,536,502,485,483,484,535,486,498,503,530,537,481,246,245,299,287,261,273,288,296,264,262,286,241,274,293,256,243,284,278,297,280,290,265,249,272,263,255,242,277,289,271,240,270,668,275,252,276,294,282,253,250,258,267,244,260,295,285,292,283,279,248,254,298,269,251,281,257,259,291,247,268,266,341,335,305,311,327,324,317,350,345,333,322,331,330,332,349,323,310,334,356,346,314,351,359,318,339,325,343,328,308,312,337,306,667,336,307,342,338,358,313,355,309,348,329,321,344,316,326,304,340,353,319,302,301,300,352,303,315,320,347,354,357,400,394,371,363,380,389,414,390,401,391,366,384,383,385,377,367,364,362,412,368,369,361,393,403,407,378,373,381,397,365,415,395,666,411,396,372,404,405,419,417,398,376,382,418,360,413,379,375,408,392,406,387,409,399,386,388,370,410,402,374,416,196,226,192,195,222,189,219,210,235,191,183,194,208,182,204,181,206,187,217,212,180,229,225,199,193,227,232,202,200,236,221,214,660,215,220,237,201,203,233,228,234,198,224,230,186,213,216,188,207,231,205,238,209,239,184,190,197,211,218,185,223,653,606,622,654,646,613,647,634,652,656,607,621,632,659,650,616,636,612,639,642,604,601,605,627,629,600,655,626,624,608,643,638,662,637,644,609,623,625,610,617,630,628,618,619,611,641,640,603,635,615,649,658,631,620,602,657,651,633,648,614,645,421,452,472,473,468,420,439,461,471,424,432,454,463,479,445,440,462,436,444,466,435,448,451,429,476,453,441,456,458,478,455,467,669,464,470,433,428,450,434,446,459,457,460,443,425,438,465,426,437,475,430,423,422,447,477,474,442,431,469,427,449","comment":"Tao(F_11,β=9) × F_61(ζ=20,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:03:11","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/a66f42c0dbb589d2e4926b34c46ae1a8f1a1bae5b52bcb2d49bdf45acbfe2517.txt"},{"canonical_hash":"33f7e4831e4ec0df0faea00342bc7713c7a440620de3c03257098ee6c933d133","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,49,11,19,40,8,48,30,32,22,58,39,29,57,56,51,52,34,44,53,27,37,35,4,13,45,24,16,54,2,6,18,59,21,28,50,43,36,12,15,5,20,42,14,41,665,46,9,47,25,7,10,17,31,38,55,33,26,3,23,121,132,124,138,178,172,173,123,179,134,139,164,125,176,133,154,170,169,146,143,136,129,162,152,141,150,149,151,128,142,168,153,175,163,160,130,122,137,131,144,127,147,166,158,156,171,661,155,120,126,157,177,159,174,167,165,148,140,161,135,145,104,85,93,119,102,100,101,92,103,115,71,87,94,97,68,60,105,111,65,75,117,90,62,79,73,77,80,78,89,74,110,61,96,86,114,91,99,118,84,76,70,66,108,112,82,106,664,81,107,69,83,98,113,95,109,88,67,72,63,116,64,573,555,552,581,592,560,586,595,549,584,558,569,565,566,588,546,599,589,567,564,570,556,585,548,596,587,559,591,580,553,554,572,557,562,541,547,583,575,579,545,551,576,598,593,568,543,663,561,574,594,597,577,550,542,578,540,582,590,571,563,544,535,511,524,490,533,531,532,523,534,486,491,518,525,528,512,506,536,482,498,495,488,521,516,504,493,502,501,503,520,494,480,505,527,517,485,522,530,489,510,496,514,499,539,483,508,537,670,507,538,513,509,529,484,526,481,519,500,492,515,487,497,243,240,271,261,252,295,258,299,285,287,255,270,294,284,269,268,273,274,279,289,275,250,282,280,246,263,290,257,266,276,244,242,251,241,254,283,272,288,281,262,265,247,253,297,264,296,668,291,259,292,248,298,260,267,286,293,277,278,249,245,256,317,353,306,332,315,313,314,305,316,328,333,301,307,310,354,348,318,324,340,337,330,303,358,346,335,344,343,345,302,336,323,347,309,359,327,304,312,331,352,338,356,341,321,325,350,319,667,349,320,355,351,311,326,308,322,300,342,334,357,329,339,383,401,368,409,419,400,393,367,397,363,399,404,403,405,416,390,384,413,361,362,365,369,392,388,418,415,394,387,374,396,380,389,402,366,372,414,410,408,411,412,395,406,378,376,370,385,666,391,377,417,407,382,371,375,379,373,360,364,398,381,386,203,197,186,217,234,195,228,231,189,183,192,212,209,208,224,180,182,225,207,190,206,191,237,188,232,238,194,233,216,187,196,202,201,198,211,227,219,235,221,223,185,239,214,229,204,181,660,193,205,230,215,213,184,222,220,236,218,226,210,199,200,604,602,611,642,653,617,649,652,612,608,621,628,603,634,600,645,644,650,630,633,629,622,606,613,651,648,618,654,643,610,620,616,601,619,627,646,638,636,640,609,614,657,635,656,631,625,662,624,632,655,605,658,615,659,641,637,639,647,626,607,623,458,444,447,435,432,422,472,477,421,470,429,423,448,459,473,469,438,439,420,452,450,455,442,445,428,425,453,475,466,426,454,427,431,443,449,474,467,451,479,424,440,464,433,476,461,456,669,436,460,478,462,457,446,437,465,463,468,471,441,434,430","comment":"Tao(F_11,β=9) × F_61(ζ=20,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:03:43","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/33f7e4831e4ec0df0faea00342bc7713c7a440620de3c03257098ee6c933d133.txt"},{"canonical_hash":"2ac7c8576e375272ca6a3f7b3248475159461dcd64d47a2be420acd5aa39ce7b","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,41,3,40,49,30,15,53,14,13,4,47,22,10,19,665,24,5,17,42,48,8,9,58,20,25,54,45,59,46,37,35,27,11,44,16,12,2,55,51,43,34,23,52,31,28,33,26,57,18,29,38,56,50,36,7,21,39,6,32,137,153,134,140,158,125,148,165,141,143,163,156,170,131,173,147,661,164,159,161,151,133,123,121,128,178,129,157,126,135,171,167,177,139,172,120,160,124,149,138,169,152,176,175,168,179,155,132,166,154,146,136,162,150,122,130,145,174,142,127,144,86,79,88,98,94,65,84,102,99,101,107,92,112,70,75,83,664,108,95,90,68,64,82,74,72,60,109,93,119,78,118,104,116,97,71,73,96,113,85,87,111,81,115,114,105,61,91,69,103,80,63,62,106,67,117,110,66,76,100,89,77,541,546,563,542,567,584,565,581,564,558,572,580,578,561,594,575,663,574,595,548,577,579,562,557,590,582,589,583,566,573,593,545,550,569,592,556,549,587,552,571,547,553,599,543,596,585,559,560,586,597,576,598,554,544,570,551,588,540,555,591,568,498,486,500,510,506,535,491,514,511,513,519,504,524,532,537,490,670,520,507,502,494,534,489,483,480,484,521,505,536,481,530,516,528,509,531,482,508,525,492,499,523,488,527,526,517,485,503,533,515,487,496,497,518,493,529,522,495,538,512,501,539,276,278,291,274,290,259,280,242,253,267,266,275,297,245,263,249,668,247,268,241,292,299,261,262,258,243,285,254,295,248,296,273,271,287,264,294,240,265,277,255,251,293,284,246,252,281,288,283,286,257,250,279,298,256,260,272,270,244,289,269,282,317,305,319,329,325,354,310,333,330,332,338,323,343,351,356,309,667,339,326,321,313,353,308,302,301,303,340,324,355,359,349,335,347,328,350,300,327,344,311,318,342,307,346,345,336,304,322,352,334,306,315,316,337,312,348,341,314,357,331,320,358,395,416,373,398,372,411,414,408,415,382,381,405,407,392,362,404,666,363,419,374,376,366,403,387,399,406,400,371,370,365,412,369,384,397,413,389,390,380,377,396,386,360,418,379,368,367,383,394,409,417,375,364,393,378,361,385,410,391,388,401,402,190,201,209,230,232,223,228,214,227,195,203,213,217,188,237,231,660,208,238,187,216,212,204,196,226,215,225,222,210,202,211,200,191,205,229,183,186,220,192,207,193,185,236,180,233,218,181,189,219,234,182,235,198,194,199,184,221,239,197,224,206,614,636,607,635,610,645,651,638,649,611,631,641,639,613,657,605,662,653,656,620,640,642,632,609,603,637,652,646,602,604,634,608,600,633,650,617,618,644,612,630,623,601,654,627,659,648,622,621,647,658,628,655,615,624,629,625,643,619,616,606,626,436,467,473,457,423,466,449,459,451,430,447,425,462,472,475,448,669,458,424,426,460,461,455,445,470,431,471,463,428,468,453,422,444,478,450,441,446,465,437,456,429,440,443,452,476,464,427,442,420,439,474,477,435,438,454,433,421,432,434,469,479","comment":"Tao(F_11,β=9) × F_61(ζ=34,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:04:18","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/2ac7c8576e375272ca6a3f7b3248475159461dcd64d47a2be420acd5aa39ce7b.txt"},{"canonical_hash":"c93dadcaf466b87e674e6ac93c73063b0c334ceb44c58f7ad6cd21981ebac3b2","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,34,7,51,16,58,665,53,2,56,12,29,59,48,39,49,20,45,15,28,6,32,30,22,17,14,55,5,36,46,42,13,19,52,43,26,23,18,21,38,57,24,8,47,41,31,4,50,9,3,27,35,37,11,33,10,40,25,54,44,128,167,130,131,134,177,146,661,168,121,158,150,179,145,138,136,139,171,123,176,135,175,164,122,142,133,137,120,132,148,155,173,144,170,169,165,160,159,178,163,162,152,153,166,149,174,172,151,140,127,157,141,154,161,156,143,124,125,147,129,126,110,116,101,90,77,82,118,664,86,104,99,63,79,117,72,70,73,87,102,81,85,75,113,94,106,76,71,105,91,68,96,89,61,93,92,114,74,100,78,112,67,65,60,115,69,95,88,64,83,109,98,84,62,66,97,107,103,80,119,111,108,562,587,552,543,558,568,594,663,597,567,557,540,551,588,561,585,553,582,591,580,595,592,573,545,590,575,550,566,577,555,586,559,546,569,572,548,576,563,564,542,549,571,570,547,560,541,556,578,565,599,574,589,544,598,593,596,579,584,581,554,583,513,519,504,524,532,537,490,670,520,507,502,494,534,489,483,480,484,521,505,536,481,530,516,528,509,531,482,508,525,492,499,523,488,527,526,517,485,503,533,515,487,496,497,518,493,529,522,495,538,512,501,539,498,486,500,510,506,535,491,514,511,245,244,278,289,269,296,266,668,271,246,274,294,283,249,299,265,267,254,261,287,282,288,276,284,250,297,286,273,298,280,262,258,295,253,270,259,241,240,252,255,264,275,242,290,263,257,285,248,268,291,247,251,279,281,293,277,292,256,243,272,260,323,329,314,334,342,347,301,667,330,317,312,304,344,359,353,351,354,331,315,346,350,340,326,338,319,341,352,318,335,302,309,333,358,337,336,327,355,313,343,325,357,306,307,328,303,339,332,305,348,322,311,349,308,356,310,320,316,345,300,324,321,400,367,381,395,392,390,408,666,417,364,385,361,396,415,393,413,384,376,380,389,418,419,365,369,416,394,397,403,373,398,363,378,387,375,374,404,366,382,401,410,386,407,371,388,402,370,377,360,391,399,414,368,372,405,362,412,406,411,409,383,379,195,225,188,187,239,184,232,660,233,185,180,186,189,226,194,220,181,211,213,210,237,236,208,200,228,221,191,183,231,193,230,198,182,202,217,205,214,196,197,215,204,218,203,206,199,229,192,216,207,190,222,227,201,209,235,234,238,224,212,223,219,624,650,605,615,617,630,655,662,656,631,616,614,602,601,625,636,612,645,639,633,652,657,641,603,647,644,619,606,607,600,649,623,627,610,634,628,640,621,620,651,629,658,611,626,622,648,659,637,608,618,643,604,609,642,654,653,632,638,646,613,635,440,439,468,469,444,430,437,669,478,451,445,428,425,438,447,465,442,436,461,455,479,477,475,452,421,473,454,431,460,426,472,446,453,435,433,432,470,448,434,424,423,456,449,422,427,420,474,459,443,429,458,471,450,457,463,476,462,466,464,441,467","comment":"Tao(F_11,β=9) × F_61(ζ=34,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:04:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/c93dadcaf466b87e674e6ac93c73063b0c334ceb44c58f7ad6cd21981ebac3b2.txt"},{"canonical_hash":"d5b37d67677d79ef3904ea56ea7864c6840ef4b0c0f7719e8c09d4d9c01c4283","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,31,57,48,17,28,30,42,10,56,20,7,47,34,40,16,38,13,27,2,58,29,11,8,41,14,49,9,50,665,55,4,54,19,36,3,6,24,53,46,32,18,33,21,35,39,59,12,15,51,5,37,25,23,22,43,52,26,44,45,175,132,156,142,158,121,144,167,136,155,153,161,138,169,145,152,129,131,139,127,141,164,140,124,165,162,166,177,178,176,661,133,160,159,172,168,171,154,151,170,147,130,150,128,126,174,122,163,149,179,123,134,157,173,120,143,137,148,135,125,146,71,104,110,91,112,80,75,95,117,62,72,115,92,97,76,89,63,103,93,65,90,106,82,79,107,61,94,119,108,60,664,68,114,113,100,96,99,73,88,98,84,102,87,66,64,83,70,105,86,109,78,69,111,101,81,74,118,85,116,67,77,548,579,591,562,588,554,540,545,577,550,542,574,596,598,552,559,584,581,557,546,595,566,593,543,563,571,569,572,544,583,663,582,589,573,568,570,565,592,594,567,556,541,558,580,585,560,551,599,597,575,553,564,576,586,547,555,587,561,590,578,549,484,539,498,514,500,480,488,518,493,535,485,503,515,520,489,512,536,538,504,531,513,527,505,481,516,525,517,495,496,534,670,528,502,501,523,519,522,486,511,521,507,537,510,532,530,506,483,526,509,497,491,529,499,524,482,487,494,508,492,533,490,259,258,289,266,257,247,286,288,290,279,275,250,276,256,292,298,246,296,243,285,260,267,287,253,277,299,244,268,278,269,668,274,241,273,249,294,255,242,282,272,265,280,248,291,251,293,297,261,254,245,270,240,295,283,281,252,262,271,284,263,264,321,326,346,305,336,318,313,351,341,334,322,339,306,353,314,303,335,325,307,330,304,348,308,317,349,358,350,343,344,333,667,327,338,337,356,352,355,323,302,354,310,324,300,331,329,309,320,359,301,345,316,328,347,357,319,312,342,311,340,332,315,371,383,404,396,382,392,380,399,406,408,391,363,417,385,368,389,365,412,364,379,372,375,418,360,400,402,401,367,413,410,666,378,362,407,374,398,419,386,388,403,416,390,397,376,411,395,393,384,394,405,370,377,361,373,387,381,415,366,414,409,369,180,221,226,195,227,191,230,200,210,214,187,207,237,223,189,192,217,220,196,185,232,205,236,183,238,204,202,211,225,216,660,215,224,212,201,203,239,184,235,206,233,198,197,219,218,193,190,222,234,208,186,213,209,199,231,188,228,194,229,181,182,652,624,648,618,649,613,611,658,632,604,617,637,653,625,615,623,641,642,621,638,656,629,600,609,607,626,630,635,651,644,662,645,650,634,631,627,646,605,655,628,657,639,620,643,640,622,602,601,654,636,616,608,633,659,610,614,606,619,647,612,603,434,438,469,435,456,444,433,468,421,463,443,458,477,455,426,449,467,460,448,425,478,452,475,473,430,436,431,457,471,424,669,465,429,428,453,454,432,440,447,451,476,461,422,464,466,420,442,437,474,423,445,439,459,479,446,441,470,450,472,462,427","comment":"Tao(F_11,β=9) × F_61(ζ=58,ω=13). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:05:13","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/d5b37d67677d79ef3904ea56ea7864c6840ef4b0c0f7719e8c09d4d9c01c4283.txt"},{"canonical_hash":"902629db8c666f5d9c4c10c2fe27cef9431e48d61f34c567db2701070f61d48e","size":671,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,43,57,3,12,40,42,37,22,56,15,19,8,29,35,11,33,18,39,2,58,41,23,20,36,9,49,21,50,665,55,26,54,14,31,25,28,46,53,7,44,13,38,16,30,34,59,24,10,51,27,32,47,45,17,4,52,48,5,6,134,122,159,136,161,147,149,166,179,158,135,164,137,168,150,123,130,132,138,154,176,175,139,146,128,173,129,125,126,157,661,121,163,162,171,167,170,120,145,169,141,131,144,155,153,140,133,174,143,124,152,178,160,172,148,177,127,142,165,156,151,104,87,72,108,74,101,96,64,79,83,105,77,109,66,97,118,84,86,110,93,119,89,111,100,90,61,63,81,70,82,664,69,76,75,60,65,68,106,117,67,113,85,116,94,92,112,103,88,115,71,99,91,73,62,102,107,80,114,78,95,98,542,559,548,588,549,599,555,579,551,581,545,590,593,584,574,560,553,576,585,554,594,562,596,570,582,563,565,557,568,573,663,572,567,558,566,564,543,571,597,561,595,578,586,569,556,589,575,583,592,547,598,580,552,577,591,540,550,587,544,541,546,511,481,519,529,521,508,515,502,526,488,512,524,530,492,504,539,489,491,531,484,528,499,532,507,500,497,501,516,517,487,670,480,523,522,495,503,494,513,538,493,534,490,537,485,483,533,510,498,536,518,506,482,520,496,509,514,527,535,525,486,505,289,288,248,298,297,257,277,252,286,271,241,247,268,296,278,284,262,282,259,276,290,253,251,272,269,285,260,254,270,255,668,243,265,242,246,280,264,267,273,240,295,249,245,287,299,279,283,291,263,261,256,266,281,274,250,258,292,244,275,293,294,322,335,342,302,344,319,314,351,337,331,323,347,303,353,315,301,332,334,304,327,300,348,305,318,349,358,350,339,340,330,667,324,346,345,356,352,355,312,311,354,307,333,310,328,326,306,321,359,309,341,317,325,343,357,320,313,338,308,336,329,316,365,412,391,415,404,364,405,400,396,366,381,392,419,371,382,386,363,377,361,378,414,403,360,367,362,370,399,388,389,393,666,394,374,373,402,401,410,407,418,372,417,397,398,379,406,416,385,411,369,390,409,395,376,413,384,408,387,368,375,380,383,203,215,185,221,200,206,210,218,191,180,238,187,235,217,236,222,201,205,182,192,230,198,232,228,212,193,195,226,227,189,660,188,183,225,196,194,213,229,233,197,231,239,224,204,209,223,208,216,234,186,237,211,190,219,181,207,199,220,184,214,202,652,639,629,609,610,637,631,643,651,602,636,620,655,640,603,647,634,615,649,641,658,624,654,608,644,627,623,613,612,630,662,638,611,614,622,626,645,604,653,625,657,642,648,618,633,646,659,600,656,619,635,621,601,605,632,607,606,650,628,616,617,455,465,450,444,428,433,474,449,430,438,457,436,443,461,458,470,432,454,469,421,477,445,475,423,478,447,448,472,437,440,669,456,451,429,435,425,463,453,468,446,460,466,434,431,479,424,420,464,476,471,441,452,426,462,467,422,473,442,427,439,459","comment":"Tao(F_11,β=9) × F_61(ζ=58,ω=47). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:05:34","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/671/902629db8c666f5d9c4c10c2fe27cef9431e48d61f34c567db2701070f61d48e.txt"},{"canonical_hash":"8a50b46d81debeceedaf71ad792268a4bca182151455e7d44f9b631f9a405c00","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,675,769,535,790,40,649,770,13,73,486,435,208,317,776,402,445,279,661,718,817,479,775,204,106,736,541,553,260,840,225,518,508,220,240,71,169,810,444,782,304,69,655,555,696,244,480,367,811,621,438,251,700,693,282,173,470,451,108,801,22,437,428,280,161,509,48,805,684,5,351,439,577,105,702,777,92,522,597,825,500,734,167,112,459,68,316,632,521,797,672,82,795,640,804,65,563,491,429,540,365,95,818,756,396,39,780,546,803,547,341,747,695,484,741,659,192,554,789,419,688,475,27,166,393,362,323,31,178,806,285,89,160,616,605,349,85,785,346,746,794,627,28,623,44,552,489,559,116,355,72,401,109,343,425,715,258,307,305,382,638,462,609,625,826,413,369,476,768,566,763,457,420,46,561,604,710,42,193,620,253,254,181,821,302,261,232,408,300,579,345,465,236,150,156,446,595,352,755,103,21,277,738,796,678,228,79,17,681,405,603,835,732,177,96,8,135,531,680,539,607,329,744,788,469,774,642,194,381,532,368,478,450,580,262,134,487,153,221,407,723,2,332,394,205,740,781,666,298,564,141,88,227,615,485,443,403,248,41,466,295,249,626,698,123,176,599,333,631,816,705,170,359,297,37,142,767,800,568,370,772,679,291,59,87,0,545,761,497,416,159,677,809,434,823,709,294,572,504,185,271,430,310,614,374,203,458,264,348,312,467,418,571,646,52,114,263,643,831,703,242,56,138,720,596,11,455,422,728,140,303,668,436,483,139,412,399,671,93,335,373,267,226,337,786,146,219,218,585,158,223,750,460,308,74,98,231,224,12,16,145,488,676,272,151,163,601,733,441,404,378,791,590,574,427,673,417,711,311,820,120,314,697,495,699,717,516,729,179,20,792,162,665,773,366,107,390,81,524,454,517,9,588,63,592,201,62,440,653,384,252,274,730,477,421,656,211,273,624,713,468,78,322,570,581,195,124,320,771,143,66,288,397,358,511,815,4,361,724,115,583,102,174,309,58,385,15,692,587,76,787,490,824,519,157,694,706,449,660,712,306,512,830,117,637,534,727,19,189,602,172,321,376,324,91,639,527,739,3,802,721,783,130,400,505,464,526,598,30,562,557,360,635,149,669,90,799,49,121,813,60,757,284,751,628,494,406,832,556,667,281,33,424,77,202,544,793,199,515,331,608,101,685,749,647,731,29,410,182,536,334,779,537,127,812,737,70,612,474,386,651,648,61,565,276,379,283,576,268,247,392,190,619,269,353,119,708,725,196,315,463,472,57,836,575,325,293,67,257,426,629,327,129,1,206,389,482,278,83,200,148,363,658,735,216,473,586,132,617,654,798,613,652,187,542,75,45,549,336,754,415,784,742,391,18,520,690,34,339,210,265,513,270,533,528,503,250,558,523,215,538,493,498,235,548,230,245,275,255,543,53,356,707,819,380,719,301,514,10,110,507,152,687,578,833,689,582,97,506,701,398,183,165,118,243,447,354,171,36,94,292,594,461,222,32,328,290,610,753,760,743,84,388,234,584,155,357,212,233,611,318,414,241,600,26,683,686,502,814,299,501,147,375,64,766,682,714,650,136,573,296,550,164,828,371,529,593,716,319,722,25,778,86,14,834,125,634,184,670,395,837,38,704,492,674,126,289,411,286,207,567,154,54,762,499,525,822,111,622,657,50,350,23,344,209,137,618,80,759,287,113,433,748,589,238,246,691,456,442,765,239,217,808,630,197,827,55,144,764,551,752,664,530,662,198,186,237,641,453,180,51,47,259,266,133,128,636,364,377,104,448,471,633,338,175,606,383,432,347,313,229,423,168,409,726,510,35,122,24,326,644,807,663,591,214,330,431,6,213,758,372,256,188,452,99,645,496,100,43,131,387,560,481,191,7,745,569,340,342,829","comment":null,"submitted_at":"2026-05-13 20:18:54","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/8a50b46d81debeceedaf71ad792268a4bca182151455e7d44f9b631f9a405c00.txt"},{"canonical_hash":"381620f7f08377903a69d16968cb4d245b3b3c2850efc01c7010c5c92ac16ca4","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,725,804,571,150,29,283,754,202,389,147,165,99,478,324,657,726,185,333,231,439,665,160,73,272,548,129,565,26,739,573,230,827,515,303,407,667,731,489,626,666,662,27,275,374,57,140,400,674,488,544,109,680,232,448,110,820,790,137,38,146,541,705,351,422,85,260,716,398,221,15,12,687,435,733,39,647,523,539,170,312,514,247,152,591,139,395,394,254,789,46,251,721,703,691,191,265,440,382,180,90,692,370,616,656,556,835,663,793,767,23,161,125,163,363,285,437,53,428,184,367,706,108,5,601,425,271,637,582,355,250,66,211,339,677,537,724,759,169,758,620,288,11,623,635,34,500,585,224,818,574,812,268,60,825,356,757,289,115,710,310,131,453,546,824,783,751,151,516,353,358,18,830,136,521,112,65,280,156,658,273,715,756,208,432,120,788,651,800,452,141,815,320,314,193,300,3,536,785,741,50,378,747,636,700,132,443,143,773,535,124,155,771,466,612,576,559,37,103,774,172,508,468,354,274,267,434,212,689,414,502,264,145,237,602,524,62,685,162,614,379,114,424,456,404,549,533,799,287,458,525,257,460,233,764,640,817,286,729,628,579,727,542,16,823,220,346,293,229,654,177,625,590,101,563,765,401,840,668,811,821,406,386,416,698,735,391,750,836,745,411,806,760,678,826,755,831,693,816,736,295,810,451,63,803,730,45,33,315,809,135,253,127,373,531,309,447,638,501,438,742,780,188,171,350,420,701,77,347,343,672,245,266,138,412,32,70,206,61,632,0,179,195,671,59,241,577,596,362,718,69,7,711,587,181,322,372,642,682,393,189,276,344,681,387,430,216,80,87,606,36,318,728,10,255,469,205,659,510,769,732,234,768,238,584,298,568,465,598,316,71,9,734,225,560,144,291,828,595,482,822,21,182,802,645,331,564,749,782,610,240,613,218,490,197,808,714,480,748,639,1,306,24,583,214,527,837,159,86,313,712,660,462,575,608,744,457,81,244,31,709,213,777,570,308,557,301,475,520,605,326,707,832,19,743,192,235,594,655,154,578,634,805,168,183,496,526,130,40,446,661,166,433,304,248,28,58,766,111,737,442,122,345,798,290,371,775,633,368,619,538,684,269,167,554,801,507,690,409,262,503,67,461,530,410,494,429,463,98,607,119,292,84,242,384,311,91,569,495,6,164,336,223,644,807,580,618,753,532,467,210,485,219,630,615,719,588,717,787,813,476,670,249,586,307,444,47,522,699,784,134,509,518,781,553,364,622,390,277,534,599,222,78,545,256,352,22,484,51,445,204,337,49,270,621,402,408,196,375,25,102,696,697,567,128,708,95,42,279,94,540,529,359,504,517,581,473,419,629,617,513,694,302,471,142,217,385,776,779,704,487,664,589,14,600,552,243,76,833,650,738,321,296,772,239,603,149,187,702,470,72,329,357,54,30,100,261,342,380,713,236,209,201,133,338,450,413,572,190,56,493,561,555,528,454,157,597,497,74,252,794,486,609,519,259,88,791,282,399,8,641,511,819,305,752,263,426,198,383,778,126,284,55,148,648,325,746,392,323,365,377,686,41,118,327,349,611,175,186,246,92,474,592,194,627,550,675,669,369,83,481,492,558,227,483,52,786,604,104,449,199,17,328,319,562,20,397,332,479,226,652,123,97,403,44,35,178,834,366,117,761,299,441,491,720,770,340,106,278,176,64,464,348,75,676,388,317,2,200,723,82,417,455,792,96,649,215,722,281,228,472,593,207,341,330,43,646,203,653,107,13,431,153,795,427,294,829,48,158,762,551,335,436,361,423,258,506,381,68,105,643,121,421,814,499,89,543,695,415,297,624,512,796,679,566,79,93,405,498,763,505,797,477,174,4,396,683,688,673,740,116,376,173,631,418,459,334,113,360,547","comment":null,"submitted_at":"2026-05-13 20:19:10","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/381620f7f08377903a69d16968cb4d245b3b3c2850efc01c7010c5c92ac16ca4.txt"},{"canonical_hash":"ecd7ba28fe843f84fbb62d07e7ad9c6fff2504f2d4864fc5de075740918127ea","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,204,804,798,546,451,541,154,583,153,73,768,576,355,262,453,725,691,414,317,349,593,803,465,208,544,774,459,206,671,752,230,315,275,366,187,84,807,82,417,303,405,239,121,270,666,519,688,327,457,755,361,747,440,251,149,209,788,699,291,809,759,578,212,170,312,831,89,126,253,717,192,244,731,437,60,410,33,762,668,443,325,404,651,376,499,637,90,469,252,331,69,591,416,538,379,781,820,748,695,295,585,516,552,655,624,716,74,5,407,808,229,816,114,62,284,177,297,72,646,698,176,710,467,620,464,371,438,672,450,245,746,247,494,320,400,837,629,821,623,278,660,234,77,50,362,813,302,513,116,412,182,532,763,396,393,471,483,496,835,571,141,515,122,565,796,49,350,148,795,309,136,97,614,727,30,498,219,822,52,447,287,645,385,99,638,833,263,139,659,51,563,194,236,53,319,744,169,254,223,779,829,271,556,549,434,311,562,178,112,724,39,753,785,461,336,825,93,505,497,786,557,173,418,384,521,76,166,543,590,491,391,729,98,354,380,117,830,388,358,670,341,143,560,566,466,527,548,343,790,791,171,776,586,408,714,101,775,580,815,411,522,328,163,137,511,743,533,326,365,495,463,547,690,374,750,514,423,196,530,220,267,356,683,7,723,766,484,631,742,322,265,605,70,419,13,435,487,696,756,720,767,504,595,555,3,381,686,713,682,656,740,255,186,409,257,477,32,330,474,596,347,448,95,439,475,56,174,554,689,664,749,526,160,115,324,276,436,778,58,834,183,237,241,784,567,175,199,228,281,589,777,782,802,26,16,594,840,797,622,597,564,579,574,792,21,584,1,612,31,569,617,11,772,602,6,607,575,403,78,59,458,528,158,810,709,285,151,542,321,132,406,96,771,481,685,360,506,517,770,581,373,369,490,738,493,92,836,701,313,633,282,214,609,152,24,197,828,640,817,722,304,392,377,258,415,47,25,131,65,603,134,94,442,711,106,827,643,613,314,224,104,352,162,503,390,207,811,0,650,288,40,732,292,109,402,619,452,268,34,102,57,480,531,63,180,444,754,783,572,264,634,441,789,573,694,246,211,108,559,329,242,286,144,120,188,233,61,165,41,301,226,421,769,460,213,222,261,649,424,184,203,344,674,279,195,819,135,539,588,587,43,145,159,123,190,198,256,764,36,118,582,814,339,644,455,296,799,38,130,669,454,243,221,793,140,534,274,179,217,91,537,805,54,318,368,501,801,316,704,488,570,364,512,476,127,280,558,398,520,800,680,401,146,761,351,191,601,647,8,260,479,678,525,745,335,430,600,661,2,215,509,687,482,100,737,718,739,189,105,128,426,429,824,164,231,654,200,150,306,266,249,48,46,227,679,592,551,218,705,80,17,760,23,741,433,462,641,540,662,332,277,667,615,693,616,394,733,524,445,14,124,630,518,294,726,248,307,15,142,628,818,432,712,826,367,658,37,599,55,611,272,636,18,700,225,489,389,697,535,736,75,345,201,728,610,657,428,12,449,794,334,66,185,446,529,238,68,639,113,193,536,269,216,125,485,577,299,823,604,308,523,598,42,387,635,147,663,87,129,20,372,812,19,735,681,625,751,240,626,472,250,708,550,715,420,342,27,181,677,88,780,107,468,383,71,168,500,456,719,333,370,161,413,492,618,395,702,4,648,508,45,273,832,167,293,422,111,357,28,337,703,235,765,632,399,757,22,545,621,676,85,653,427,10,289,9,298,79,67,707,172,721,119,310,359,346,348,86,103,675,553,507,734,363,283,202,382,608,706,29,397,35,806,157,431,155,684,470,133,205,232,773,110,353,375,386,300,473,338,561,665,478,758,502,81,305,44,510,64,156,486,378,83,290,652,340,692,730,606,210,425,673,642,138,568,259,787,627,323","comment":null,"submitted_at":"2026-05-13 20:19:28","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/ecd7ba28fe843f84fbb62d07e7ad9c6fff2504f2d4864fc5de075740918127ea.txt"},{"canonical_hash":"632f437584e0bd18113dab81143d01f8bdc879756ac4cde1d58e2cbb805dc1a1","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,117,769,517,458,148,241,74,335,480,36,826,112,612,776,212,324,660,243,651,817,602,761,493,691,252,495,516,184,71,676,459,87,685,455,34,340,426,512,632,298,747,453,79,763,681,460,229,555,273,103,814,76,690,446,400,341,621,462,767,290,589,352,266,220,94,322,417,395,527,524,261,336,156,647,215,616,391,692,68,236,737,370,135,139,754,399,260,330,311,684,83,743,444,222,572,253,20,501,72,835,535,731,786,614,554,198,722,384,557,576,9,376,355,245,22,428,377,677,18,452,151,317,280,85,642,412,463,57,210,390,411,44,611,522,91,498,668,31,244,635,204,821,766,500,800,107,536,55,218,607,257,478,626,594,323,332,2,537,628,346,295,225,364,719,104,100,405,702,271,583,727,14,27,125,422,348,744,203,581,250,682,191,301,226,559,492,360,382,190,32,749,687,494,292,394,63,19,283,255,231,387,624,325,732,427,586,306,365,688,710,207,277,127,154,518,319,669,627,820,655,111,779,138,238,520,264,425,646,728,367,374,170,110,566,211,342,366,568,477,235,544,114,488,712,333,667,547,461,305,69,729,711,233,664,705,46,515,622,202,625,259,815,272,837,420,650,122,424,641,106,149,551,723,774,570,665,496,78,720,274,137,738,329,61,830,439,789,698,530,217,656,528,726,567,782,121,781,248,45,234,819,597,194,750,469,756,465,108,790,558,177,526,21,686,278,695,289,247,811,600,768,490,81,157,449,25,540,675,538,730,792,748,258,770,174,638,580,666,88,577,77,791,1,445,799,689,227,506,736,171,328,563,369,410,662,472,165,599,542,230,105,38,456,539,561,7,300,109,276,183,64,483,337,281,724,707,291,115,371,549,338,310,350,193,175,347,240,717,466,181,17,379,216,482,423,552,734,48,372,571,573,119,672,4,344,545,797,179,93,6,232,136,30,735,775,671,796,694,219,454,543,263,585,82,804,741,162,680,753,643,582,450,511,413,818,408,353,383,363,813,823,368,840,403,788,778,398,418,388,373,783,378,803,798,773,358,828,793,393,808,833,620,228,508,489,254,659,831,636,810,700,65,101,267,41,128,144,832,510,309,546,485,617,678,718,645,197,706,447,251,414,52,146,431,752,275,312,140,158,385,345,303,514,406,80,326,574,39,637,84,608,606,407,13,42,596,504,421,3,70,265,507,564,200,437,697,375,404,598,293,206,397,396,742,759,316,302,448,29,123,631,615,673,209,805,223,713,827,765,503,640,505,60,484,192,304,96,249,701,541,262,654,834,56,491,142,523,825,73,430,721,434,715,159,562,784,269,10,777,693,132,674,116,525,733,565,663,824,474,795,26,294,703,102,239,755,113,531,630,605,644,50,199,470,182,213,816,86,802,237,780,224,590,167,587,550,11,740,699,268,746,648,349,98,35,801,548,809,758,509,270,442,603,401,307,246,601,75,205,409,402,321,153,47,8,569,380,141,764,785,592,634,284,553,189,92,242,172,745,653,806,521,464,807,595,16,751,40,318,54,28,359,327,529,652,714,67,155,351,99,532,161,173,95,623,473,168,709,313,457,90,62,49,762,618,150,23,285,468,416,354,584,441,593,502,37,297,288,629,591,443,201,195,499,24,392,432,486,143,169,670,279,66,633,533,126,440,575,725,334,794,661,787,152,120,315,282,186,487,53,124,296,343,180,471,221,739,578,419,757,163,519,579,613,704,256,436,145,308,331,89,479,708,118,649,187,822,696,829,299,760,610,475,33,657,356,178,451,467,357,59,534,160,166,287,129,476,619,389,381,433,320,58,185,481,438,588,130,208,196,497,134,386,5,716,51,560,772,429,556,771,176,415,604,43,12,188,286,513,836,0,133,314,683,147,435,164,15,679,639,97,658,812,214,131,339,361,362,609","comment":null,"submitted_at":"2026-05-13 20:20:13","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/632f437584e0bd18113dab81143d01f8bdc879756ac4cde1d58e2cbb805dc1a1.txt"},{"canonical_hash":"75a3c6dc1b84f48b23cc56234776ab69cb6ad48609545e139a7bd85ee1a2f3d8","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,814,804,564,537,427,451,285,181,723,437,698,761,295,506,637,517,252,152,278,60,505,42,497,338,732,822,596,516,479,558,492,580,266,162,711,337,231,410,802,5,752,107,13,229,283,177,136,238,576,341,282,364,184,144,606,272,343,489,119,423,502,749,828,276,102,79,297,192,275,168,17,795,321,298,573,386,441,524,185,678,463,101,771,11,725,452,783,206,64,194,239,416,790,187,623,217,213,671,324,316,270,97,374,495,813,328,157,553,83,769,257,476,50,215,522,626,812,748,69,286,746,468,176,615,430,683,788,485,622,190,422,685,534,494,308,77,228,396,307,518,320,250,232,219,27,126,68,331,603,209,583,403,779,122,211,547,684,9,477,767,317,826,145,663,178,20,726,667,574,514,470,488,300,1,554,773,766,361,431,670,668,306,796,412,442,450,54,724,334,204,121,245,391,378,384,197,578,63,227,302,303,681,619,84,326,214,513,72,311,733,201,6,673,729,612,305,675,59,720,458,436,420,279,475,366,447,96,519,736,589,643,457,137,405,125,682,160,24,794,8,797,706,806,699,418,644,146,0,332,527,587,460,44,26,200,756,264,695,186,786,504,440,290,718,798,81,421,597,296,350,432,478,714,544,662,35,142,459,52,768,461,348,246,496,832,277,833,100,560,611,754,515,550,149,507,103,268,707,633,171,395,552,150,404,33,216,831,579,634,127,322,672,424,784,737,731,765,408,482,25,115,577,14,327,413,792,155,132,735,188,557,639,701,19,400,584,742,582,141,836,789,120,638,221,429,30,694,3,677,161,721,140,472,241,567,659,777,697,658,762,542,398,23,105,569,208,347,679,774,385,755,394,15,821,4,117,104,48,265,243,785,604,563,106,335,92,666,182,189,7,498,288,369,319,618,234,287,363,158,46,346,212,411,138,38,344,775,312,131,36,691,401,32,94,359,233,224,588,148,82,237,179,571,313,255,608,629,353,325,336,207,128,523,154,543,57,247,555,240,464,837,520,433,147,501,759,712,40,251,616,273,632,318,565,73,129,466,70,512,661,738,382,362,357,304,660,367,640,829,635,352,834,650,284,819,645,824,299,809,372,289,294,314,630,655,377,840,309,772,467,444,816,415,203,393,692,236,156,34,750,342,18,653,562,716,112,389,674,135,757,654,170,810,10,195,397,381,473,627,713,781,751,455,700,709,291,793,499,259,39,688,539,380,76,435,690,21,536,620,355,710,205,445,301,356,31,509,602,595,49,791,426,549,465,191,86,719,407,665,803,483,546,269,75,62,438,621,471,548,490,256,134,159,807,45,78,808,469,717,570,743,210,764,323,631,525,528,90,652,744,484,174,486,258,521,225,823,114,601,167,540,758,93,271,453,267,646,585,220,169,85,333,55,448,535,818,481,647,727,500,262,753,109,253,739,817,37,641,88,151,198,462,799,649,419,648,29,388,439,594,165,669,592,745,687,811,532,805,130,330,780,99,242,358,349,2,87,599,43,406,153,613,493,696,593,260,133,41,47,657,230,98,510,95,491,763,65,533,263,545,590,827,456,172,651,702,329,345,591,244,676,58,373,199,218,56,508,614,222,379,116,113,628,371,370,703,680,480,610,281,310,249,387,529,617,425,741,526,734,51,53,340,293,163,74,111,503,368,586,568,12,292,108,609,642,443,164,575,511,67,139,722,530,80,261,474,636,248,730,708,392,446,16,375,254,704,776,376,280,531,71,89,66,339,202,624,566,143,354,686,770,123,383,399,166,782,110,760,454,664,28,390,820,572,728,175,600,91,274,715,607,196,551,360,800,561,61,598,22,315,223,118,173,417,605,365,778,801,180,556,559,434,414,193,747,226,835,740,625,351,705,693,541,402,428,235,538,656,124,183,787,825,689,487,830,409,815,449,581","comment":null,"submitted_at":"2026-05-13 20:20:31","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/75a3c6dc1b84f48b23cc56234776ab69cb6ad48609545e139a7bd85ee1a2f3d8.txt"},{"canonical_hash":"f5ace93a48889ba6f7af2f98340b7e30bc6b3c2a861a5dd1705b8787ba78f304","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,202,804,651,719,489,196,324,609,523,634,644,130,110,733,747,505,335,419,370,163,95,458,408,236,251,342,225,745,70,475,647,418,285,725,749,562,36,601,497,832,77,376,610,766,145,430,625,616,533,67,121,629,356,172,506,572,579,624,611,761,193,807,253,339,706,575,13,2,436,414,728,770,363,71,561,123,239,618,382,395,831,308,834,434,650,782,39,232,10,37,349,516,517,538,589,776,48,621,249,186,203,595,56,578,427,177,630,410,778,287,154,25,449,362,423,466,704,212,663,483,386,276,455,534,35,98,343,705,85,697,226,699,743,300,482,49,628,461,20,405,573,374,283,209,734,444,773,422,792,214,631,82,420,206,558,837,619,167,269,502,117,170,248,606,501,111,464,41,68,40,669,321,632,539,231,158,612,460,667,99,24,246,90,311,536,391,710,765,141,372,437,298,476,640,799,222,788,354,608,164,821,646,424,588,64,433,187,229,267,668,757,378,17,345,717,260,380,785,28,1,233,509,138,708,590,397,515,139,576,290,411,84,559,388,333,556,687,652,768,473,296,480,341,88,322,75,597,689,653,750,266,292,709,59,816,783,471,171,802,415,428,641,384,635,367,184,457,182,454,603,794,432,30,819,526,346,755,221,338,485,658,14,393,301,694,700,529,478,602,235,89,738,80,65,416,657,327,148,532,495,524,360,358,431,701,412,213,275,737,101,409,570,16,732,683,666,591,723,8,325,247,823,119,347,74,679,323,256,642,220,286,241,78,401,622,413,740,677,50,463,34,331,280,100,549,643,546,168,758,781,61,155,822,594,600,484,137,543,208,587,131,522,191,366,741,521,254,440,739,319,626,152,102,42,53,268,722,514,581,421,315,238,109,91,22,6,520,691,383,33,402,813,762,790,560,557,673,350,713,726,272,265,108,399,114,3,678,404,243,353,527,113,320,696,565,270,426,490,795,277,586,11,767,731,519,27,818,718,727,96,407,355,830,571,585,228,375,12,262,681,389,392,504,780,340,698,81,716,510,133,23,712,752,446,547,134,703,31,255,373,815,661,803,313,15,477,448,836,237,452,204,400,44,144,779,352,787,729,568,623,655,156,312,244,439,369,456,685,5,645,826,234,194,481,169,192,777,303,613,438,302,442,359,69,829,377,793,593,467,146,227,429,390,675,605,492,744,273,564,136,445,58,827,592,259,47,160,178,491,72,66,548,746,157,786,107,371,596,525,105,518,304,115,284,659,314,135,664,294,498,649,289,654,513,639,120,503,508,493,309,299,125,840,833,26,441,128,693,387,7,566,250,542,18,76,499,257,580,368,129,707,711,775,676,223,810,753,544,29,735,73,637,104,715,638,326,672,396,215,674,465,541,310,45,617,281,318,195,261,627,336,763,328,406,4,173,684,83,468,551,79,211,55,648,317,291,682,554,205,63,496,112,614,450,183,791,329,106,165,162,201,569,52,751,459,278,264,553,530,51,279,584,344,127,92,577,258,181,771,511,812,764,474,142,198,43,512,545,351,528,140,38,759,176,122,46,62,425,507,469,801,87,274,116,620,540,365,742,671,124,494,245,688,828,500,218,702,252,537,417,21,330,805,197,364,151,724,174,447,472,656,486,307,563,774,199,443,798,680,263,147,435,361,582,479,150,599,97,769,736,126,132,817,550,814,598,179,636,166,54,288,219,789,487,379,797,811,695,760,306,94,153,316,398,240,332,531,19,607,662,185,242,357,282,207,806,784,161,809,453,149,660,690,334,756,567,615,796,57,754,381,188,574,535,337,488,348,305,210,633,103,748,403,190,714,385,462,824,297,772,189,0,670,394,721,552,808,686,86,451,820,143,60,230,730,9,216,175,224,583,159,217,293,665,295,692,93,271,180,118,800,32,835,720,470,200,604,555,825","comment":null,"submitted_at":"2026-05-13 20:20:47","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/f5ace93a48889ba6f7af2f98340b7e30bc6b3c2a861a5dd1705b8787ba78f304.txt"},{"canonical_hash":"8b7ea92b587e7c8993a66a88b0ab0708045cb93f179ac9c78ca06f42e02bd4e5","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,61,769,771,220,361,164,751,600,489,190,673,60,48,776,482,382,239,480,216,817,812,787,687,772,807,652,628,120,739,64,251,445,274,417,561,7,209,252,297,13,25,638,155,398,698,669,441,444,621,565,716,199,396,412,623,295,500,442,115,527,255,806,734,192,208,833,266,289,275,315,71,460,26,804,547,573,66,245,178,405,724,402,506,774,285,803,49,432,123,487,221,598,283,163,829,108,781,485,90,390,340,263,755,633,626,401,161,150,2,695,403,449,204,617,708,114,247,589,226,834,95,760,793,56,172,422,168,420,268,714,550,101,496,288,389,694,312,134,353,351,336,28,741,728,645,576,40,702,466,567,22,23,384,165,562,736,689,641,17,723,307,585,648,640,129,112,498,571,418,711,393,359,87,194,693,742,768,391,664,237,140,543,436,685,306,282,439,686,325,764,36,438,583,836,248,773,372,215,338,470,740,557,19,546,148,75,299,835,195,337,601,564,414,753,528,424,53,47,72,376,421,671,89,65,179,649,670,524,206,12,18,459,493,718,379,599,566,302,160,762,413,580,627,326,257,643,731,171,559,635,684,250,407,808,213,801,618,473,1,729,290,128,241,187,495,264,410,779,437,116,800,334,110,183,699,356,733,707,658,159,122,394,358,746,45,27,614,595,186,139,33,581,572,504,651,474,317,341,342,758,52,676,654,701,597,200,419,58,426,184,141,296,732,569,429,381,0,529,227,383,606,533,77,763,706,63,301,386,388,99,347,659,354,146,434,232,82,625,681,205,189,574,534,538,688,57,602,431,737,455,203,457,207,21,828,725,130,799,261,423,357,542,284,360,78,568,270,4,820,214,310,821,323,531,136,515,169,484,368,660,37,185,196,366,591,668,661,404,281,55,518,605,639,43,717,514,132,327,756,481,624,212,79,743,125,450,816,73,794,198,318,563,256,452,526,265,488,202,131,69,352,16,510,815,537,823,744,279,349,720,228,305,355,320,809,541,367,759,370,143,210,31,224,70,333,433,525,294,465,578,147,830,735,831,271,76,552,243,88,467,14,425,106,280,240,324,231,798,173,555,791,44,400,463,765,427,719,293,790,118,397,100,177,273,501,254,608,512,492,80,477,535,330,588,377,745,153,86,234,98,443,778,475,551,770,380,211,41,253,343,24,304,819,157,586,479,476,634,663,363,619,38,656,655,277,712,399,32,74,509,346,180,738,127,50,191,577,322,513,332,217,174,42,596,286,644,137,629,587,665,371,409,610,519,486,748,373,201,666,523,722,761,84,29,704,85,593,91,783,385,348,162,497,335,158,448,775,258,824,225,540,750,103,556,46,309,822,777,782,672,832,667,682,642,692,827,837,697,840,662,802,792,657,677,647,632,797,637,447,811,344,11,521,138,715,505,260,789,223,810,483,193,300,532,197,313,350,818,126,454,119,726,757,558,631,166,408,713,451,554,575,374,406,630,622,594,102,679,321,548,287,612,156,15,92,703,145,311,544,109,67,364,747,242,690,691,3,584,784,339,59,308,218,6,246,415,805,516,440,813,478,133,269,121,188,710,219,536,238,142,135,362,83,825,328,754,462,730,428,365,9,826,520,278,517,111,236,796,700,795,182,613,430,329,490,468,298,105,259,314,244,709,788,502,780,545,51,387,34,96,167,453,230,491,446,721,292,97,549,752,8,674,570,553,20,316,369,696,786,345,249,785,39,235,603,113,395,319,507,392,458,653,503,499,609,154,170,646,590,117,267,469,181,262,494,35,416,464,604,767,331,176,149,461,539,607,616,68,104,151,560,579,62,10,81,472,814,375,229,530,152,276,93,766,678,222,291,592,615,378,727,144,30,124,636,456,411,107,511,54,522,705,435,303,650,471,508,175,272,94,675,683,620,5,611,680,749,233,582","comment":null,"submitted_at":"2026-05-13 20:21:06","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/8b7ea92b587e7c8993a66a88b0ab0708045cb93f179ac9c78ca06f42e02bd4e5.txt"},{"canonical_hash":"df7a67b7bc669b986000c5a2e312bb94a9636439d16150c6f9c17f13c83ec120","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,675,804,499,809,587,125,1,716,294,710,211,678,767,246,718,735,766,284,466,228,288,808,219,305,93,771,802,3,772,69,792,245,59,64,31,769,369,141,113,353,144,711,778,336,573,153,429,274,86,565,589,165,699,249,50,193,575,505,56,140,99,366,487,583,237,484,233,460,315,182,576,776,743,806,15,98,408,821,330,90,828,732,483,758,475,308,790,200,107,325,623,285,586,646,195,753,85,234,25,459,327,137,470,364,82,492,389,577,630,706,171,343,686,509,401,805,773,108,241,194,251,257,372,548,555,673,37,38,291,471,422,392,762,289,656,126,413,763,218,29,244,488,796,469,598,702,112,561,222,833,205,742,53,352,423,755,410,407,52,272,703,720,611,437,688,266,619,600,516,344,467,520,312,326,542,454,381,590,657,689,426,556,79,208,143,230,76,653,382,162,299,530,614,606,47,453,746,301,204,595,432,267,750,737,558,181,511,683,280,780,242,781,398,322,80,581,473,111,298,187,132,229,641,320,103,722,14,465,20,148,649,349,351,178,268,584,424,84,35,523,547,526,160,269,331,431,658,41,282,694,81,765,281,629,417,231,491,247,761,545,730,63,196,447,433,314,276,385,538,610,62,142,461,713,123,666,592,154,794,355,788,323,404,719,744,692,820,151,507,834,363,607,416,721,97,7,670,6,129,679,254,104,334,220,302,145,444,634,647,61,546,569,168,510,643,532,253,580,588,451,508,198,457,624,827,747,57,271,191,756,412,693,179,172,415,442,540,226,760,616,456,533,428,725,521,311,357,708,605,515,513,134,150,173,421,376,307,574,593,60,225,551,585,321,339,66,258,71,74,652,537,462,259,639,648,203,522,734,774,529,21,396,166,419,169,110,685,622,835,338,572,359,22,378,672,803,681,660,77,814,759,370,138,504,188,637,341,594,119,633,94,570,292,498,659,91,536,361,500,279,278,210,441,434,482,51,45,158,669,557,324,578,170,5,661,458,227,420,485,214,566,800,831,34,117,100,300,223,707,207,342,768,603,88,283,418,474,175,340,131,801,128,328,512,12,554,793,156,102,135,360,825,726,384,799,697,386,650,159,749,612,494,562,724,368,11,671,409,798,354,617,414,559,731,754,676,17,830,164,16,517,365,655,373,333,105,391,729,133,72,667,567,680,161,829,687,318,149,544,519,92,358,815,399,789,118,640,2,602,146,714,350,696,374,665,411,502,739,783,625,448,525,397,812,728,553,427,741,609,377,476,400,176,262,296,601,157,256,43,506,745,199,42,668,252,438,147,837,496,452,67,367,236,201,615,626,387,68,543,189,599,700,390,757,286,550,455,70,608,136,425,122,738,345,232,4,347,180,463,836,177,479,631,770,712,388,10,571,49,23,13,250,840,44,787,797,255,270,265,39,18,275,33,777,28,260,782,8,54,695,709,635,810,539,824,582,406,380,32,394,514,682,120,497,691,597,784,87,348,477,273,531,287,114,183,552,46,240,356,493,663,632,319,40,436,495,654,89,638,541,439,329,124,96,446,527,564,664,215,674,346,503,248,163,642,297,127,468,393,310,430,185,717,224,106,317,775,813,613,9,636,293,75,791,213,651,332,445,78,591,464,24,121,290,30,197,217,628,239,823,403,192,19,440,786,303,727,816,212,116,73,243,785,478,26,627,677,375,534,690,383,764,779,115,27,819,704,174,501,596,395,736,807,620,705,740,152,206,604,723,443,83,202,95,795,450,0,335,313,337,295,826,480,486,535,209,186,822,304,306,528,221,167,751,155,65,263,644,139,563,36,264,518,579,733,405,48,216,817,481,261,715,402,190,618,238,811,435,818,489,748,568,490,662,235,109,472,560,752,184,621,362,832,698,524,645,379,130,549,101,316,55,371,309,58,277,684,449,701","comment":null,"submitted_at":"2026-05-13 20:21:22","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/df7a67b7bc669b986000c5a2e312bb94a9636439d16150c6f9c17f13c83ec120.txt"},{"canonical_hash":"c700d2e020b3b8809a7f34bf91f7c8a46cfaae1265b2975f19e7546a88c03fcb","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,618,804,148,544,781,631,571,411,325,627,122,444,558,304,485,560,87,55,432,169,678,290,13,185,832,0,653,198,116,68,391,765,753,223,367,112,628,205,433,191,669,662,33,532,235,267,493,535,316,266,296,359,521,578,106,160,755,783,212,147,156,620,259,188,152,499,641,483,217,386,648,520,788,16,270,342,37,150,255,237,48,610,776,1,468,238,131,114,773,696,361,502,40,461,766,474,732,72,118,559,405,194,580,293,492,460,756,587,97,759,395,442,419,351,436,486,526,722,271,467,724,816,321,80,629,211,540,706,89,644,498,564,93,412,268,425,435,234,214,244,263,687,219,667,450,697,239,420,677,278,440,51,561,208,803,463,43,67,279,740,500,656,233,605,145,322,663,514,141,312,596,723,543,28,428,362,101,429,328,305,780,186,107,792,15,693,54,612,674,280,606,822,196,553,320,802,438,34,668,76,175,622,338,287,598,790,733,159,599,569,210,353,85,503,833,324,326,649,635,306,821,94,496,542,729,711,277,32,472,360,257,74,341,368,384,397,726,836,339,225,78,525,709,286,813,584,231,487,557,650,518,7,645,579,555,831,363,355,506,513,226,704,334,379,252,659,609,482,281,220,392,104,95,251,758,245,509,600,735,458,46,139,396,171,140,495,38,591,26,162,121,317,651,62,203,227,593,801,764,531,158,189,102,456,691,408,592,441,575,113,761,356,182,779,465,389,554,469,497,447,284,690,298,402,714,655,70,354,530,527,634,373,83,457,516,346,230,236,17,79,344,589,261,262,806,818,619,365,731,670,534,371,572,204,50,299,404,741,388,173,707,427,480,128,671,546,415,512,794,590,471,744,313,484,197,421,5,713,602,453,837,454,834,770,190,782,621,44,18,613,91,335,295,647,132,302,683,533,689,352,174,318,14,176,479,585,541,422,736,199,665,192,466,410,475,418,45,529,451,739,507,123,168,294,366,77,308,789,666,702,399,567,700,99,477,374,508,826,2,103,90,311,247,221,358,640,716,246,215,654,734,350,574,331,547,387,604,329,501,550,767,688,181,424,23,307,19,807,49,137,323,423,626,652,144,607,787,300,357,718,195,340,694,10,775,96,538,135,481,437,582,288,138,60,207,556,414,92,522,398,680,565,717,381,754,455,179,459,681,309,431,390,751,715,615,778,573,332,53,119,524,254,242,136,510,61,260,243,183,142,155,473,738,638,42,6,151,750,820,180,164,69,201,81,703,637,827,673,795,377,611,4,603,30,285,443,292,824,679,772,343,8,120,799,426,209,712,517,202,577,143,385,489,376,393,551,283,539,746,676,749,675,409,133,476,710,348,528,642,608,777,449,708,9,684,127,86,616,829,597,206,382,297,330,39,800,448,125,222,347,586,166,488,275,269,588,646,21,170,41,504,793,796,57,157,490,134,595,835,785,617,29,548,310,59,814,728,333,698,315,601,434,20,154,282,71,797,817,110,594,701,75,462,349,370,660,88,84,624,719,378,22,823,407,639,241,811,752,11,416,494,213,47,576,124,265,643,636,58,66,743,786,337,515,478,825,760,193,129,791,165,264,581,748,111,625,52,36,583,161,218,63,830,661,146,768,178,505,519,568,566,745,633,172,56,249,327,406,815,394,303,163,446,470,695,536,562,784,289,769,413,187,452,730,314,549,177,570,686,153,65,685,464,774,108,403,184,720,272,491,630,828,240,364,375,27,537,301,319,383,757,672,445,258,430,224,248,253,273,692,682,229,840,126,771,250,401,167,563,763,109,31,232,810,699,623,812,149,345,809,24,657,200,105,117,3,819,25,372,632,64,439,115,545,417,380,276,216,98,369,762,614,256,12,511,664,100,742,552,808,73,721,336,737,658,228,274,798,805,400,727,35,725,291,523,747,82,705,130","comment":null,"submitted_at":"2026-05-13 20:22:05","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/c700d2e020b3b8809a7f34bf91f7c8a46cfaae1265b2975f19e7546a88c03fcb.txt"},{"canonical_hash":"473befc40cb7a5a43aab9f4af65086b79aaed75e4d71776f6caca69e379fa533","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,93,769,584,291,173,582,419,214,29,18,661,129,424,776,158,727,658,206,0,817,730,200,829,369,192,210,450,302,530,211,242,386,298,473,745,290,186,98,566,145,603,638,46,299,680,1,163,5,628,409,787,591,136,668,279,102,685,563,71,167,739,175,737,304,542,14,370,423,550,711,368,3,57,318,322,708,108,284,613,836,311,235,717,665,394,196,604,155,82,317,488,474,85,703,545,647,109,437,706,226,213,641,363,433,124,378,674,328,489,452,531,416,380,100,721,272,67,553,491,513,258,440,482,27,520,512,449,232,773,686,288,751,54,692,684,823,462,23,390,672,212,420,728,388,34,429,238,356,342,731,492,599,831,55,295,150,306,116,143,77,230,750,571,51,712,622,142,837,660,305,653,126,289,240,201,61,264,152,65,113,316,399,87,724,581,789,562,771,139,546,12,828,677,393,361,498,505,671,689,395,733,243,497,343,115,256,28,425,519,504,149,509,169,164,209,559,194,159,524,174,199,204,544,184,539,554,514,494,179,221,80,308,532,278,768,360,654,636,540,533,396,358,642,793,47,511,104,312,4,252,432,597,824,616,759,122,364,281,78,30,187,229,26,166,275,324,91,688,340,812,574,757,583,725,695,802,177,587,747,16,606,715,265,112,178,81,341,185,330,20,796,564,219,814,573,156,749,357,528,527,766,307,391,273,464,69,353,763,455,247,637,355,58,427,788,649,216,478,42,631,75,805,506,95,669,657,19,716,323,651,808,267,484,547,555,62,447,475,223,548,526,428,8,713,411,119,825,236,375,565,276,753,518,32,237,756,135,415,381,496,487,454,293,639,413,89,468,445,517,691,697,297,795,48,263,525,33,620,222,551,398,676,248,261,741,472,74,682,510,738,120,439,453,282,833,503,400,348,430,780,44,17,366,694,224,754,456,807,21,117,190,569,161,359,630,752,270,346,801,578,319,73,592,720,86,25,819,362,683,182,611,183,335,435,371,625,681,477,743,287,283,22,38,403,746,515,458,405,49,507,556,266,687,444,508,785,699,227,253,79,125,220,589,476,561,45,339,702,140,704,202,106,598,650,137,244,633,740,821,379,41,285,382,612,296,181,827,203,735,197,471,176,816,101,626,822,374,593,40,198,36,645,334,834,280,132,767,88,377,239,205,215,607,698,76,742,446,809,336,11,673,568,180,601,133,151,325,710,690,744,15,260,797,352,791,107,172,309,629,385,2,605,233,667,438,333,351,277,246,495,337,485,679,536,726,723,818,835,557,383,457,105,558,92,567,431,623,310,245,157,404,794,165,765,782,294,269,321,586,675,407,614,131,66,118,729,345,588,466,602,127,35,171,693,762,193,811,764,83,31,96,579,372,640,621,286,234,329,632,268,570,37,350,459,94,696,53,64,523,70,422,418,522,800,783,758,761,501,644,301,774,481,707,111,249,384,617,208,594,344,207,72,826,387,832,225,50,709,655,781,141,436,162,700,326,619,734,663,572,250,170,274,412,123,732,97,315,799,10,596,441,624,255,128,804,168,792,146,331,577,417,320,6,414,786,705,442,646,590,406,470,803,90,114,218,262,664,820,543,479,652,231,521,56,772,421,719,259,300,148,576,147,648,397,784,60,121,755,627,516,257,585,68,537,659,401,52,9,815,465,313,365,538,798,718,241,600,24,813,490,228,13,830,332,662,656,552,480,634,130,560,292,408,410,271,790,84,376,748,43,463,493,134,610,338,500,541,770,110,666,7,443,251,103,643,486,389,349,392,714,191,608,779,254,670,160,426,153,402,760,618,722,609,777,434,736,615,775,448,467,217,39,347,189,499,840,534,154,144,529,549,483,810,580,701,469,460,63,367,188,461,195,635,806,314,354,451,678,138,535,303,575,99,373,327,595,778,59,502","comment":null,"submitted_at":"2026-05-13 20:22:34","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/473befc40cb7a5a43aab9f4af65086b79aaed75e4d71776f6caca69e379fa533.txt"},{"canonical_hash":"ae98156863f5cf10a2dcddee66e0155acccb1947abbd089bf2ccdc838c59a10c","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,9,769,420,405,648,787,168,527,143,739,11,76,353,776,348,736,50,565,594,817,669,724,292,678,218,505,676,394,448,657,480,96,310,732,209,479,331,38,84,476,177,141,695,763,463,793,268,410,135,672,417,658,427,450,646,718,452,729,510,372,136,364,90,249,423,688,418,205,723,377,254,285,827,632,302,651,78,514,333,725,645,58,117,531,721,7,161,281,216,56,350,631,357,659,547,757,282,703,121,278,188,682,185,39,346,640,574,799,211,53,566,615,235,112,99,567,30,526,439,655,560,541,169,171,589,250,88,207,735,814,127,436,17,771,685,118,801,612,469,210,47,28,554,619,466,14,5,201,87,303,611,124,179,64,260,741,745,591,446,449,236,551,283,599,592,147,301,137,534,393,183,654,490,798,677,542,229,709,180,752,468,70,432,347,51,330,414,768,354,808,673,239,636,762,213,442,403,340,500,355,552,126,190,812,80,440,61,664,306,575,103,32,69,596,556,152,786,13,60,184,750,241,597,539,186,829,129,746,454,608,578,563,381,568,401,396,371,618,356,391,583,406,361,366,603,416,598,613,573,623,411,711,94,794,151,504,562,276,715,149,25,48,821,187,521,561,34,67,138,610,341,323,486,230,699,26,475,115,777,155,91,517,390,535,305,368,477,248,727,671,274,638,773,389,158,322,397,443,380,733,379,295,16,312,467,105,433,717,145,744,264,507,642,833,525,689,148,358,465,387,238,837,277,605,816,499,102,336,182,627,564,318,516,271,484,481,626,710,706,225,29,144,89,630,62,20,789,805,133,344,809,164,576,338,122,166,40,49,431,584,519,63,12,245,434,577,836,83,650,726,221,202,625,825,109,730,308,314,79,261,806,52,471,92,779,700,172,123,215,624,206,204,506,595,690,474,559,10,616,326,795,766,617,33,544,751,299,456,108,491,65,602,134,77,270,580,601,18,246,834,609,675,311,4,791,755,191,459,780,293,37,157,189,363,772,518,384,472,150,647,153,243,86,738,317,722,512,694,392,666,385,21,438,269,530,470,212,633,300,110,749,464,162,304,0,275,251,316,196,42,756,496,82,23,680,760,298,549,113,139,606,614,796,785,194,461,607,585,742,173,538,130,550,686,337,667,792,320,219,412,758,170,383,653,458,644,106,422,788,232,41,532,263,404,453,315,533,258,639,214,125,399,101,407,545,764,487,753,681,485,783,165,332,400,227,378,662,737,36,259,307,508,460,502,462,693,382,637,100,375,233,828,428,728,832,520,712,374,272,684,140,290,656,740,22,284,587,586,660,176,142,441,119,3,296,444,174,93,132,231,59,835,529,546,255,819,195,66,493,367,813,767,345,131,445,692,483,359,641,408,557,85,713,257,198,244,447,360,778,402,528,31,160,540,253,643,327,759,634,782,395,482,279,163,222,748,120,522,373,621,622,319,57,705,629,600,15,701,313,811,784,220,511,494,800,24,266,97,128,537,425,543,342,224,388,111,46,704,178,691,325,175,649,237,409,747,555,797,674,223,498,280,488,492,203,822,683,1,702,697,413,262,365,297,200,818,515,95,503,208,707,370,455,734,369,228,497,6,267,823,457,71,679,240,35,339,197,429,44,804,620,572,426,159,820,831,579,571,104,437,419,553,807,398,803,714,75,335,668,247,435,495,234,473,73,421,334,716,509,154,192,2,328,815,424,156,720,826,226,114,349,343,54,68,582,731,830,291,581,45,524,199,774,309,321,501,765,74,790,590,167,256,761,781,570,289,181,8,98,770,824,55,27,665,415,663,548,116,696,242,802,273,352,430,708,687,558,719,252,478,362,287,193,604,72,294,775,670,265,451,288,351,628,840,593,386,376,588,635,810,329,107,569,489,217,754,523,652,743,661,81,513,698,43,146,324,536,286,19","comment":null,"submitted_at":"2026-05-13 20:22:50","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/ae98156863f5cf10a2dcddee66e0155acccb1947abbd089bf2ccdc838c59a10c.txt"},{"canonical_hash":"6a96e1646a141fe14eb0dab5010944e0bd44835dc9d18390c1d30c516816a975","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,391,769,365,148,451,264,260,116,323,430,314,680,777,776,163,772,241,281,257,817,293,160,307,355,688,367,133,808,376,747,753,330,53,12,193,404,348,352,806,452,533,625,145,187,566,346,511,420,327,252,670,709,105,669,275,624,567,434,509,131,39,40,555,89,278,291,724,432,319,741,526,120,786,194,251,435,460,157,233,149,283,538,75,297,606,766,678,409,457,321,816,350,565,238,80,683,227,203,556,362,162,543,701,686,809,793,38,60,587,618,750,361,67,59,574,132,378,732,205,329,142,130,394,261,695,412,218,282,442,792,536,615,204,591,224,569,55,310,481,127,582,500,733,373,613,449,104,727,745,681,524,235,0,748,760,699,69,325,388,696,91,48,426,628,539,7,128,72,464,30,656,88,79,265,418,37,627,779,285,499,269,702,29,588,833,545,659,456,474,639,249,398,381,58,525,549,245,82,700,813,335,129,101,594,568,829,138,758,395,787,389,518,729,531,256,658,333,610,690,296,746,199,407,200,272,586,213,324,791,596,739,801,668,147,630,447,209,405,212,528,334,266,287,620,188,756,450,140,399,223,541,599,763,641,22,254,530,705,106,73,612,757,644,63,87,134,834,14,441,479,386,250,340,573,26,66,51,166,56,186,181,156,36,141,176,1,191,146,151,21,201,16,31,61,41,196,206,46,351,444,476,49,799,99,122,28,679,722,577,108,71,740,495,219,57,676,728,564,783,519,368,50,810,364,175,485,721,153,585,322,231,299,493,247,370,174,482,665,182,633,836,704,561,832,382,100,341,537,308,289,248,621,237,165,372,164,711,331,655,575,298,693,221,496,764,553,354,822,360,475,90,472,143,527,172,312,723,103,794,603,629,136,94,300,778,735,117,210,514,490,23,416,363,214,674,439,45,52,717,471,805,671,572,44,423,421,694,510,798,623,64,737,234,534,320,814,592,2,383,230,114,123,691,65,366,137,86,743,825,459,43,755,579,463,429,107,93,42,504,593,461,13,126,661,353,290,34,664,725,713,35,270,784,707,550,619,795,406,84,562,274,448,559,646,710,762,139,484,578,408,768,535,617,92,446,345,20,604,259,78,68,19,255,780,823,27,111,649,662,626,169,580,501,827,477,317,253,377,660,226,359,95,177,294,170,336,698,558,480,532,831,242,716,303,453,767,413,97,609,24,32,396,715,583,622,25,3,828,774,651,489,540,280,83,785,654,494,74,703,682,736,508,197,397,521,168,262,648,115,273,600,385,781,286,379,337,189,719,552,190,246,427,576,677,422,374,643,731,571,332,110,503,318,184,268,192,425,714,595,392,309,547,380,516,675,185,652,470,216,159,821,85,491,706,284,467,759,326,243,208,548,650,616,522,419,570,232,167,433,124,520,5,4,96,544,469,602,589,240,634,631,563,77,244,835,824,765,393,431,637,70,744,635,217,292,455,546,311,601,152,410,271,761,228,507,802,673,144,339,672,180,590,498,487,771,387,313,369,158,304,179,638,837,542,263,726,236,375,468,47,18,295,718,712,411,773,98,466,358,730,789,800,279,112,598,666,687,402,653,390,342,195,328,782,202,267,605,384,557,581,685,513,173,642,222,316,276,807,198,811,150,640,551,415,512,344,357,560,749,647,812,645,349,465,288,611,462,211,155,517,754,154,302,414,488,81,225,229,486,738,109,529,689,820,118,315,505,454,697,183,400,734,338,751,277,796,497,445,523,663,301,483,356,804,684,76,62,788,815,220,54,33,113,428,803,239,597,119,371,830,584,515,742,819,458,614,720,8,424,790,708,121,102,401,438,9,607,636,770,436,752,17,10,692,347,207,492,178,437,125,440,632,343,502,306,135,417,797,443,775,15,403,554,818,840,11,171,161,6,478,608,305,215,667,506,258,657,826,473","comment":null,"submitted_at":"2026-05-13 20:23:06","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/6a96e1646a141fe14eb0dab5010944e0bd44835dc9d18390c1d30c516816a975.txt"},{"canonical_hash":"29114da6b2104ef81c020a93ef8aa1bc3b71ec816d4186c3cb104944af226769","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,793,314,572,269,540,627,487,332,335,731,714,466,206,363,787,565,82,268,651,663,179,145,195,448,623,112,614,1,522,823,657,520,411,654,538,203,665,348,427,551,547,768,215,489,36,412,356,367,434,723,679,610,375,19,739,835,227,174,775,831,583,473,125,672,172,480,569,509,271,113,69,218,539,231,491,101,774,33,640,277,305,834,45,369,53,634,502,355,382,230,328,391,16,625,371,748,680,500,815,694,392,527,183,637,754,703,51,531,553,838,34,449,469,442,239,707,293,302,84,103,339,67,404,95,146,109,421,626,683,410,705,837,561,508,316,745,676,177,435,163,106,306,746,323,497,444,526,632,689,743,386,350,464,548,749,387,675,11,377,437,833,733,557,495,620,225,664,29,46,178,810,366,692,159,290,511,256,110,212,262,216,494,458,38,660,559,589,568,354,18,238,465,816,65,794,54,157,795,819,86,133,182,712,409,415,681,244,37,688,750,751,344,596,321,311,73,426,513,111,89,114,566,168,307,151,807,440,298,100,710,758,512,61,510,357,528,669,338,9,537,26,479,647,381,644,713,690,365,541,825,240,813,402,401,424,193,600,452,764,555,17,428,631,378,315,249,15,175,248,186,347,587,629,160,97,481,467,294,127,194,580,729,607,773,603,643,802,711,673,732,827,74,341,57,202,171,131,616,229,730,292,498,329,666,85,153,446,736,400,283,586,93,735,394,425,134,296,558,507,595,397,536,639,21,699,56,447,396,820,708,474,333,505,759,454,235,685,642,4,352,753,188,808,360,376,532,98,702,136,671,591,678,141,334,288,301,207,503,405,139,62,297,741,430,346,700,451,399,79,234,158,740,832,621,90,264,32,618,209,77,201,330,535,788,107,140,263,358,726,622,309,609,190,646,782,709,482,567,30,443,658,560,461,327,319,722,143,331,390,161,83,219,450,523,698,75,99,761,192,576,606,419,282,286,691,817,436,47,308,121,760,720,124,247,144,142,223,645,232,677,39,3,58,130,118,779,374,478,276,71,50,588,514,496,839,836,574,236,310,780,485,544,612,22,180,102,734,525,20,165,585,716,254,599,199,772,320,592,132,648,383,317,299,608,636,191,472,778,433,253,486,196,27,590,562,641,617,170,325,613,456,25,777,304,258,530,204,322,438,704,604,353,783,72,259,653,477,185,721,137,345,12,638,724,289,155,181,279,423,797,602,122,92,342,10,661,706,803,189,476,582,205,373,550,598,575,462,624,278,684,492,208,220,728,6,543,738,439,805,659,552,372,744,416,556,361,24,490,432,417,380,662,318,41,615,828,670,459,406,517,14,718,407,763,343,649,818,769,674,351,210,422,533,652,830,605,362,484,546,198,515,31,370,429,66,542,695,579,149,8,246,806,252,44,483,809,549,682,379,501,455,237,784,519,785,650,123,593,280,228,135,55,241,147,63,76,408,840,757,791,801,413,393,388,752,250,398,265,781,260,418,786,275,767,771,270,776,747,796,403,737,742,762,255,245,150,7,457,368,184,5,597,176,633,619,545,471,656,117,274,719,273,628,577,701,87,453,284,340,570,200,798,337,792,156,717,755,431,312,187,693,78,173,715,42,281,571,70,214,326,119,303,686,601,94,445,385,349,116,812,414,756,518,52,727,420,581,441,324,224,197,822,129,88,766,696,725,166,104,291,765,395,80,287,126,336,668,389,313,148,493,611,105,154,814,789,233,584,488,242,285,81,49,460,563,68,257,506,128,152,811,384,655,211,251,687,790,60,13,554,524,468,169,40,635,521,64,564,120,770,364,272,96,213,504,667,826,48,300,804,534,266,167,578,222,829,28,226,108,475,59,164,221,573,799,697,267,594,35,138,217,529,821,91,115,630,470,824,261,43,243,800,516,463,23,162,295,499,359","comment":"Size-841 = 29² idempotent right-cancellative magma satisfying Eq 677 and Eq 255 (but NOT Eq 3345). Constructed using the exceptional Zassenhaus near-field of order 29².\n\nThe multiplicative group of this near-field has order 840 = 29² − 1 with structure Z₅ × Z₇ × SL(2, 3) (the binary tetrahedral group of order 24, extended by cyclic factors Z₅ and Z₇ — a non-cyclic group of order 840). The automorphism group of the magma is the sharply 2-transitive (Z/29)² ⋊ (Z₅ × Z₇ × SL(2, 3)) of order 706,440 = 841 × 840.\n\nOperation: x ◇ y = x + f(y − x) on the additive group (Z/29)² ≅ GF(841), where f is left-multiplication by a fixed near-field element c of order 10 in the mult group. f has cycle structure (1, 10⁸⁴) — fixed at 0, with 84 orbits of length 10 partitioning F_841* (the 84 cosets of ⟨c⟩ in the order-840 multiplicative group).\n\nf is NOT F_29-linear (so this is NOT the simple linear F_841 magma of the form x ◇ y = x + c(y − x) over GF(841) with commutative ·): in the basis used by the display reorder, f(1, 0) + f(0, 1) = (8, 23) ≠ (7, 3) = f(1, 1) in (Z/29)² coordinates. The axis-additivity of f together with its global non-additivity is the structural fingerprint of the exceptional near-field's non-distributive multiplication.\n\nDirect analog of magma#5ebfbb80 (size 121 = 11², exceptional near-field of order 11²), which has the same template but with Z₅ × SL(2, 3) replacing Z₅ × Z₇ × SL(2, 3), and which additionally satisfies Eq 3345.\n\nDisplay reorder presents elements as (i, j) ↦ τ₁^i τ₂^j(0) at index 29i + j, where τ₁, τ₂ are commuting order-29 fix-free magma automorphisms (the hidden additive translations by '1' and '2' in (Z/29)²). Under this reorder the Cayley table is fully (Z/29)²-translation-invariant; the rendered image shows diagonal banding across the 841×841 grid.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:11:58","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/29114da6b2104ef81c020a93ef8aa1bc3b71ec816d4186c3cb104944af226769.txt"},{"canonical_hash":"ad16fb07e4c35cac3d07e2f16567bdc4ecd101447386c42678c456082914cdd1","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,1,463,668,594,538,133,69,840,63,86,520,563,638,462,29,8,815,658,284,433,273,801,30,315,183,482,792,40,62,22,830,701,663,224,285,793,7,15,240,84,821,134,643,93,823,101,244,20,41,800,293,233,673,712,772,49,48,55,808,485,145,334,50,822,225,470,308,683,771,21,2,176,487,458,408,309,266,36,837,181,707,536,569,131,672,38,291,558,791,272,490,572,831,528,755,584,112,785,78,301,116,401,465,762,221,508,675,248,540,634,313,639,380,706,152,99,637,68,34,636,467,576,747,450,174,773,307,756,360,384,573,184,114,254,625,488,177,325,32,779,3,719,522,810,735,796,596,429,109,627,219,486,451,533,381,783,97,753,67,426,124,655,602,629,744,702,585,331,173,489,553,354,725,550,368,355,424,591,103,819,106,700,399,249,496,238,494,327,836,236,827,321,575,290,758,275,506,386,121,654,155,393,689,344,412,318,652,686,258,657,4,835,182,392,209,268,98,674,685,107,76,319,502,137,621,624,443,353,179,765,811,111,546,336,697,588,818,201,557,631,239,66,670,526,383,438,457,159,789,542,260,215,605,409,839,298,263,297,750,312,447,214,704,681,366,295,400,466,577,724,208,578,80,142,529,480,543,703,743,186,5,127,352,162,834,35,456,713,246,161,648,351,421,774,516,693,509,541,730,519,10,251,342,464,481,25,341,809,262,469,65,708,595,734,100,45,570,122,337,414,633,474,316,616,144,60,799,571,517,347,698,512,241,306,217,653,207,709,373,587,688,154,166,592,705,678,125,252,135,132,6,64,661,118,620,136,746,667,58,247,395,165,679,269,317,294,782,739,628,662,18,778,211,52,531,88,81,549,153,650,816,330,556,761,539,445,415,527,430,391,812,12,292,185,760,205,598,157,245,814,448,579,237,427,387,613,442,763,139,532,203,243,454,780,644,599,89,394,722,326,9,422,188,589,559,333,33,56,37,764,766,288,500,741,232,23,108,732,305,642,564,498,94,323,607,223,61,47,71,651,255,375,220,483,85,455,300,478,535,194,113,274,175,229,601,198,104,19,28,286,339,525,410,350,684,42,14,218,200,728,385,163,314,51,665,523,583,432,265,441,11,27,794,222,826,170,503,102,434,43,477,618,358,610,608,338,781,115,388,370,304,833,691,72,59,91,310,364,612,126,807,16,680,476,515,574,158,501,322,838,721,83,461,497,752,193,423,547,204,820,54,348,586,676,299,795,195,664,660,168,513,716,261,687,335,742,717,376,382,711,13,786,505,367,196,180,751,253,484,749,767,614,604,733,692,802,530,777,120,287,770,26,57,226,369,228,788,757,146,829,44,190,405,499,444,495,593,31,690,407,453,39,440,646,471,123,493,178,659,635,210,79,775,403,371,518,270,603,346,666,609,264,813,92,192,568,475,259,745,105,17,77,435,562,199,817,417,234,723,267,329,784,340,277,197,790,187,803,590,372,452,332,437,754,694,623,567,140,406,626,160,682,53,231,759,390,363,736,710,130,420,699,510,379,439,320,600,143,647,641,806,748,473,630,720,343,374,289,171,361,548,70,787,87,82,250,581,278,95,565,24,545,560,615,632,129,96,669,695,151,283,46,645,768,402,345,280,362,521,167,324,460,191,622,552,365,731,804,413,656,727,832,216,671,524,150,737,359,479,740,828,349,561,544,271,468,138,164,212,611,279,328,537,206,110,73,230,504,147,436,425,119,449,824,582,825,213,714,416,491,74,172,718,149,311,726,617,276,554,227,303,257,202,696,169,776,281,396,411,156,128,534,282,597,75,805,507,446,302,398,148,431,566,511,459,472,377,397,389,492,619,117,715,256,357,235,141,242,90,606,797,378,514,729,677,428,769,189,418,419,798,649,640,580,551,555,356,404,296,738","comment":"Size-841 = 29² idempotent right-cancellative magma — non-standard linear construction.\n\nSize 841, fully idempotent, RC. L_0 cycle 1 + 84·10 (left-multiplier has order 10 — consistent with a Phi_10-related multiplier). R_0 cycle 1 + 12·70 (right-multiplier has order 70).\n\nVerified NOT to be:\n  - F_29² Type-1 linear magma (= AG(2, 29) affine line). All 4 primitive 10th roots in F_29² give 2 distinct iso classes magma#cc0cd58750be and magma#ee91772f0657, neither matching this magma.\n  - F_29² Type-2 linear magma. All 4 Phi_2_5 roots in F_29² give 2 distinct iso classes magma#8469938fe79d and magma#630bb9976070 (both non-fully-idempotent), neither matching this magma.\n\nSo this is likely either:\n  - The Zassenhaus exceptional near-field of order 29² = 841 (Zassenhaus near-fields exist at p² for p ∈ {5, 7, 11, 23, 29, 59}). The Zassenhaus near-field of order 841 has multiplicative group of order 840.\n  - A \"twisted AG(2, 29)\" magma with only some of the 30 parallel classes preserved as sub-magmas (analog of the 2-class / 4-class / 8-class twisted AG(2, 11) family at size 121).\n\nDetermining the exact construction would require deeper analysis: enumerating size-29 sub-magmas (currently expensive due to size 841), or computing |Aut| and comparing to expected automorphism orders for each candidate construction.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:12:21","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/841/ad16fb07e4c35cac3d07e2f16567bdc4ecd101447386c42678c456082914cdd1.txt"},{"canonical_hash":"cc0cd58750beea3d84d4a9b7c9fe98e32dbc56f7badc5df665772e5c4a63b188","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,769,198,573,776,817,697,62,735,664,129,412,585,401,318,301,213,58,426,429,103,767,72,385,678,567,259,655,319,197,532,661,539,169,458,262,337,571,85,708,236,275,150,131,531,422,325,510,373,206,36,25,624,369,711,420,9,523,533,775,840,810,498,558,805,825,795,780,493,785,513,508,553,835,538,503,800,518,543,548,820,528,815,830,790,770,423,204,504,696,497,162,284,44,455,746,404,589,60,1,171,408,545,290,457,496,96,185,240,271,743,120,606,302,227,782,811,608,163,734,804,803,690,224,602,643,350,107,732,138,464,461,23,248,336,283,366,620,377,94,699,700,27,662,801,356,97,153,367,128,794,689,451,680,17,238,592,772,343,410,598,610,722,724,84,454,793,760,13,214,652,326,633,738,285,399,691,115,452,584,492,601,491,55,157,297,91,66,349,222,180,166,39,488,235,403,450,199,266,540,741,499,186,111,621,641,761,353,200,317,512,419,490,255,242,177,604,305,216,438,299,5,472,758,149,59,16,511,135,519,470,345,225,287,681,440,56,442,256,212,552,731,156,551,728,478,147,389,393,81,105,189,339,574,530,170,591,559,29,45,378,629,14,666,267,713,136,515,30,425,537,463,90,155,330,41,716,202,174,576,210,427,141,374,324,544,342,241,536,89,18,638,158,694,243,415,729,765,331,102,799,22,348,727,798,657,361,133,685,777,615,459,219,806,372,456,597,603,215,329,541,671,520,468,46,581,379,246,19,71,542,335,179,146,347,564,718,430,160,207,432,549,383,272,35,95,721,83,298,715,178,617,479,381,42,749,658,476,565,677,819,365,38,392,797,818,122,263,109,826,635,747,281,644,623,239,742,792,471,173,346,813,560,612,639,117,672,474,618,258,814,376,234,104,360,37,78,821,33,744,293,630,387,653,710,8,605,12,148,279,717,233,362,647,719,587,123,321,79,837,789,698,449,338,684,796,788,405,446,351,755,593,675,92,187,196,226,651,15,140,159,359,521,252,480,315,561,309,363,768,522,26,265,529,614,121,448,701,482,327,69,500,75,434,390,660,203,632,134,323,431,77,264,704,822,669,406,63,702,572,774,781,740,590,218,108,683,773,578,67,417,306,288,99,667,168,695,355,469,341,382,32,613,808,648,73,253,625,705,816,809,607,737,28,371,634,787,739,229,112,466,194,175,50,686,261,161,152,110,535,34,292,447,736,483,86,579,494,230,61,557,733,398,344,596,280,445,217,556,394,268,752,244,183,47,570,43,127,640,628,720,386,481,370,823,831,649,303,484,663,824,802,114,286,88,622,754,682,397,595,778,311,208,436,827,707,745,688,352,665,328,709,68,786,113,2,395,139,269,411,779,223,583,439,637,82,674,577,416,444,582,143,750,333,118,274,588,679,316,712,670,791,74,228,87,783,832,357,3,400,784,642,600,441,693,714,7,11,433,555,636,506,294,250,756,130,0,237,418,514,467,172,195,465,753,599,312,181,144,300,507,106,54,211,414,616,380,278,659,193,673,53,124,568,562,421,407,771,254,424,580,812,650,98,396,692,833,762,313,57,834,137,296,730,764,101,748,232,631,49,594,413,501,276,307,509,289,409,176,462,245,611,209,167,751,6,295,190,125,428,502,460,65,550,477,21,475,646,322,260,310,10,64,524,626,205,495,609,304,154,70,116,358,354,182,443,763,516,191,766,517,247,221,165,388,726,676,586,76,151,435,554,100,546,51,24,184,723,437,40,334,473,251,340,569,142,277,220,525,384,547,282,619,487,80,656,364,320,703,534,706,505,231,164,485,368,270,453,4,201,145,257,314,31,126,332,192,20,526,566,527,829,93,402,188,132,391,836,668,291,687,249,48,725,828,489,119,759,757,575,563,375,308,807,627,273,52,645,486,654","comment":"F_29² Type-1 affine line magma at size 841.\n\nSize 841 = 29², fully idempotent, RC. Linear over the extension field F_29² = F_29[α]/⟨α² − 2⟩.\n\nOperation: x ◇ y = (1−β)·x + β·y in F_29², with β a primitive 10th root of unity in F_29² (= root of Phi_10(x) = x⁴ − x³ + x² − x + 1). F_29² has |F_29²*| = 840 = 2³·3·5·7, divisible by 10, so 4 primitive 10th roots exist; up to Galois conjugacy these form 2 orbits of 2, giving 2 distinct iso classes at size 841 (this magma corresponds to one of the two Galois orbits; the other is magma#ee91772f0657).\n\nThis is the \"AG(2, 29) affine line over F_29²\" magma. Sub-magma structure: NO size-29 sub-magmas (since the Phi_10 root β lies in F_29² \\ F_29, the F_29 prime subfield is not preserved by the operation). Every pair of distinct elements generates the full 841-element magma.\n\nCompanion to the other F_29² linear magmas at size 841 in the DB: magma#cc0cd58750be (the other Type-1 iso class) and the two Type-2 magmas magma#8469938fe79d, magma#630bb9976070 (Phi_2_5-root constructions).\n\nThe size-841 family also includes magma#ad16fb07 (an exceptional non-standard construction, possibly the Zassenhaus near-field of order 841) and various other entries — see size-841 page commentary.\n\n[text written by Claude]","submitted_at":"2026-05-20 19:20:58","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/841/cc0cd58750beea3d84d4a9b7c9fe98e32dbc56f7badc5df665772e5c4a63b188.txt"},{"canonical_hash":"ee91772f06572f92f169bfc2282dae2327f52fa3b4914b2d581f54c44f2ea9af","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"838,839,804,559,802,205,100,52,472,171,81,153,110,242,201,239,614,38,192,92,725,522,713,672,678,767,327,285,760,465,674,367,652,508,758,780,46,630,661,821,333,395,284,675,426,437,39,717,744,538,445,252,827,621,255,488,623,384,244,718,808,57,206,492,765,70,212,730,290,175,115,97,332,772,158,197,737,529,86,43,683,774,141,619,677,809,477,126,417,552,31,798,259,358,711,183,215,521,32,35,573,530,140,84,781,271,360,714,579,494,403,119,510,443,664,526,697,71,317,232,828,604,549,82,90,703,161,757,135,750,229,794,182,195,512,462,668,143,310,191,829,63,792,715,42,258,321,399,595,313,570,302,238,571,612,78,144,736,226,184,484,9,142,330,15,334,481,406,286,366,638,112,133,424,393,511,433,563,116,74,21,350,383,519,240,500,60,551,165,542,261,249,569,208,109,22,654,555,407,771,788,704,701,547,659,398,355,170,27,706,26,556,114,709,79,65,178,793,121,505,574,776,568,210,254,412,438,524,266,525,516,353,545,230,778,541,418,251,588,198,11,644,509,796,50,726,532,423,594,99,12,373,397,490,729,155,501,274,106,134,375,473,558,695,650,352,275,764,304,66,694,606,702,415,800,485,812,59,318,743,369,272,422,806,493,608,430,446,646,637,518,596,436,790,463,49,640,359,754,831,684,420,405,662,837,685,768,265,447,56,598,727,636,475,548,343,377,262,294,489,411,263,243,189,486,429,307,231,339,138,575,741,20,117,283,149,335,643,600,83,147,371,404,617,14,291,326,576,582,23,587,835,572,666,825,830,815,8,33,671,840,810,567,577,676,691,686,805,3,696,18,592,13,681,562,28,820,773,129,150,368,453,791,193,536,370,496,392,589,45,6,413,540,269,520,94,721,639,246,225,136,724,7,527,504,583,347,710,186,457,789,752,77,227,37,824,698,177,130,85,823,692,58,173,190,745,733,599,101,787,305,507,224,156,544,799,280,667,87,234,148,47,554,755,673,720,609,105,467,797,833,762,517,68,237,166,200,834,322,708,187,196,76,95,288,376,459,312,122,152,581,434,25,88,331,456,746,605,296,194,580,648,19,213,108,340,622,268,344,154,409,416,236,311,103,137,216,248,34,620,5,292,396,602,663,761,449,474,389,320,560,471,561,356,169,123,209,346,167,303,324,228,132,319,204,591,419,658,0,211,223,341,351,315,756,287,278,306,162,164,590,444,391,29,98,298,118,466,469,597,615,145,499,131,716,535,584,531,363,578,719,634,264,40,365,448,803,2,276,515,1,491,786,124,557,220,89,408,387,188,690,641,523,364,807,732,299,645,632,603,267,54,410,61,382,468,425,452,348,795,689,270,553,441,836,738,480,601,759,394,128,281,10,479,174,233,625,454,361,329,4,766,566,308,253,633,476,172,221,607,565,316,107,401,325,179,73,297,362,618,822,739,421,328,41,647,379,616,533,432,390,660,503,460,250,440,69,314,656,753,669,483,247,712,670,816,775,777,688,214,75,337,48,482,735,102,91,814,497,120,534,682,176,180,742,624,62,295,202,146,813,700,163,779,723,217,817,811,478,309,455,427,642,769,770,277,651,245,385,374,451,357,707,748,435,655,611,323,613,665,699,64,498,528,36,199,627,293,439,301,345,241,586,610,113,386,157,751,218,414,127,461,24,159,282,336,653,349,464,93,585,273,381,30,181,151,782,740,687,207,222,487,539,300,728,53,125,67,784,342,502,629,168,80,819,747,705,219,96,185,818,693,72,431,257,470,51,680,450,354,785,289,543,628,763,400,749,458,513,338,722,260,657,826,44,626,372,631,442,832,679,635,428,734,550,203,537,495,380,593,731,402,139,256,55,378,111,388,801,17,279,546,514,104,506,783,649,564,160,235,16","comment":"F_29² Type-1 affine line magma at size 841.\n\nSize 841 = 29², fully idempotent, RC. Linear over the extension field F_29² = F_29[α]/⟨α² − 2⟩.\n\nOperation: x ◇ y = (1−β)·x + β·y in F_29², with β a primitive 10th root of unity in F_29² (= root of Phi_10(x) = x⁴ − x³ + x² − x + 1). F_29² has |F_29²*| = 840 = 2³·3·5·7, divisible by 10, so 4 primitive 10th roots exist; up to Galois conjugacy these form 2 orbits of 2, giving 2 distinct iso classes at size 841 (this magma corresponds to one of the two Galois orbits; the other is magma#cc0cd58750be).\n\nThis is the \"AG(2, 29) affine line over F_29²\" magma. Sub-magma structure: NO size-29 sub-magmas (since the Phi_10 root β lies in F_29² \\ F_29, the F_29 prime subfield is not preserved by the operation). Every pair of distinct elements generates the full 841-element magma.\n\nCompanion to the other F_29² linear magmas at size 841 in the DB: magma#cc0cd58750be (the other Type-1 iso class) and the two Type-2 magmas magma#8469938fe79d, magma#630bb9976070 (Phi_2_5-root constructions).\n\nThe size-841 family also includes magma#ad16fb07 (an exceptional non-standard construction, possibly the Zassenhaus near-field of order 841) and various other entries — see size-841 page commentary.\n\n[text written by Claude]","submitted_at":"2026-05-20 19:22:22","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/841/ee91772f06572f92f169bfc2282dae2327f52fa3b4914b2d581f54c44f2ea9af.txt"},{"canonical_hash":"8469938fe79d665c1e81678a8fd11c19a78afe7d93aebf2b2bd55138a23e4b4f","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"840,836,821,761,806,506,746,656,791,686,491,461,731,566,641,431,776,521,671,701,476,581,446,536,716,596,551,611,626,119,563,266,676,246,462,699,303,667,174,5,9,2,767,544,558,725,103,320,59,77,765,415,433,700,65,606,182,689,104,543,548,710,251,88,661,305,231,44,447,62,684,750,288,400,652,838,159,685,24,50,20,591,17,167,752,674,529,33,417,379,488,413,690,191,43,340,601,692,778,171,469,625,807,483,367,624,650,531,228,71,107,592,245,614,99,361,89,385,528,637,533,823,695,144,236,670,4,31,646,412,290,27,216,576,406,34,432,152,47,737,669,659,735,514,273,209,789,165,410,790,653,393,437,106,112,356,757,634,124,696,766,264,648,435,272,336,162,815,85,779,552,158,193,523,72,792,402,468,364,352,473,609,398,635,675,516,176,213,405,56,325,92,586,577,677,230,763,599,156,84,454,346,610,359,262,585,343,587,414,702,803,426,235,140,784,312,519,86,45,673,256,798,308,123,496,509,520,274,545,315,487,11,3,66,370,201,513,561,622,391,518,73,808,837,680,137,129,409,221,722,655,654,19,644,70,720,631,499,397,258,275,389,617,456,342,703,153,304,96,373,833,814,75,338,550,517,615,732,170,116,828,539,345,292,67,265,549,286,526,575,194,751,774,249,150,633,395,420,775,257,638,321,378,147,422,800,91,7,97,764,341,537,742,143,619,178,109,508,681,164,712,770,745,721,113,16,227,744,589,29,608,219,148,10,291,120,79,734,348,603,478,311,117,365,651,507,812,810,57,418,777,310,387,0,453,571,349,562,337,662,458,215,594,748,383,584,620,141,660,8,501,439,161,331,198,595,390,269,324,39,332,76,455,172,612,694,583,826,225,495,713,222,166,419,817,253,756,429,708,430,396,497,145,416,218,184,344,407,247,658,570,241,328,783,572,293,399,108,687,481,788,494,831,505,220,259,125,530,769,300,297,472,504,40,6,134,281,261,714,682,87,90,559,740,335,38,53,715,621,704,578,691,477,318,189,83,782,573,118,74,780,448,26,197,18,394,51,206,355,707,186,640,498,639,546,32,607,629,376,55,503,705,58,616,793,484,822,382,665,243,122,260,114,224,180,805,408,121,371,649,711,279,450,351,830,794,173,538,804,48,668,452,127,772,139,781,663,287,177,100,567,208,374,600,602,717,441,155,327,101,688,813,138,524,289,330,81,277,358,52,818,250,799,534,60,271,323,511,535,560,502,404,471,718,319,388,829,353,532,747,131,554,307,280,301,590,632,357,168,111,428,36,565,630,185,423,360,28,564,541,179,785,736,1,759,22,234,82,135,749,618,326,380,522,825,727,760,128,242,604,623,163,306,94,363,493,132,666,827,284,12,37,187,709,421,510,237,434,268,444,445,512,54,199,339,347,470,627,598,240,728,181,832,771,723,411,160,233,149,276,697,105,755,13,730,719,706,333,98,588,35,463,212,296,729,102,574,350,68,636,593,492,204,797,133,795,41,239,820,136,664,294,366,809,553,63,467,787,796,302,115,223,195,46,386,726,465,425,188,819,683,142,154,678,192,582,42,733,403,368,762,569,295,605,372,126,15,645,438,21,556,486,334,424,547,146,322,316,647,183,443,580,200,375,579,299,14,724,525,449,459,527,214,362,642,255,196,786,49,248,80,202,436,252,283,460,69,354,485,613,743,427,738,175,254,151,309,824,78,802,317,238,61,741,440,834,157,693,597,835,679,381,568,482,811,130,210,401,480,203,698,169,207,314,739,464,542,377,270,801,263,217,267,475,369,628,442,190,839,540,474,229,657,211,64,95,451,298,30,500,758,753,329,479,392,816,232,490,643,205,555,244,226,110,313,515,768,754,557,285,278,282,384,457,93,489,672,25,466,23,773","comment":"F_29² Type-2 linear magma at size 841 (non-fully-idempotent).\n\nSize 841 = 29², NOT fully idempotent (only 1 idempotent: the F_29² zero element), right-cancellative. Linear over the extension field F_29² = F_29[α]/⟨α² − 2⟩.\n\nOperation: x ◇ y = α_coef·x + β·y in F_29², with β a root of Phi_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 and α_coef = -β³ − β − 1. This is Pace Nielsen's \"Type 2\" construction. Phi_2_5 has 4 roots in F_29², forming 2 Galois-conjugate orbits → 2 distinct iso classes at size 841 (this magma is one Galois orbit; the other is magma#630bb9976070).\n\nSub-magma structure: NO size-29 sub-magmas. Every pair of distinct elements generates the full 841-element magma.\n\nCompanion to the F_29² Type-1 magmas at size 841: magma#cc0cd58750be and magma#ee91772f0657 (both fully idempotent). The 4 F_29² linear magmas at size 841 (2 Type-1 + 2 Type-2) cover the full Pace Nielsen classification at this size.\n\nThe size-841 family also includes magma#ad16fb07 (an exceptional non-standard construction) and other entries — see size-841 page commentary.\n\n[text written by Claude]","submitted_at":"2026-05-20 19:24:24","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/841/8469938fe79d665c1e81678a8fd11c19a78afe7d93aebf2b2bd55138a23e4b4f.txt"},{"canonical_hash":"630bb9976070344e98c9999a26a945327c3751915ba5457360e4ea3e91dda33d","size":841,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"840,836,581,821,746,686,566,716,491,806,431,761,731,446,461,671,656,521,551,641,596,701,506,776,476,536,611,791,626,376,479,134,496,239,750,663,147,595,40,168,212,135,755,688,534,797,57,265,249,166,777,175,649,652,32,426,101,773,46,699,644,542,33,297,661,125,404,414,495,216,828,522,15,225,760,814,356,817,218,348,262,591,34,268,500,518,433,361,153,151,464,197,762,119,120,160,481,740,634,224,673,637,735,519,93,648,782,831,132,42,203,580,250,758,25,234,286,390,444,505,809,559,707,99,349,562,157,383,826,208,24,122,74,756,84,350,660,128,381,665,573,683,687,598,362,226,513,290,113,502,749,302,605,214,148,289,445,538,321,696,766,156,804,627,373,204,323,647,330,623,600,367,402,499,104,480,21,684,19,333,629,813,247,527,507,576,94,31,95,282,6,253,646,745,485,415,799,503,389,341,838,399,802,256,178,657,127,635,186,630,779,726,360,70,568,353,543,319,403,529,54,834,397,332,796,653,532,351,677,320,475,44,146,97,60,314,609,501,670,324,554,210,724,825,452,27,266,51,209,830,727,738,3,428,53,432,571,763,258,105,340,346,725,816,138,619,117,136,5,100,449,658,188,182,622,565,747,720,235,409,504,743,410,78,86,145,633,219,466,767,391,511,678,2,150,549,280,792,667,43,494,254,162,183,770,812,264,190,16,788,149,765,610,110,703,72,181,664,441,301,520,722,577,421,137,23,143,588,613,405,824,41,172,106,89,365,396,698,377,459,574,364,398,39,771,675,680,702,271,142,645,375,368,418,429,811,366,490,193,650,794,85,558,544,412,668,692,59,672,201,741,583,334,69,347,547,335,406,221,295,58,177,827,9,780,718,679,526,165,807,509,198,279,803,625,87,456,693,564,682,269,785,205,164,52,196,116,73,228,694,822,294,26,579,800,67,236,192,795,541,524,818,471,697,103,211,310,422,733,180,213,640,708,284,179,7,274,189,498,430,308,275,523,632,98,306,315,487,681,608,734,751,585,287,141,352,590,789,387,199,612,484,133,358,14,291,337,259,300,575,174,472,774,483,666,372,835,593,184,293,719,597,260,736,469,508,570,118,617,272,343,200,126,176,50,757,62,354,49,793,531,296,462,344,482,458,20,754,768,370,584,440,288,700,81,601,639,4,83,90,435,237,206,492,470,465,561,400,37,79,784,669,92,488,35,80,374,318,267,326,614,13,823,798,238,384,232,631,787,512,730,30,651,454,276,357,493,322,820,555,244,578,408,285,169,602,560,278,257,159,704,328,457,582,185,759,245,416,468,721,61,557,676,124,423,240,371,363,18,533,714,17,140,510,537,775,832,277,283,448,659,312,114,231,8,829,233,606,515,241,55,317,163,553,781,642,338,638,417,528,517,620,304,336,171,388,662,615,514,305,764,112,460,711,819,102,345,382,161,329,685,108,467,66,742,443,586,47,36,624,339,739,11,107,753,68,778,355,75,516,569,420,281,425,222,447,273,316,592,38,628,56,28,713,589,0,695,535,436,158,115,187,380,392,379,786,717,737,152,603,419,48,411,474,413,690,131,709,10,82,810,833,45,437,111,299,88,837,594,251,556,486,109,748,655,194,243,309,815,207,539,712,325,195,723,191,77,808,477,473,783,455,96,223,450,65,369,546,359,217,385,303,616,22,252,772,64,311,497,769,599,715,654,29,76,139,386,548,155,790,298,327,227,621,572,438,378,729,525,427,463,129,424,530,691,255,215,839,552,292,674,246,248,331,643,728,710,173,395,801,167,63,123,607,71,604,550,130,407,732,618,121,705,1,12,220,451,202,394,752,434,489,91,563,313,636,393,442,439,270,567,261,154,170,342,587,744,478,545,230,307,263,401,805,242,453,540,144,706,229,689","comment":"F_29² Type-2 linear magma at size 841 (non-fully-idempotent).\n\nSize 841 = 29², NOT fully idempotent (only 1 idempotent: the F_29² zero element), right-cancellative. Linear over the extension field F_29² = F_29[α]/⟨α² − 2⟩.\n\nOperation: x ◇ y = α_coef·x + β·y in F_29², with β a root of Phi_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 and α_coef = -β³ − β − 1. This is Pace Nielsen's \"Type 2\" construction. Phi_2_5 has 4 roots in F_29², forming 2 Galois-conjugate orbits → 2 distinct iso classes at size 841 (this magma is one Galois orbit; the other is magma#8469938fe79d).\n\nSub-magma structure: NO size-29 sub-magmas. Every pair of distinct elements generates the full 841-element magma.\n\nCompanion to the F_29² Type-1 magmas at size 841: magma#cc0cd58750be and magma#ee91772f0657 (both fully idempotent). The 4 F_29² linear magmas at size 841 (2 Type-1 + 2 Type-2) cover the full Pace Nielsen classification at this size.\n\nThe size-841 family also includes magma#ad16fb07 (an exceptional non-standard construction) and other entries — see size-841 page commentary.\n\n[text written by Claude]","submitted_at":"2026-05-20 19:25:12","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/841/630bb9976070344e98c9999a26a945327c3751915ba5457360e4ea3e91dda33d.txt"},{"canonical_hash":"bde94d924405614379074d630d35c62190dc88b710b49afba074eb7fa3407559","size":880,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,594,719,749,601,1,593,722,748,602,5,585,718,742,605,14,586,725,755,599,8,596,724,743,612,12,590,716,745,610,756,762,760,759,613,6,591,713,750,598,9,597,723,741,611,2,584,715,751,604,7,595,711,744,600,4,587,720,753,607,3,583,714,754,606,10,592,721,747,603,11,589,717,746,609,13,588,712,752,608,44,570,539,397,688,42,569,547,406,689,40,576,540,404,680,35,567,544,401,681,37,574,537,402,683,32,579,548,399,686,409,582,549,411,695,43,577,538,394,682,38,568,534,408,692,39,571,541,400,685,36,573,536,403,694,30,580,545,395,684,31,581,546,396,693,41,575,543,405,690,33,578,542,398,687,34,572,535,407,691,370,799,328,657,434,369,798,320,658,437,364,801,319,654,431,367,804,330,646,432,378,807,324,650,443,375,803,331,647,439,660,812,809,662,446,373,794,321,659,435,371,808,325,651,444,372,796,326,653,436,377,806,323,649,442,368,795,322,655,430,366,805,329,645,433,376,797,327,652,440,374,802,332,648,438,365,800,333,656,441,787,634,361,335,426,782,644,356,345,421,790,637,350,338,423,784,630,358,347,429,791,638,349,339,427,788,635,362,336,416,811,663,661,810,445,792,639,351,340,415,781,643,355,344,417,779,642,354,343,428,786,633,360,334,422,780,641,353,342,424,783,631,357,346,425,785,632,359,348,418,789,636,363,337,419,793,640,352,341,420,554,391,59,526,668,561,387,57,529,673,559,390,53,521,670,564,381,48,524,665,557,389,51,532,678,565,382,56,525,677,566,412,410,550,679,551,385,58,528,667,558,388,50,533,666,560,386,52,527,675,556,393,49,531,676,562,380,46,519,672,553,392,47,523,674,555,383,54,520,664,552,384,55,522,669,563,379,45,530,671,777,727,25,705,618,764,728,24,701,617,763,732,29,710,626,768,739,23,704,621,774,737,15,709,627,767,735,17,696,619,778,758,757,761,629,765,726,26,698,615,773,736,16,708,628,775,729,27,699,614,766,738,20,706,624,769,740,22,703,622,771,731,19,697,620,776,730,28,700,616,772,733,21,707,625,770,734,18,702,623,467,843,870,233,261,476,839,867,239,266,473,844,871,230,259,472,835,874,236,270,468,836,866,241,272,471,842,869,235,265,480,875,877,447,813,477,838,862,232,267,470,831,864,243,263,478,837,863,229,268,479,830,865,242,273,469,833,873,237,260,474,841,861,240,271,475,840,860,231,269,465,834,868,234,264,466,832,872,238,262,177,487,84,215,295,167,489,83,228,298,179,495,87,225,303,170,496,89,221,294,178,501,76,224,299,171,499,78,214,289,198,502,486,196,413,165,492,82,222,291,176,500,88,223,302,166,491,85,216,292,168,490,75,227,300,173,493,81,219,301,175,497,77,220,293,169,488,86,226,297,172,494,80,218,296,174,498,79,217,290,121,147,109,158,73,131,142,119,153,68,124,136,112,161,70,133,144,105,155,60,125,135,113,162,74,122,148,110,159,62,482,483,481,484,879,126,137,114,163,63,130,141,118,152,64,129,140,117,150,61,120,146,108,157,69,128,139,116,151,71,132,143,106,154,72,134,145,107,156,65,123,149,111,160,66,127,138,115,164,67,99,187,200,504,307,90,182,205,506,312,96,186,203,503,305,93,193,207,509,304,100,189,208,516,315,94,184,210,514,309,485,195,197,518,414,91,188,213,510,317,102,194,199,505,314,92,183,212,507,313,101,190,201,517,316,97,191,202,508,308,98,192,206,515,306,103,181,209,513,318,104,185,211,511,310,95,180,204,512,311,817,258,451,853,279,815,248,450,852,277,819,254,460,856,284,821,250,455,851,282,828,257,461,846,285,820,249,456,847,280,878,448,464,876,814,826,245,458,854,275,829,256,462,845,286,827,252,463,857,288,825,255,457,858,287,823,246,453,850,274,822,251,454,849,281,816,247,449,855,278,818,253,459,859,283,824,244,452,848,276","comment":"Size-880 (= 11 × 16 × 5) magma decomposing as a triple direct product: Tao(F_11, β=5) × F_16(ζ=8, ω=6) × F_5(2,4). The first two factors together form the size-176 non-right-cancellative magma 43f0cc11 — a Tao G × M fiber-bundle construction with abelian base F_11 and fiber F_16, with cocycle determined by the quadratic-residue / non-residue character of base differences. Direct-multiplying with F_5(2,4) (a 5-element right-cancellative linear magma) gives this size-880 magma. The product is non-right-cancellative and idempotent (every element x satisfies x ◇ x = x), inherited from the Tao factor.","submitted_at":"2026-04-28 18:54:44","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/880/bde94d924405614379074d630d35c62190dc88b710b49afba074eb7fa3407559.txt"},{"canonical_hash":"afce520f8ac59c1f1650099d15f61f59ce74aadc72ef09edd2b3aed080bf7c8e","size":931,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,277,230,235,273,548,261,289,776,267,250,283,764,245,709,256,542,554,770,28,528,305,294,506,614,512,540,782,518,807,534,788,801,713,813,626,620,794,2,543,246,251,290,274,278,555,225,284,777,549,231,771,712,765,268,262,236,3,269,772,778,556,291,544,263,241,550,226,257,247,237,766,232,285,279,252,4,286,238,227,264,557,270,280,767,258,242,292,773,253,710,248,551,545,761,5,552,254,243,281,265,287,546,233,275,768,558,239,762,711,774,259,271,228,1,260,763,769,547,282,553,272,249,541,234,266,255,229,775,240,276,288,244,30,374,496,501,628,355,634,368,821,640,183,380,827,178,723,189,349,361,815,31,350,179,184,369,629,375,362,491,363,822,356,497,816,707,828,641,635,502,32,642,817,823,345,370,351,636,174,357,492,630,180,503,829,498,364,376,185,33,365,504,493,637,346,643,377,830,631,175,371,818,186,724,181,358,352,824,34,359,187,176,378,638,366,353,499,372,831,347,489,825,708,819,632,644,494,35,633,826,832,354,379,360,645,182,348,500,639,188,495,820,490,373,367,177,36,335,166,171,652,316,658,329,845,646,744,341,833,756,705,750,310,322,839,37,311,757,745,330,653,336,323,161,342,846,317,167,840,751,834,647,659,172,38,648,841,847,324,331,312,660,752,318,162,654,758,173,835,168,343,337,746,39,344,155,163,661,325,649,338,836,655,753,332,842,747,706,759,319,313,848,40,320,748,754,339,662,327,314,169,333,837,326,154,849,760,843,656,650,164,41,657,850,838,315,340,321,651,743,309,170,663,749,165,844,153,334,328,755,6,198,483,488,676,421,664,151,851,670,466,203,857,461,721,472,415,409,863,7,416,462,467,204,677,205,410,478,206,852,422,484,864,720,858,671,665,473,8,672,865,853,411,194,417,666,457,423,479,678,463,474,859,485,193,199,468,9,159,475,480,667,412,673,200,860,679,458,195,866,469,722,464,424,418,854,10,407,470,459,201,668,160,419,486,196,861,413,476,855,719,867,680,674,481,11,681,856,862,420,202,408,675,465,414,487,669,471,482,868,477,197,152,460,12,576,448,453,577,216,583,570,875,589,431,564,881,426,717,437,210,222,869,13,211,427,432,571,578,559,223,443,565,876,217,449,870,716,882,590,584,454,14,591,871,877,224,572,212,585,438,218,444,579,428,455,883,450,566,560,433,15,567,456,445,586,207,592,561,884,580,439,573,872,434,718,429,219,213,878,16,220,435,440,562,587,568,214,451,574,885,208,441,879,715,873,581,593,446,17,582,880,886,215,563,221,594,430,209,452,588,436,447,874,442,575,569,425,18,388,689,156,600,406,605,383,899,595,693,157,887,702,725,698,401,396,893,19,402,703,694,384,601,389,397,685,158,900,392,690,894,726,888,596,606,905,20,597,895,901,398,385,403,607,699,393,686,602,704,682,889,691,150,390,695,21,728,737,738,736,732,734,730,890,735,740,729,896,739,742,741,731,733,902,22,394,696,700,391,608,381,404,192,386,891,399,683,903,727,897,603,598,687,23,604,904,892,405,190,395,599,692,400,191,609,697,688,898,684,387,382,701,24,520,796,784,622,524,610,514,797,616,301,508,803,296,790,307,536,530,809,25,537,297,302,515,623,521,531,791,509,798,525,779,810,714,804,617,611,785,26,618,811,799,532,516,538,612,308,526,792,624,298,786,805,780,510,522,303,27,511,787,793,613,533,619,505,806,625,293,517,812,304,781,299,527,539,800,29,627,802,808,523,507,529,621,300,535,783,615,306,795,814,789,519,513,295,924,48,53,59,49,47,46,44,54,45,52,43,51,55,56,58,50,42,57,925,105,97,96,104,99,103,106,111,102,110,107,112,108,98,109,101,100,113,926,121,128,127,115,124,118,122,114,119,130,120,116,129,126,131,125,123,117,927,71,66,68,60,74,65,70,63,64,75,69,61,77,67,76,73,72,62,928,89,90,91,86,80,84,87,94,85,78,88,95,83,92,81,79,82,93,929,141,147,148,137,149,139,142,145,138,133,140,143,132,146,134,136,135,144,930,906,922,921,909,912,910,908,917,911,920,907,916,919,923,918,913,914,915","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_19(7,3).","submitted_at":"2026-04-28 19:37:56","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/931/afce520f8ac59c1f1650099d15f61f59ce74aadc72ef09edd2b3aed080bf7c8e.txt"},{"canonical_hash":"0310063693b50bf3df322ebd4e180731f72dabb5f72d1c40a9931c9cd32074ee","size":931,"satisfies_255":true,"right_cancellative":false,"idempotent":false,"display_reorder":"0,827,174,179,186,459,192,821,662,198,490,815,668,484,169,478,471,465,656,28,426,883,871,674,161,680,420,705,686,515,432,693,509,877,521,155,167,699,2,460,473,479,828,193,816,472,175,822,669,466,180,663,485,657,187,199,170,3,194,670,658,461,817,467,188,474,455,181,200,480,176,664,318,829,823,486,4,818,182,171,195,468,201,830,653,189,481,824,659,475,177,487,462,456,665,5,469,482,488,819,184,825,463,183,831,660,457,172,654,476,666,196,190,178,1,185,661,667,470,826,458,197,483,464,173,191,489,168,655,319,820,832,477,30,707,240,245,853,357,859,719,560,865,370,713,548,382,251,376,351,363,554,31,358,371,377,708,860,714,352,241,720,549,364,246,561,365,555,854,866,252,32,861,550,556,359,715,347,855,372,353,247,867,378,242,562,322,709,721,366,33,716,248,237,862,348,868,710,551,856,379,722,557,373,243,367,360,354,545,34,349,380,368,717,851,723,361,249,711,558,355,238,552,374,546,863,857,244,35,852,559,547,350,724,356,864,381,362,239,858,369,250,553,323,718,712,375,36,648,337,343,896,502,902,642,209,890,737,636,214,731,331,725,496,508,204,37,503,738,726,649,903,637,497,338,643,215,491,344,210,732,320,897,891,332,38,904,216,205,504,638,492,898,739,498,345,892,727,339,211,333,650,644,733,39,639,346,334,887,493,893,651,217,899,728,645,206,740,340,734,505,499,212,40,494,729,735,640,894,646,506,905,652,207,500,335,218,741,321,888,900,341,41,895,208,213,495,647,501,889,730,507,336,901,736,330,203,342,641,635,742,6,291,304,309,615,749,603,285,850,609,438,297,838,450,315,444,743,755,844,7,750,439,445,292,604,298,744,305,286,839,756,310,833,451,845,616,610,316,8,605,840,846,751,299,757,599,440,745,311,611,446,306,834,326,293,287,452,9,300,312,301,606,758,612,294,841,600,447,288,847,441,307,453,752,746,835,10,759,448,454,283,613,289,753,313,295,848,747,302,842,442,836,607,601,308,11,614,849,837,760,290,748,608,449,754,303,602,437,314,843,325,284,296,443,12,219,405,411,261,570,267,231,773,255,583,225,761,595,417,589,564,576,767,13,571,584,590,220,268,226,565,406,232,762,577,412,774,596,768,262,256,418,14,269,763,769,572,227,578,263,585,566,413,257,591,407,775,401,221,233,597,15,228,414,402,270,579,258,222,764,264,592,234,770,586,408,598,573,567,776,16,580,593,581,229,259,235,574,415,223,771,568,403,765,587,777,253,265,409,17,260,772,778,563,236,569,254,594,575,404,266,582,416,766,410,230,224,588,18,537,273,277,785,391,791,531,798,779,626,543,804,620,282,632,385,397,810,19,392,627,633,538,792,544,386,274,532,805,398,278,799,621,811,786,780,202,20,793,806,812,393,527,399,787,628,387,279,781,634,275,800,317,539,533,622,21,528,329,327,794,400,782,540,807,788,617,534,813,629,328,623,394,388,801,22,383,618,624,529,783,535,395,280,541,814,389,271,808,630,802,795,789,276,23,784,797,803,384,536,390,796,619,396,272,790,625,281,809,324,530,542,631,24,682,695,701,163,434,151,676,517,157,873,688,523,885,689,879,428,422,511,25,435,874,880,683,152,671,429,696,677,524,423,702,518,886,512,164,158,690,26,153,525,513,436,672,424,165,875,430,703,159,881,697,519,691,684,678,869,27,673,704,692,154,425,160,685,526,166,882,679,514,876,698,870,419,431,520,29,162,516,522,427,681,433,156,884,421,694,150,872,706,510,700,675,687,878,924,44,51,45,58,48,52,50,47,46,55,56,59,42,57,49,54,43,53,925,106,111,102,99,108,104,101,113,110,96,112,109,100,105,107,98,97,103,926,118,119,124,123,131,129,125,128,120,114,116,117,115,130,126,121,127,122,927,73,66,77,62,64,63,60,70,71,68,67,76,65,72,74,75,69,61,928,83,94,95,89,87,84,90,88,92,91,85,79,86,93,82,78,81,80,929,148,144,145,142,140,132,146,134,138,135,147,137,139,149,143,136,133,141,930,906,917,916,909,914,911,907,920,910,923,908,919,921,915,922,912,913,918","comment":"Direct product of a non-right-cancellative factor and a small linear (right-cancellative) factor: (nRC-49 b91b0b41) × F_19(7,4).","submitted_at":"2026-04-28 19:39:08","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/931/0310063693b50bf3df322ebd4e180731f72dabb5f72d1c40a9931c9cd32074ee.txt"},{"canonical_hash":"3259f7fbd1876f7e94c4385de572269b173e077045206f09a992ef4ae18e0a41","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,21,11,25,3,4,2,29,12,5,17,942,14,24,16,9,20,13,19,7,10,15,28,27,6,18,8,23,22,26,49,59,50,58,36,48,45,56,32,41,38,34,943,39,33,46,37,51,40,43,30,53,55,54,44,52,47,31,35,42,57,69,61,89,77,83,68,65,75,79,60,85,81,955,86,80,66,84,70,88,63,78,72,74,73,64,71,67,87,82,62,76,548,541,543,567,547,545,566,561,565,554,553,540,960,556,568,569,550,546,551,560,562,552,558,555,563,549,542,559,544,557,564,279,271,282,273,270,283,286,298,288,294,285,276,940,277,296,281,284,297,295,299,287,280,290,293,292,274,275,289,272,278,291,459,471,475,477,453,450,466,454,452,464,461,470,958,462,465,479,460,476,473,472,451,456,478,457,458,467,463,455,468,469,474,696,699,694,712,709,701,711,707,704,717,703,692,959,697,702,716,691,710,714,700,708,713,693,698,695,715,706,719,718,705,690,666,661,665,676,673,680,660,669,662,671,664,663,946,667,688,675,672,674,684,681,670,685,668,689,686,678,687,683,682,679,677,156,162,165,154,169,167,161,177,150,160,159,163,950,176,155,179,173,168,174,171,151,175,166,170,172,157,164,152,153,158,178,817,820,819,814,815,813,827,824,816,812,825,830,945,810,836,833,818,823,821,834,828,832,839,838,835,822,829,837,831,811,826,387,369,383,363,365,379,368,384,388,372,367,378,936,389,381,373,375,364,377,374,371,385,382,361,380,360,386,370,366,362,376,591,578,572,584,574,579,593,575,589,580,587,596,934,598,581,594,592,576,583,588,570,585,590,599,597,571,582,573,577,595,586,863,858,869,859,860,866,855,853,840,841,849,847,944,864,850,842,856,861,867,865,852,848,846,862,845,868,851,854,843,844,857,330,336,351,340,339,350,355,345,342,349,354,347,938,331,353,344,346,338,343,357,332,333,352,334,358,359,348,337,341,356,335,261,244,245,243,242,260,267,247,255,251,263,258,941,264,256,268,262,241,253,249,254,265,246,266,250,240,259,257,269,252,248,874,887,896,881,880,873,878,870,899,875,894,890,933,898,893,872,895,885,886,876,888,871,897,883,892,877,889,884,891,879,882,633,650,635,657,656,641,632,636,631,653,637,646,947,638,634,652,659,655,648,630,644,649,654,651,658,640,643,645,647,639,642,95,114,104,111,117,106,110,94,109,99,98,115,954,101,112,113,97,116,118,93,90,119,103,100,107,96,91,92,105,102,108,395,405,415,412,411,402,404,396,397,398,407,392,937,409,408,394,406,410,419,417,391,418,414,413,416,400,393,403,390,399,401,752,760,756,755,761,774,751,772,754,773,779,766,952,750,767,763,768,776,753,765,771,770,777,775,778,764,762,758,757,769,759,309,308,328,315,314,302,304,322,303,318,317,313,939,305,316,307,327,301,310,321,323,311,329,319,320,326,312,300,325,306,324,900,912,908,913,919,924,902,929,910,911,906,914,932,923,926,917,905,920,922,918,915,901,909,927,928,925,916,907,904,903,921,219,217,212,223,232,222,214,233,215,238,210,226,948,229,211,239,216,230,225,221,231,224,213,218,220,236,228,235,234,227,237,724,734,732,739,736,729,737,727,730,745,726,741,956,744,725,720,731,723,740,728,735,738,733,721,722,748,743,747,746,742,749,809,802,792,797,796,780,789,785,784,788,806,804,953,799,782,783,805,795,793,791,781,794,807,800,808,801,786,790,803,798,787,426,428,439,429,442,422,437,427,438,423,448,445,957,433,447,432,421,443,434,430,446,435,440,441,431,436,420,444,425,424,449,205,199,202,209,180,204,182,192,196,185,184,200,949,187,197,198,207,181,208,191,193,183,189,186,194,206,201,190,203,188,195,135,145,146,144,124,134,141,142,130,137,126,132,951,127,131,122,125,147,136,139,129,149,121,120,140,148,133,128,123,138,143,508,502,506,483,482,484,496,492,509,503,491,480,930,486,490,504,494,485,488,498,505,507,481,493,489,499,487,501,500,495,497,621,616,613,617,618,600,624,614,627,603,612,601,935,604,605,606,629,619,628,611,609,623,625,626,622,620,608,610,602,607,615,522,518,538,524,537,517,511,520,532,530,521,512,931,531,536,529,516,514,513,539,510,519,515,526,523,533,528,525,527,535,534","comment":"Tao(F_31,β=2) × F_31(ζ=2,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 16:55:26","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/3259f7fbd1876f7e94c4385de572269b173e077045206f09a992ef4ae18e0a41.txt"},{"canonical_hash":"ecd0e67db3fe709a9aadcf96a47e02aa91e9bf5fc38f051f204498fb478a9ecd","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,7,3,13,10,9,26,4,21,12,25,23,5,22,8,18,6,28,24,20,17,16,29,14,2,15,19,11,942,27,42,33,46,54,37,31,40,56,58,57,30,55,34,49,44,39,50,36,52,53,51,45,35,32,59,41,38,47,43,943,48,62,80,66,73,84,87,88,75,77,76,78,74,81,61,64,86,89,83,71,72,70,65,82,79,69,60,85,67,63,955,68,549,550,561,557,562,540,543,563,569,566,544,560,553,541,555,568,545,559,551,554,548,558,556,547,542,546,565,564,552,960,567,294,296,275,290,289,273,299,281,283,286,279,287,274,272,297,295,282,288,285,293,280,278,276,292,271,277,270,284,291,940,298,477,470,457,465,478,476,453,463,458,454,479,473,456,460,467,469,451,475,462,466,452,464,468,455,474,461,472,459,471,958,450,696,701,713,718,716,692,705,712,695,709,693,702,707,698,699,708,703,690,706,694,711,704,691,717,719,710,700,697,715,959,714,683,665,684,682,662,664,686,673,669,677,666,679,675,667,680,678,672,685,688,676,668,674,689,681,661,660,671,687,663,946,670,157,158,173,165,179,166,159,174,162,160,154,172,163,170,155,161,169,167,176,168,164,156,175,153,177,152,171,151,150,950,178,827,838,831,826,813,834,833,832,816,812,818,835,811,830,820,839,823,837,817,810,825,836,821,828,814,819,822,824,815,945,829,389,369,381,372,385,380,363,382,383,360,364,378,374,371,386,370,362,379,384,388,368,366,387,365,376,367,377,361,373,936,375,592,577,578,585,584,572,588,579,581,596,594,590,570,591,589,580,598,574,583,587,599,571,582,576,593,597,573,575,586,934,595,851,857,847,854,852,865,850,846,841,859,869,855,863,860,868,858,849,864,867,861,848,853,840,856,843,862,866,845,844,944,842,337,335,356,347,349,343,342,338,355,332,334,341,358,351,345,336,350,357,333,359,339,346,340,348,330,353,344,354,331,938,352,257,241,252,268,264,262,261,253,247,254,269,248,249,244,266,240,251,263,260,258,259,267,250,243,242,256,245,255,265,941,246,898,892,877,884,874,887,886,876,870,878,897,875,881,880,885,896,882,888,879,890,872,883,895,899,889,893,891,894,873,933,871,633,638,659,639,649,642,644,658,656,652,635,645,636,637,643,651,634,641,655,650,654,640,657,630,648,632,646,653,647,947,631,112,113,116,106,111,99,101,117,93,114,102,95,110,94,104,115,96,98,108,103,97,107,105,119,100,118,91,92,109,954,90,393,390,416,401,400,417,398,415,391,409,411,414,396,405,397,410,399,418,395,419,392,402,412,404,403,408,406,407,394,937,413,774,772,767,777,761,769,779,750,773,778,765,756,757,753,776,754,763,762,760,752,758,755,768,759,764,766,771,775,751,952,770,314,323,329,315,300,319,318,301,321,307,308,302,326,305,303,328,309,320,324,306,313,316,327,312,317,310,322,311,325,939,304,921,918,912,908,901,903,902,927,928,904,929,922,906,916,909,905,923,925,926,919,915,910,911,907,924,913,914,900,917,932,920,239,220,224,233,238,225,227,223,214,229,212,216,230,219,218,231,217,213,232,215,222,226,228,237,234,211,221,210,235,948,236,724,729,739,746,744,740,742,737,723,722,726,730,734,733,732,735,731,727,721,720,738,741,743,745,747,736,728,725,748,956,749,788,790,787,783,807,808,800,786,805,785,802,806,789,798,801,781,794,797,804,803,809,791,782,795,793,792,799,780,784,953,796,449,440,435,441,428,430,436,434,429,438,427,433,423,442,437,439,426,431,432,447,420,421,424,444,422,446,443,445,425,957,448,189,190,201,197,202,183,208,203,209,181,184,200,193,182,195,180,185,199,191,194,188,198,196,187,207,186,205,204,192,949,206,142,132,146,121,136,139,140,122,124,123,130,120,133,149,144,138,126,135,128,129,127,145,134,131,125,141,137,147,143,951,148,505,500,485,494,491,508,493,506,503,481,480,495,497,482,492,486,483,488,504,507,484,499,498,502,490,509,496,489,487,930,501,624,623,628,610,609,618,604,629,619,621,605,613,626,600,602,622,615,611,620,625,612,601,606,616,617,603,614,607,627,935,608,526,530,527,513,521,510,519,528,517,512,533,522,511,523,529,536,516,537,539,535,525,524,534,514,531,538,518,520,532,931,515","comment":"Tao(F_31,β=2) × F_31(ζ=2,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:07:44","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/ecd0e67db3fe709a9aadcf96a47e02aa91e9bf5fc38f051f204498fb478a9ecd.txt"},{"canonical_hash":"bbe4461e8ecc5f34817a33716d5b69ce46b8ea5178da048dcddd4d815f918122","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,23,22,7,20,14,4,15,17,10,6,18,25,2,21,3,9,28,13,26,24,27,942,16,5,19,29,8,12,11,34,56,52,59,41,53,40,30,36,45,58,46,54,57,51,39,43,44,55,37,42,35,33,943,38,31,47,32,50,49,48,81,75,71,61,68,72,88,78,83,63,77,64,73,76,70,86,60,62,74,84,69,82,80,955,85,87,65,79,89,67,66,551,546,552,555,568,564,540,569,548,562,543,547,549,558,567,557,565,550,561,560,553,563,566,960,545,542,559,554,541,556,544,295,278,298,297,284,291,272,287,275,277,285,289,293,299,281,290,279,276,288,271,273,274,280,940,282,292,283,294,296,286,270,457,463,458,468,472,475,465,466,473,478,470,459,477,455,450,467,462,474,453,456,471,451,479,958,476,454,452,464,460,469,461,717,713,698,699,704,702,716,719,718,715,701,703,693,697,714,694,706,696,712,691,690,708,709,959,710,707,700,695,711,692,705,681,683,685,675,688,674,668,676,663,672,666,669,677,679,665,689,678,671,673,684,661,660,687,946,662,664,680,686,670,667,682,160,177,161,162,173,155,167,171,165,178,170,159,166,154,152,176,151,174,164,156,169,158,175,950,157,168,179,153,150,163,172,824,823,819,820,812,827,834,814,837,810,832,829,825,828,817,833,826,839,811,830,813,836,821,945,822,838,818,835,815,831,816,372,370,381,368,379,364,382,369,384,371,365,362,388,385,360,363,373,374,380,383,387,386,375,936,361,367,377,378,389,366,376,583,573,589,571,587,584,582,577,586,595,588,575,592,585,572,570,593,591,581,590,576,598,596,934,580,599,578,597,579,594,574,858,863,867,866,847,849,853,860,841,862,850,842,868,840,857,844,845,859,848,843,852,869,856,944,854,855,846,865,861,851,864,340,339,331,352,333,336,356,355,345,338,346,334,349,335,332,358,342,348,359,343,344,350,337,938,353,330,354,351,341,347,357,269,254,255,258,245,249,244,264,266,263,240,247,250,268,260,265,262,267,253,251,248,256,252,941,261,246,242,257,259,241,243,896,882,887,885,876,892,872,895,889,881,886,871,870,893,898,880,874,883,879,884,877,897,875,933,890,888,878,899,894,873,891,632,647,658,657,651,640,659,633,644,648,646,638,654,639,635,650,655,656,637,643,642,653,636,947,649,645,630,641,634,631,652,107,92,94,95,115,110,119,111,90,108,113,93,105,100,104,99,102,106,117,116,112,109,103,954,97,91,101,96,118,98,114,390,399,408,407,412,417,393,395,394,400,404,416,401,392,411,398,405,403,402,418,397,410,419,937,409,415,414,406,396,391,413,776,769,772,778,774,751,770,773,771,750,753,752,777,761,758,764,779,755,766,760,759,763,765,952,754,768,762,775,767,756,757,311,301,312,320,319,323,318,303,305,309,314,325,327,324,329,300,310,328,308,326,307,322,306,939,316,304,302,321,317,313,315,912,913,927,928,919,920,929,909,910,914,925,923,916,900,926,904,903,911,921,922,901,902,915,932,905,908,918,906,907,924,917,229,232,219,221,223,215,233,217,216,239,234,222,220,218,231,230,211,226,237,214,235,213,228,948,227,238,236,210,212,225,224,745,725,738,726,724,748,744,720,730,743,749,728,721,737,747,746,723,742,740,735,732,734,727,956,722,733,731,736,739,741,729,785,784,804,803,799,780,793,796,787,805,789,781,809,792,797,794,808,791,783,806,802,801,788,953,786,782,800,807,795,790,798,427,448,439,438,441,434,426,433,444,430,445,420,424,421,432,429,436,449,443,447,423,425,435,957,422,428,442,437,431,446,440,188,198,181,180,184,190,208,185,195,193,209,194,191,199,183,203,186,187,192,196,205,189,182,949,197,204,200,206,207,202,201,144,143,139,136,133,140,132,122,123,127,135,128,141,134,138,121,149,126,142,124,148,145,147,951,125,120,129,146,137,131,130,503,487,481,485,490,500,501,494,495,509,483,491,502,508,497,484,504,482,496,489,493,492,480,930,486,505,488,499,498,507,506,623,621,615,614,628,603,601,616,611,610,606,626,624,602,609,600,625,622,617,618,604,619,605,935,608,612,613,629,620,607,627,520,539,515,536,535,516,513,511,530,533,528,529,534,517,531,521,525,526,512,532,527,522,524,931,519,538,518,510,537,523,514","comment":"Tao(F_31,β=2) × F_31(ζ=4,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:47:45","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/bbe4461e8ecc5f34817a33716d5b69ce46b8ea5178da048dcddd4d815f918122.txt"},{"canonical_hash":"1335ae05af610ef1191c2bae06feba7010f90da0e5ae99845bbfd269090efd6e","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,13,26,7,6,2,25,9,21,29,27,12,942,11,14,5,15,22,8,19,23,24,16,3,10,20,4,17,18,28,54,36,50,53,57,41,33,34,51,49,32,47,45,943,40,42,37,44,56,39,38,46,52,58,55,30,59,31,43,48,35,73,83,89,72,76,68,80,81,70,60,79,63,65,955,88,69,84,67,75,86,85,62,71,77,74,78,61,87,66,64,82,554,543,545,561,555,560,568,546,564,563,549,566,569,960,540,553,562,550,551,559,541,547,542,548,558,556,567,552,557,544,565,280,282,296,283,270,278,299,286,287,271,281,273,285,940,297,292,279,277,289,288,291,272,295,290,284,276,298,293,275,294,274,470,469,463,473,462,476,468,465,467,459,472,454,475,958,479,452,451,478,456,460,466,461,477,474,457,455,458,453,471,450,464,692,700,712,699,702,698,710,714,716,707,713,693,697,959,695,694,703,708,717,715,709,691,701,696,711,718,704,719,705,706,690,671,665,675,670,668,681,673,687,688,689,679,682,680,946,660,667,677,674,676,661,678,684,686,666,664,663,669,685,672,662,683,173,170,174,158,160,157,163,179,164,176,172,168,178,950,152,155,151,167,166,162,177,153,169,154,165,161,175,156,150,171,159,819,839,831,829,834,816,828,825,821,818,832,835,838,945,824,826,837,822,827,817,810,814,823,813,830,833,812,815,811,820,836,366,371,365,382,374,364,388,380,367,379,377,372,363,936,375,386,389,362,370,376,361,385,369,381,384,373,378,383,360,368,387,578,585,575,599,573,593,598,589,596,592,597,584,588,934,570,574,582,571,587,590,586,576,580,577,579,591,594,572,583,581,595,869,840,841,857,864,856,861,858,849,859,850,851,844,944,847,845,843,862,848,866,860,852,842,853,867,854,868,865,846,855,863,346,353,339,348,342,338,336,359,350,340,333,355,337,938,343,351,345,335,349,354,358,357,352,356,334,331,341,332,344,347,330,240,265,254,249,245,268,261,262,264,259,242,267,257,941,255,251,263,256,253,247,244,250,252,246,269,243,260,248,241,258,266,877,896,874,876,872,884,882,885,892,887,899,890,895,933,894,873,883,881,875,891,878,897,880,898,879,870,886,871,893,888,889,637,648,659,653,652,654,641,657,633,644,658,632,656,947,645,631,635,639,647,643,630,651,649,650,640,636,638,634,646,642,655,97,103,99,115,90,114,119,100,107,117,110,93,106,954,101,96,116,98,94,113,105,92,102,109,112,91,118,95,111,104,108,390,412,408,416,414,415,394,396,404,391,407,400,409,937,405,403,395,418,393,399,413,417,411,401,392,410,397,402,406,419,398,767,763,751,759,756,779,772,752,768,761,778,762,755,952,777,776,774,754,764,750,770,757,773,775,760,758,771,766,753,765,769,300,320,322,312,319,311,315,307,301,314,323,303,316,939,306,302,313,324,325,317,305,308,328,309,327,318,329,310,326,321,304,916,923,915,928,902,909,914,927,918,906,901,929,907,932,925,908,921,912,924,926,920,904,913,903,911,905,922,917,910,919,900,220,211,222,235,210,236,226,232,212,225,223,234,230,948,229,233,218,224,228,231,239,237,238,214,221,213,219,215,217,227,216,734,723,741,726,749,732,739,730,744,727,736,729,747,956,746,731,737,742,745,725,738,733,720,748,740,724,743,728,722,735,721,782,808,790,805,789,804,799,797,806,795,796,788,783,953,793,792,798,800,780,786,784,785,809,787,781,803,794,791,807,802,801,441,445,420,425,426,424,427,435,449,430,440,433,428,957,422,437,439,432,444,434,431,438,446,421,448,443,429,436,442,423,447,206,181,196,183,199,182,188,197,193,192,201,190,198,949,208,205,184,202,203,186,207,189,180,209,185,200,191,204,187,195,194,138,129,144,128,141,135,146,121,126,133,145,130,148,951,134,136,123,147,140,125,124,149,127,142,139,122,143,120,137,132,131,486,487,496,502,501,503,482,494,500,490,483,481,485,930,507,489,493,498,484,508,497,505,504,492,509,480,491,506,488,499,495,620,629,617,619,604,618,603,624,600,612,621,610,615,935,616,627,606,626,614,613,607,623,628,622,602,605,611,601,625,609,608,527,532,523,516,535,536,524,530,537,525,522,512,526,931,538,520,514,515,511,510,539,518,533,513,528,517,529,531,521,519,534","comment":"Tao(F_31,β=2) × F_31(ζ=4,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:49:20","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/1335ae05af610ef1191c2bae06feba7010f90da0e5ae99845bbfd269090efd6e.txt"},{"canonical_hash":"85c84627965ce5fc41b307f6a2b18ce3fd81e2cc5ba9a1d09715e9c668d63cf4","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,3,27,19,21,23,942,28,14,6,10,12,5,4,22,2,11,9,16,17,8,26,25,7,18,24,13,15,20,29,40,49,50,34,41,36,38,943,33,30,46,39,55,44,45,37,59,53,56,42,52,43,31,35,48,57,47,51,58,54,32,88,69,89,81,60,83,85,955,80,78,66,86,74,64,65,84,61,72,75,62,71,63,87,82,68,76,67,70,77,73,79,560,552,544,558,540,550,543,960,553,546,565,562,554,545,561,557,555,547,559,549,564,556,566,542,567,541,548,563,551,569,568,292,298,276,281,273,277,282,940,287,284,295,280,288,270,278,290,291,283,272,297,286,289,293,299,274,296,275,271,279,294,285,456,464,455,454,479,452,469,958,470,465,473,477,462,475,451,457,468,476,478,474,460,471,458,459,450,467,472,453,461,466,463,698,708,705,694,704,707,713,959,712,690,703,693,706,709,697,716,717,710,695,714,702,719,699,700,691,701,692,696,711,718,715,667,679,661,677,670,674,669,946,663,668,673,664,676,682,666,662,688,681,684,689,672,687,685,665,683,675,671,678,660,680,686,163,159,161,164,167,171,162,950,160,175,151,165,170,177,153,155,156,176,166,173,150,178,168,154,157,169,174,152,172,158,179,823,813,815,826,838,825,835,945,810,821,819,822,818,839,814,833,817,828,811,827,831,816,830,829,837,832,836,812,824,820,834,384,368,389,383,366,373,365,936,388,378,385,382,361,380,381,377,360,379,370,376,387,364,386,367,371,362,372,369,363,375,374,580,581,598,582,595,594,570,934,578,579,599,575,577,571,593,588,597,591,585,583,573,587,590,596,589,574,572,586,576,584,592,849,855,842,853,868,860,852,944,863,844,862,854,859,840,848,865,867,858,851,857,847,856,841,864,845,866,843,861,869,850,846,357,346,342,353,334,333,352,938,344,348,343,354,351,345,356,359,347,336,355,332,340,335,339,358,349,341,330,331,350,338,337,248,257,256,249,244,268,262,941,265,263,260,250,258,246,247,240,267,253,259,245,252,255,251,243,269,241,261,242,266,254,264,897,876,871,881,882,873,891,933,885,874,886,880,872,883,896,877,870,893,895,894,879,892,888,875,887,898,890,884,889,878,899,631,637,648,646,654,650,645,947,630,635,632,653,651,658,647,649,652,659,633,636,638,655,644,640,643,641,642,634,639,656,657,100,98,96,101,91,111,108,954,97,113,105,102,112,115,104,94,95,114,99,110,107,93,106,90,117,92,116,103,109,119,118,411,394,397,398,415,408,390,937,419,392,396,399,409,418,412,404,400,417,410,407,395,403,405,416,406,414,402,413,401,393,391,779,772,757,775,764,778,769,952,761,756,773,752,765,755,751,750,766,777,754,768,758,763,771,774,767,776,753,759,770,762,760,324,312,302,319,305,314,309,939,310,306,323,318,311,300,317,327,328,307,316,313,322,329,321,304,326,301,308,320,315,325,303,919,904,901,905,914,916,912,932,918,926,929,928,922,906,927,900,925,907,909,924,911,913,917,920,903,921,908,915,910,902,923,210,229,225,212,217,228,223,948,222,227,216,213,226,230,211,235,239,231,215,224,220,234,219,218,233,221,237,214,232,238,236,726,736,742,727,732,723,739,956,738,744,731,728,743,735,725,721,745,737,720,740,730,748,734,733,747,729,741,724,722,746,749,780,796,799,783,798,806,788,953,791,797,801,781,805,794,802,786,790,795,808,782,793,784,804,785,803,800,807,809,792,787,789,446,434,429,447,427,444,435,957,424,421,432,448,443,441,445,439,430,442,422,423,449,431,425,428,436,440,420,433,438,437,426,208,204,189,206,184,181,191,949,205,200,195,192,180,190,194,187,188,198,207,185,197,186,196,182,203,183,199,193,209,202,201,134,133,120,148,135,130,142,951,147,145,140,143,126,138,139,131,121,124,127,136,123,137,144,149,132,128,141,122,129,125,146,495,487,485,504,488,490,480,930,500,502,505,484,492,496,494,508,507,481,482,498,497,491,493,499,506,486,483,489,509,503,501,604,618,620,626,622,614,623,935,627,605,602,608,601,612,607,628,611,613,617,606,625,615,603,621,610,629,619,616,600,609,624,529,515,512,514,523,522,530,931,510,539,526,511,520,527,534,533,536,525,518,532,513,531,521,524,538,535,516,528,519,517,537","comment":"Tao(F_31,β=2) × F_31(ζ=8,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:50:17","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/85c84627965ce5fc41b307f6a2b18ce3fd81e2cc5ba9a1d09715e9c668d63cf4.txt"},{"canonical_hash":"7ff29f8104d4183e84ee0f757e9ad6c5573db5b5ae4ce8320d865e94f9e0bc7c","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,14,17,11,10,25,12,8,26,21,7,27,22,20,29,6,942,19,23,15,13,28,24,2,18,9,5,4,16,3,55,36,30,50,47,59,41,48,44,38,52,51,40,31,53,32,34,943,39,37,58,35,45,56,57,33,49,43,46,54,42,74,83,78,89,67,61,60,68,64,85,71,70,88,87,72,79,81,955,86,84,77,82,65,75,76,80,69,63,66,73,62,549,556,569,565,567,561,548,559,564,566,543,552,541,544,568,558,542,960,553,562,555,547,554,540,546,550,551,563,545,560,557,275,287,289,278,290,292,273,293,294,297,277,279,298,271,276,284,283,940,280,285,274,282,288,286,281,295,296,299,270,291,272,469,468,455,473,452,466,477,470,462,460,464,472,463,450,474,451,457,958,456,453,475,459,467,471,465,454,476,479,461,478,458,700,714,715,701,719,693,711,694,702,698,691,708,705,713,716,697,706,959,690,696,717,712,704,707,709,699,703,695,710,692,718,676,680,663,664,679,669,668,678,665,682,671,673,667,687,670,689,674,946,685,660,661,672,684,681,688,677,683,675,686,662,666,170,178,151,155,177,166,158,167,154,169,160,152,156,174,179,162,157,950,173,163,161,159,172,171,175,153,168,164,176,165,150,818,829,823,820,814,825,832,834,828,819,837,815,830,813,835,824,817,945,836,816,822,831,812,839,811,810,838,833,826,821,827,381,363,382,387,365,375,385,376,386,367,369,372,366,370,361,389,364,936,360,378,383,388,371,373,362,380,379,377,368,374,384,593,580,590,598,594,582,573,571,584,586,592,588,589,578,595,581,596,934,574,570,591,576,579,577,597,575,585,583,572,599,587,843,844,850,842,859,840,847,853,868,855,865,858,861,841,849,862,860,944,867,863,852,866,856,854,848,857,851,869,845,864,846,337,336,355,351,354,346,357,333,352,350,340,330,343,335,332,359,339,938,338,348,353,341,345,344,342,356,349,358,334,347,331,243,266,242,247,255,258,246,256,263,262,252,251,245,253,241,260,269,941,250,261,240,265,264,244,268,248,249,257,254,259,267,897,873,896,892,875,889,882,890,893,894,881,886,884,874,872,899,883,933,885,898,876,880,871,878,870,891,877,887,879,888,895,633,638,631,652,649,647,656,658,646,645,639,636,654,657,635,637,642,947,650,630,648,640,643,653,655,634,651,659,641,644,632,90,117,98,107,96,103,114,101,106,105,115,109,94,116,97,100,93,954,110,104,119,113,108,111,112,92,91,99,95,102,118,416,390,413,409,393,406,400,408,410,411,415,396,391,392,414,405,402,937,403,404,395,399,394,401,398,417,397,419,418,407,412,774,767,757,760,765,779,770,763,756,768,759,776,766,751,761,775,753,952,754,778,758,772,755,752,762,769,777,764,771,773,750,308,314,312,317,310,329,322,324,316,315,321,303,304,320,311,326,306,939,319,327,313,300,302,305,323,318,307,325,301,328,309,925,907,926,922,908,905,912,920,928,910,903,915,918,914,900,919,902,932,916,921,927,913,911,917,906,924,923,909,901,929,904,221,235,234,220,233,213,230,215,216,219,228,222,224,238,237,210,225,948,226,211,236,227,239,223,229,218,217,214,231,212,232,728,749,748,729,747,727,721,723,730,733,742,736,738,741,744,725,734,956,735,724,745,740,737,722,743,732,731,720,739,726,746,801,798,788,806,803,802,792,808,795,800,789,787,799,783,790,809,805,953,791,780,781,782,786,793,796,785,784,807,797,804,794,439,441,443,444,430,448,421,424,432,433,445,434,420,425,423,446,438,957,437,447,442,431,436,427,422,440,429,426,435,449,428,205,184,198,191,199,187,180,203,190,189,196,192,208,197,200,202,207,949,193,188,209,183,194,206,182,181,204,186,195,201,185,138,142,147,133,125,132,129,126,122,144,135,134,128,146,136,148,140,951,145,143,131,141,123,139,130,149,127,120,124,137,121,503,483,492,480,481,496,489,509,502,482,506,504,495,493,499,485,501,930,494,486,490,508,505,491,488,497,498,484,507,487,500,610,622,618,611,600,603,605,620,602,617,628,614,601,625,624,608,613,935,626,629,619,616,623,604,607,627,612,621,606,609,615,532,529,516,527,511,539,521,519,526,533,522,524,523,518,530,525,534,931,517,528,513,536,531,535,537,515,514,512,538,510,520","comment":"Tao(F_31,β=2) × F_31(ζ=8,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:51:28","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/7ff29f8104d4183e84ee0f757e9ad6c5573db5b5ae4ce8320d865e94f9e0bc7c.txt"},{"canonical_hash":"67e60649a876f594e58ef264595dba3874a9d4608eaced8c58e77104addc7bcc","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,27,14,19,942,22,12,2,11,6,5,9,8,18,16,17,10,24,21,26,20,28,23,7,15,3,29,25,4,13,34,42,55,46,40,943,45,41,50,47,39,56,53,43,37,35,36,52,38,59,44,49,54,33,57,30,31,32,48,58,51,81,69,74,65,88,955,64,68,89,66,86,75,72,62,84,82,83,71,85,61,63,60,73,80,76,78,87,79,67,77,70,559,557,541,563,569,960,554,548,555,542,544,549,552,566,556,568,547,543,565,546,545,560,561,550,558,562,553,540,551,567,564,284,276,294,274,270,940,283,295,277,292,275,279,298,286,287,293,296,280,289,297,272,288,285,271,273,281,278,291,290,299,282,472,471,452,460,465,958,475,462,464,467,457,450,451,468,473,479,463,474,454,466,476,456,470,455,453,459,458,469,478,461,477,697,704,717,715,713,959,714,716,718,703,710,712,693,706,700,699,696,695,709,701,707,690,694,708,691,692,698,719,705,702,711,685,684,664,678,671,946,667,687,682,688,679,674,666,677,675,670,660,676,663,680,673,661,669,689,668,662,672,683,681,665,686,177,156,172,155,157,950,152,165,162,151,153,154,170,159,163,164,160,161,158,173,175,174,168,176,179,169,150,167,166,171,178,825,828,818,831,827,945,821,822,839,820,816,836,834,811,814,823,810,824,812,817,837,813,819,815,826,832,829,838,833,830,835,384,381,369,374,365,936,385,376,388,382,375,362,373,368,366,378,379,380,372,364,370,363,371,387,386,361,367,389,360,383,377,582,581,578,599,577,934,583,579,593,591,572,598,573,595,584,580,594,589,588,570,576,587,585,590,596,597,592,571,586,574,575,852,862,841,853,868,944,867,846,840,851,864,859,858,849,856,850,847,845,842,861,863,869,854,855,844,848,865,843,860,866,857,334,352,335,350,351,938,359,331,337,333,353,341,332,343,348,357,356,355,354,347,344,346,345,339,358,330,336,340,342,349,338,249,261,252,268,267,941,245,256,265,262,251,246,241,260,269,250,259,258,264,240,253,242,257,254,247,244,248,255,263,243,266,893,891,883,898,890,933,880,878,873,894,872,884,896,871,886,895,876,877,882,889,879,888,881,887,875,874,892,899,885,870,897,655,643,645,657,644,947,654,635,646,633,636,637,653,652,650,639,630,656,649,648,659,642,640,651,641,631,632,647,638,658,634,115,113,98,106,97,954,110,101,111,100,92,102,91,94,112,96,107,108,119,117,93,116,104,103,114,105,109,99,118,95,90,407,390,400,408,404,937,414,397,393,409,392,415,411,419,401,410,406,405,399,391,417,402,398,418,403,413,416,394,396,412,395,760,752,755,771,769,952,751,756,774,779,776,759,765,762,754,757,777,778,766,764,767,763,775,768,753,750,761,770,758,772,773,304,314,328,318,313,939,323,303,324,326,301,322,308,311,316,327,321,320,310,300,329,305,302,306,315,317,319,325,307,312,309,915,900,918,910,928,932,901,911,922,903,917,905,902,916,920,929,914,927,908,909,919,906,921,913,925,924,912,904,923,907,926,231,216,225,212,228,948,229,213,223,211,230,232,219,214,215,210,217,235,237,222,227,226,221,238,236,218,234,224,239,220,233,745,726,740,723,742,956,743,721,739,733,744,741,722,727,736,746,734,730,724,749,748,720,731,738,729,735,747,737,732,725,728,802,783,790,808,805,953,782,781,791,806,785,788,796,797,804,807,801,789,786,794,792,793,787,803,799,800,784,798,780,809,795,446,430,443,449,434,957,437,426,420,440,423,442,436,433,435,441,445,444,421,448,432,447,439,431,422,424,428,427,438,429,425,206,204,199,191,208,949,184,188,185,192,194,189,202,182,181,207,187,193,180,196,195,197,198,183,205,190,203,200,201,209,186,144,123,134,128,126,951,143,127,139,129,147,135,122,121,132,145,146,120,124,138,142,131,133,141,136,149,148,140,130,137,125,498,485,486,493,505,930,492,490,497,491,506,484,508,480,501,494,481,500,502,499,483,509,487,489,507,495,482,496,503,504,488,606,626,602,627,604,935,611,621,615,623,628,612,610,616,614,619,605,608,607,617,600,618,624,622,629,601,625,603,613,620,609,519,518,510,517,536,931,524,526,539,511,522,529,512,520,531,528,538,521,513,533,514,532,525,523,515,534,537,527,530,516,535","comment":"Tao(F_31,β=2) × F_31(ζ=16,ω=5). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:52:43","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/67e60649a876f594e58ef264595dba3874a9d4608eaced8c58e77104addc7bcc.txt"},{"canonical_hash":"896897f8edc8be98bcea089912fa4887494b65ce40513f341dddb3e11f5ffb97","size":961,"satisfies_255":true,"right_cancellative":false,"idempotent":true,"display_reorder":"0,1,24,28,27,29,11,22,16,12,15,25,23,3,10,19,20,2,13,8,18,21,942,6,5,4,26,14,7,9,17,54,52,53,35,55,32,49,44,37,50,31,58,57,59,43,30,34,51,47,38,41,45,943,40,46,33,42,56,39,36,48,73,71,72,82,74,79,62,63,84,89,87,77,76,61,69,78,81,70,66,85,67,64,955,88,65,80,68,75,86,83,60,554,566,545,540,563,544,543,558,559,548,556,560,551,569,549,565,562,557,555,568,561,567,960,552,546,553,541,542,547,550,564,294,288,298,278,275,286,290,274,273,291,299,281,296,285,276,292,283,284,277,297,282,270,940,279,295,293,272,289,280,287,271,455,459,460,457,475,461,476,474,458,451,472,464,466,473,456,469,452,454,453,467,462,470,958,471,477,468,465,478,463,479,450,706,717,710,715,701,708,692,703,705,702,714,711,716,704,707,712,696,698,690,699,719,694,959,695,718,700,709,691,697,713,693,663,675,689,684,679,661,678,680,660,677,688,670,685,671,664,683,667,686,669,681,665,674,946,662,668,676,687,682,673,672,666,172,153,174,156,166,169,168,152,171,151,178,157,179,165,173,159,164,160,155,167,177,163,950,162,158,150,176,154,161,175,170,812,820,835,822,832,815,830,824,839,826,833,827,816,819,817,810,836,818,823,831,828,814,945,821,813,825,829,811,837,834,838,379,383,366,385,362,381,370,364,378,365,377,387,368,363,380,388,376,373,367,360,372,369,936,361,384,374,371,389,375,382,386,572,573,576,584,593,583,595,590,589,570,592,578,588,575,574,582,599,580,571,594,597,587,934,581,579,598,586,591,585,596,577,869,844,845,861,854,841,851,862,840,864,857,853,847,856,852,867,866,865,848,859,855,843,944,849,860,863,858,868,846,850,842,331,349,345,332,355,330,353,339,341,344,358,333,348,352,351,338,356,334,337,354,357,350,938,359,335,343,336,346,347,340,342,247,251,252,254,243,267,240,242,264,241,262,257,253,255,248,256,245,269,250,265,246,259,941,258,266,244,268,260,261,249,263,890,894,889,871,881,899,877,874,896,876,884,873,870,880,898,879,897,888,883,872,891,885,933,886,892,875,878,887,893,882,895,633,639,657,644,646,638,651,648,630,650,654,637,636,634,632,645,656,631,640,647,658,641,947,642,653,649,652,643,655,659,635,113,119,117,93,92,108,107,90,112,97,104,99,94,110,114,118,101,105,116,109,100,102,954,103,95,91,98,106,96,115,111,410,402,401,413,393,391,390,404,409,400,397,396,414,416,411,417,403,398,412,392,407,406,937,405,415,394,418,399,419,395,408,769,756,757,760,775,777,778,761,764,771,770,753,752,767,768,759,772,774,754,776,762,765,952,779,758,750,763,766,773,755,751,329,322,320,313,311,326,325,307,306,309,324,301,304,327,318,300,302,315,323,310,312,316,939,317,321,308,328,314,303,319,305,927,904,916,924,907,929,910,915,900,909,923,913,918,906,922,912,901,928,908,911,926,903,932,920,905,902,921,925,919,917,914,236,234,238,232,219,222,216,215,221,220,233,225,235,223,237,226,239,211,228,218,231,213,948,212,230,217,229,210,214,227,224,724,745,743,748,730,737,733,732,723,731,749,742,744,738,736,739,725,727,741,722,747,721,956,729,746,734,740,728,726,720,735,805,791,787,785,794,803,807,795,804,808,784,782,786,788,806,781,801,809,793,802,790,798,953,799,780,797,792,789,800,796,783,426,428,436,424,443,441,445,442,425,446,432,434,447,422,427,431,423,439,449,444,440,429,957,430,420,435,437,438,448,433,421,180,192,193,189,198,201,200,184,181,182,204,209,207,187,205,191,197,183,203,186,196,185,949,208,194,202,188,190,195,206,199,138,136,137,129,139,126,121,133,125,144,146,142,141,143,132,147,128,135,123,120,149,134,951,148,122,127,131,140,145,130,124,492,490,484,505,501,487,497,502,500,496,481,507,482,489,488,509,480,485,503,491,504,483,930,499,508,495,494,493,506,498,486,609,624,613,603,617,600,625,628,620,626,615,601,606,604,610,605,618,607,623,622,621,629,935,612,611,627,608,614,619,602,616,513,534,526,521,531,514,524,529,515,525,517,533,538,510,512,537,527,519,518,528,522,532,931,536,535,530,539,511,516,520,523","comment":"Tao(F_31,β=2) × F_31(ζ=16,ω=25). Tao's G × M fiber-bundle construction: an abelian base group G acts on a fiber set M via a 2-cocycle determined by the quadratic-residue / non-residue character of base differences.","submitted_at":"2026-04-28 18:55:27","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/896897f8edc8be98bcea089912fa4887494b65ce40513f341dddb3e11f5ffb97.txt"},{"canonical_hash":"ba90950a375d5ba801c3af4f51afc3935a0f0d9c653ccb0c888cc9d3bd90d3da","size":961,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,3,414,30,701,51,485,732,502,423,790,858,159,212,359,799,537,899,108,765,898,442,757,275,521,381,235,389,818,131,932,1,422,107,388,50,358,274,17,789,764,817,484,798,520,413,857,897,130,731,536,380,29,158,441,931,501,913,234,700,211,756,924,827,464,254,747,249,333,320,138,307,347,715,591,606,170,664,678,576,955,621,198,549,65,651,636,185,457,847,43,565,83,553,110,53,277,792,820,801,416,885,719,383,161,934,901,703,759,425,391,361,5,767,487,508,860,118,524,32,444,504,237,214,96,56,780,804,888,386,937,691,428,364,770,511,121,20,507,217,113,280,823,404,722,149,904,762,394,8,490,863,527,447,225,960,881,878,284,875,876,296,880,872,882,873,295,293,289,877,294,869,287,879,883,870,283,292,297,290,871,286,285,874,288,291,916,35,192,72,628,685,613,354,327,739,834,557,449,658,205,583,177,707,145,241,471,90,839,643,541,947,671,598,299,340,261,928,174,47,704,189,142,69,238,625,468,682,87,610,851,351,640,324,538,736,959,831,668,554,595,461,311,655,337,202,258,580,2,778,730,233,372,412,440,421,816,535,699,273,856,930,106,483,379,210,16,896,500,402,797,28,755,788,129,912,49,519,157,925,321,171,550,44,748,716,956,186,828,139,665,66,566,250,592,622,458,465,308,679,652,84,334,607,199,848,255,348,577,637,926,957,251,653,349,45,666,466,200,322,187,593,85,578,734,67,309,849,172,829,623,335,638,717,567,680,256,551,140,459,608,101,376,775,222,727,13,230,893,369,497,409,399,437,794,418,25,813,752,532,785,696,126,270,909,868,61,942,516,103,154,480,915,738,144,597,684,204,642,34,833,240,298,612,582,540,191,556,470,339,353,176,946,71,448,89,260,326,706,670,627,657,853,922,619,318,455,168,477,547,305,41,676,745,649,713,81,953,331,183,604,825,196,136,845,662,267,78,345,563,574,247,634,589,917,355,206,91,300,614,558,146,948,36,313,569,840,341,686,450,242,672,178,740,163,629,262,599,644,472,584,73,835,708,542,923,306,954,846,248,169,650,826,346,620,42,332,663,635,463,714,197,564,319,677,184,253,590,548,82,137,575,456,746,605,64,100,496,531,515,12,432,908,375,408,784,117,229,24,867,774,398,695,153,892,812,60,221,436,125,479,368,751,941,726,808,269,98,810,373,749,772,529,219,782,724,693,10,123,227,282,890,906,366,865,494,58,406,939,396,513,434,115,806,151,430,492,22,94,417,689,488,505,793,162,362,525,111,886,760,509,223,821,935,6,18,54,720,426,861,215,802,902,768,445,278,384,392,119,927,467,735,336,141,350,594,173,681,958,201,68,639,460,46,86,830,257,252,323,310,718,609,667,579,624,552,654,188,850,568,99,783,891,940,431,773,124,495,116,811,725,907,397,478,530,228,59,807,374,694,367,514,23,220,268,407,152,750,11,866,435,919,180,616,601,315,837,452,193,165,133,474,842,544,659,302,264,38,75,688,357,742,560,646,571,710,244,93,631,950,586,328,929,733,360,443,819,702,859,109,382,4,503,800,758,132,52,160,766,236,415,424,523,276,933,486,213,884,390,31,791,900,522,914,239,352,669,203,190,88,737,312,175,626,641,555,259,143,611,945,656,48,469,325,596,581,70,852,832,338,705,683,539,462,918,147,687,630,836,301,570,179,473,356,949,451,263,709,615,841,741,585,207,37,243,600,543,559,342,164,74,92,314,673,645,920,194,303,561,951,316,843,674,245,181,166,265,647,587,838,545,343,79,617,134,39,572,329,453,660,743,632,602,475,76,711,33,534,15,911,411,105,27,777,698,895,63,439,482,754,729,272,499,518,420,378,787,232,855,401,156,815,209,128,371,944,796,97,692,493,150,528,889,512,809,9,57,429,218,905,433,387,122,405,491,781,365,114,763,226,938,21,723,864,805,771,281,395,102,894,419,127,104,728,400,533,62,377,370,26,271,155,14,438,786,943,776,498,814,910,481,231,795,697,517,208,410,753,854,95,363,822,862,385,506,761,55,769,403,526,936,216,393,779,510,721,446,690,112,7,803,120,148,224,427,279,489,887,19,903,921,675,824,573,476,952,266,618,744,195,246,546,330,77,317,648,135,633,304,182,344,454,712,844,588,40,603,562,167,80,661","comment":"Size-961 = 31² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 31) line family. The 992 = 32 × 31 size-31 sub-magmas are exactly the lines of AG(2, 31); every pair of distinct points lies on a unique line.\n\nConstruction parameter: ALL 32 parallel classes use the SAME α = 27. Each line is isomorphic to magma#543c5479 (= x ◇ y = 5x + 27y mod 31, the F_31 linear magma with α = 27 ∈ {15, 23, 27, 29} = primitive 10th roots of unity in F_31 = roots of Φ_10 mod 31).\n\nEquivalently, this is the medial direct product F_31(α=27) × F_31(α=27), a single F_31²-linear quasigroup with\n\n  (x₁, x₂) ◇ (y₁, y₂) = ((1 − 27)·x_i + 27·y_i mod 31)_(i=1,2)\n\nSibling magmas at size 961, all 4 constant-α direct products: magma#fc322ba7, magma#2b8e3c08, magma#5f44e78d, plus this one (α=27).\n\nDisplay reorder coordinates each point as F_31² (a, b) at index 31·a + b. F_31 addition is computable in the magma itself via the identity\n\n  x + y = T(R_0⁻¹(x), L_0⁻¹(y))\n\nwhere R_0(x) = T[x, 0] (= ×(1 − α) in F_31) and L_0(x) = T[0, x] (= ×α). This lets us recover canonical → F_31² labels by BFS over the ⟨R_0, L_0⟩ action on canonical 1 (giving the horizontal axis F_31 × {0}), then on a chosen vertical generator (giving the vertical axis), then combining via the addition formula above. Under this reorder the Cayley table is fully (Z/31)²-translation-invariant AND every cell matches the medial-product formula exactly — visually a clean rainbow-diagonal pattern.\n\n[text written by Claude]","submitted_at":"2026-05-13 12:18:05","submitted_by":"dwrensha","url":"https://eq677-magmas.icarm.cloud/magmas/961/ba90950a375d5ba801c3af4f51afc3935a0f0d9c653ccb0c888cc9d3bd90d3da.txt"},{"canonical_hash":"2b8e3c0857adde3bd7a822129cd9972fb3e4f89fdb5fe0b7d88d61100613a576","size":961,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,7,466,887,399,932,716,282,177,682,84,387,854,514,526,450,591,823,321,362,227,100,265,786,580,154,619,659,735,189,44,1,472,405,722,183,90,860,532,597,327,233,271,556,625,741,50,13,893,938,288,688,393,520,456,829,338,106,792,130,665,195,960,812,806,813,800,802,807,810,794,814,796,805,801,793,804,803,818,819,808,816,820,811,799,809,795,822,817,815,798,821,797,926,210,650,145,777,121,353,844,441,505,378,673,303,953,908,28,65,756,640,571,256,218,312,612,547,875,75,168,707,420,487,920,59,204,750,644,634,139,565,771,250,115,242,347,336,838,606,435,541,499,869,372,69,697,162,297,731,947,414,902,481,22,927,219,674,211,313,304,651,583,954,146,548,909,778,876,29,122,76,66,354,169,757,845,708,641,442,421,572,506,488,257,379,914,429,53,535,198,493,744,863,668,396,628,93,133,691,559,186,765,291,274,725,109,941,236,408,341,896,330,475,832,16,600,916,865,561,943,834,200,95,276,898,431,670,158,238,18,495,135,727,332,55,368,767,410,602,746,693,111,477,537,630,293,343,921,70,243,60,698,348,205,163,307,751,298,839,645,732,607,635,948,436,140,415,542,566,903,500,772,482,870,251,23,373,116,924,503,638,166,119,906,610,208,376,569,705,351,26,545,648,701,254,418,842,63,873,143,301,246,485,439,754,73,775,951,310,4,789,453,285,47,268,529,719,192,103,517,935,738,230,857,402,662,365,390,890,622,324,87,469,127,826,685,10,553,594,180,928,846,910,220,709,779,675,642,877,212,443,30,314,422,123,305,573,77,652,507,37,584,489,355,955,258,170,147,380,758,549,6,721,859,326,555,49,937,392,828,791,194,404,89,596,270,740,892,687,455,105,664,471,182,531,232,624,12,287,519,337,129,919,749,138,249,346,605,498,68,296,413,21,203,633,770,241,837,540,371,161,946,480,58,643,564,114,335,434,868,696,730,901,915,942,94,430,237,134,54,409,692,536,342,560,199,897,157,494,331,766,745,476,292,864,833,275,669,17,726,367,601,110,629,3,284,528,102,737,401,389,323,156,9,179,452,267,191,934,856,364,621,468,684,593,788,46,718,516,229,661,889,86,825,582,918,248,497,412,632,836,160,57,113,867,900,137,604,295,202,240,370,479,563,433,729,748,345,67,20,769,539,945,672,334,695,917,411,159,866,603,239,562,747,19,944,694,496,835,112,136,201,478,728,96,538,333,247,631,56,899,294,369,432,344,768,671,460,656,783,359,447,384,279,884,41,616,262,318,523,81,713,463,216,151,97,850,511,679,959,34,762,577,224,588,881,174,426,461,680,319,657,930,524,784,35,82,360,733,714,448,578,464,385,225,187,280,589,152,885,882,98,42,175,851,617,397,512,263,922,567,840,71,904,646,244,501,703,61,773,608,699,483,636,349,871,949,206,252,437,164,24,141,308,374,416,752,117,543,299,458,614,125,586,382,711,32,654,260,848,879,277,491,760,781,316,509,172,912,214,575,357,551,677,424,39,149,222,445,79,957,462,886,715,681,853,449,320,99,579,658,43,465,931,176,386,525,852,226,785,618,188,36,398,281,83,513,590,361,264,153,734,925,144,352,504,302,27,639,217,546,167,486,649,120,440,702,907,755,255,611,74,419,209,776,843,377,952,64,570,311,874,706,913,534,743,395,132,185,273,940,340,474,599,52,522,667,92,558,290,108,407,329,15,428,197,862,627,690,764,724,235,895,831,923,165,609,568,25,700,841,142,484,72,309,637,905,375,350,647,417,872,245,753,950,502,118,207,704,544,253,62,300,438,774,5,325,936,790,88,739,454,470,231,286,128,858,48,827,403,269,686,663,530,11,366,720,554,391,193,595,891,104,181,623,518,2,101,388,8,266,855,467,787,515,888,581,527,400,155,451,933,620,592,717,660,824,283,736,322,178,190,363,683,45,228,85,459,358,278,615,552,492,126,678,761,587,425,782,383,40,317,712,150,510,33,223,173,655,446,883,261,80,215,849,958,576,880,457,585,31,847,490,315,911,356,423,221,956,124,710,259,306,780,171,574,676,148,78,613,381,653,878,759,508,213,550,38,444,929,394,272,473,521,557,406,427,626,723,830,742,184,339,51,91,107,14,861,763,894,533,131,939,598,666,289,328,196,689,234","comment":"Size-961 = 31² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 31) line family. The 992 = 32 × 31 size-31 sub-magmas are exactly the lines of AG(2, 31); every pair of distinct points lies on a unique line.\n\nConstruction parameter: ALL 32 parallel classes use the SAME α = 15. Each line is isomorphic to magma#7ba82cf6 (= x ◇ y = 17x + 15y mod 31, the F_31 linear magma with α = 15 ∈ {15, 23, 27, 29} = primitive 10th roots of unity in F_31 = roots of Φ_10 mod 31).\n\nEquivalently, this is the medial direct product F_31(α=15) × F_31(α=15), a single F_31²-linear quasigroup with\n\n  (x₁, x₂) ◇ (y₁, y₂) = ((1 − 15)·x_i + 15·y_i mod 31)_(i=1,2)\n\nSibling magmas at size 961, all 4 constant-α direct products: magma#fc322ba7, magma#5f44e78d, magma#ba90950a, plus this one (α=15).\n\nDisplay reorder coordinates each point as F_31² (a, b) at index 31·a + b. F_31 addition is computable in the magma itself via the identity\n\n  x + y = T(R_0⁻¹(x), L_0⁻¹(y))\n\nwhere R_0(x) = T[x, 0] (= ×(1 − α) in F_31) and L_0(x) = T[0, x] (= ×α). This lets us recover canonical → F_31² labels by BFS over the ⟨R_0, L_0⟩ action on canonical 1 (giving the horizontal axis F_31 × {0}), then on a chosen vertical generator (giving the vertical axis), then combining via the addition formula above. Under this reorder the Cayley table is fully (Z/31)²-translation-invariant AND every cell matches the medial-product formula exactly — visually a clean rainbow-diagonal pattern.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:15:25","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/961/2b8e3c0857adde3bd7a822129cd9972fb3e4f89fdb5fe0b7d88d61100613a576.txt"},{"canonical_hash":"3c1d2230e6d607f73abfa71c2eebd989d8b9366ea7b9f0ec007a81544de058b9","size":961,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,189,826,329,956,259,233,303,546,594,761,51,618,366,153,708,129,380,628,34,766,583,566,304,229,285,937,322,817,186,1,636,193,841,409,307,105,505,176,645,788,606,939,443,573,40,45,571,422,954,603,768,655,167,504,119,300,413,849,206,610,754,657,730,884,800,390,592,228,377,416,692,290,497,902,570,845,574,925,480,317,695,417,369,234,585,400,811,886,718,643,741,929,719,579,221,898,159,808,538,769,451,407,54,164,866,379,367,872,179,63,415,449,787,531,803,155,897,210,598,729,932,666,850,900,660,355,812,484,638,765,203,144,72,32,686,26,256,8,701,53,73,138,196,762,608,493,831,359,640,927,840,774,782,86,947,360,117,412,878,920,278,499,62,5,318,527,664,668,542,289,29,55,510,266,907,892,410,107,354,946,91,330,231,321,791,896,523,19,323,462,236,895,511,860,191,604,312,141,295,605,184,862,498,875,226,470,328,15,514,899,797,699,632,614,688,401,728,621,327,293,836,479,421,197,362,541,767,81,64,760,528,352,202,444,453,854,314,324,625,720,389,246,42,794,43,248,255,642,893,564,133,853,381,387,786,9,474,732,960,716,458,25,770,403,365,837,149,548,877,658,239,104,615,280,264,631,120,704,609,340,298,838,469,428,218,368,512,744,80,65,751,525,378,213,437,463,852,309,343,637,712,385,232,59,778,58,230,405,530,31,344,454,242,891,482,846,168,589,311,157,296,588,175,844,495,879,252,478,339,3,539,912,775,672,630,616,683,781,915,123,394,876,923,282,494,39,13,305,526,652,648,543,302,21,46,483,262,904,894,396,101,376,931,70,337,247,346,75,930,370,815,509,624,746,212,154,89,37,685,24,272,10,702,48,88,128,219,749,622,500,828,371,644,916,834,798,790,856,911,656,375,139,819,515,771,465,399,47,163,888,383,363,882,180,38,391,467,785,522,824,143,914,205,595,735,945,650,948,713,582,194,913,601,250,353,433,679,301,496,909,558,861,554,918,481,306,676,432,361,244,576,406,816,868,714,641,738,757,659,734,870,827,384,488,183,671,784,587,938,438,555,61,56,557,427,955,590,772,661,160,489,121,291,393,857,209,620,17,626,222,833,397,316,103,288,550,599,750,50,612,364,145,724,137,382,634,35,745,578,562,319,249,275,940,345,810,173,18,16,170,801,338,953,269,245,490,215,717,905,125,273,452,136,146,448,271,99,922,731,216,487,687,516,544,617,299,950,737,411,758,943,308,629,568,521,700,577,95,207,477,653,447,225,556,237,418,647,455,192,82,600,320,865,747,779,286,132,944,492,485,949,150,258,777,748,873,331,142,349,187,310,646,93,908,919,84,654,297,188,334,140,783,726,569,281,536,435,835,802,112,809,855,430,533,263,575,722,773,829,456,743,547,98,162,639,181,126,565,752,476,814,667,680,952,41,890,534,69,235,832,858,227,76,535,880,44,941,675,665,100,475,502,325,36,807,804,49,326,507,457,124,740,7,398,698,707,429,776,166,277,869,267,177,780,436,709,689,392,27,755,540,335,127,14,591,357,586,20,97,348,529,611,425,871,90,690,151,386,567,821,204,195,822,545,404,131,697,87,867,440,635,711,83,847,106,677,678,118,843,94,705,185,439,581,926,12,942,240,198,268,372,450,374,276,201,254,951,22,901,596,426,190,238,217,260,358,466,356,284,214,224,958,28,910,597,423,169,721,78,859,102,694,693,122,863,67,727,174,442,580,917,6,935,388,561,806,211,220,805,551,402,135,674,74,887,441,627,513,332,113,4,602,373,607,30,111,351,524,619,424,883,71,681,147,796,161,283,885,261,182,792,445,723,682,414,23,756,108,473,491,342,33,820,823,52,341,486,459,116,739,11,408,673,725,420,92,243,842,848,251,85,518,874,57,936,696,651,830,460,736,549,110,165,623,178,114,563,759,472,813,649,691,957,60,864,519,839,825,96,818,851,419,520,265,553,710,799,156,350,172,313,670,68,903,924,77,662,294,171,333,158,789,706,559,279,517,446,933,501,508,928,148,270,795,763,881,336,584,66,208,471,663,434,253,572,241,431,669,461,223,79,593,347,889,764,793,274,134,742,395,753,934,315,633,560,532,703,503,200,715,906,115,287,464,130,152,468,257,109,921,733,199,506,684,537,552,613,292,959","comment":"Size-961 = 31² idempotent right-cancellative magma satisfying Eq 677 and Eq 255 — but in a DIFFERENT family from the AG(2, 31) line construction (sibling magmas magma#2b8e3c08, magma#5f44e78d, magma#ba90950a, magma#fc322ba7 use that template).\n\nDistinguishing features:\n  • <0, 1> has size 961 — 2 elements generate the whole magma, so there are no size-31 (= AG(2, 31) line) sub-magmas through 0. This rules out the AG(2, 31) line family.\n  • L_0 = T[0, ·] has cycle structure (1, 60¹⁶): 16 orbits of length 60 plus the fixed point at 0. So L_0 has order 60 (vs. order 10 for the AG-line family).\n  • The carrier is F_961 = GF(31²) additively (= (Z/31)² as elementary abelian 31²-group). Translation by 1 in this hidden structure is an order-31 fix-free magma automorphism (verified by extending {σ(0)=1, σ(1)=754}); commutativity then yields a second independent translation τ₂, giving the full (Z/31)² translation group.\n\nStructure: x ◇ y = x + f(y − x) on (Z/31)², where f has cycle structure (1, 60¹⁶) — 16 cosets of an order-60 subgroup ⟨c⟩ in F_961* (which has order 960 = 16 · 60). On each coset f acts as multiplication by some near-field element; the 16-way coset decomposition makes this a 16-coset 'Tao Type II'-style piecewise-linear construction on F_961.\n\nIn the display-reorder coordinates, f is F_31-linear along each AXIS (f((c, 0)) = c · (8, 12) and f((0, d)) = d · (16, 8) mod 31) but NOT F_31-linear globally: f((1, 1)) = (23, 5) ≠ (24, 20) = f((1, 0)) + f((0, 1)). This axis-additivity-without-global-linearity is the structural fingerprint of NEAR-FIELD multiplication (compare magma#5ebfbb80 for the exceptional near-field of order 11², and magma#29114da6 for the exceptional near-field of order 29²). Since 31 is NOT in the Zassenhaus exceptional list {5, 7, 11, 23, 29, 59}, the near-field underlying this magma is presumably a Dickson near-field of order 31² with the order-2 Frobenius automorphism, with c of order 60 in the Dickson multiplicative group.\n\nDisplay reorder presents elements as (i, j) ↦ τ₁ⁱ τ₂ʲ(0) at index 31i + j, where τ₁, τ₂ are commuting order-31 fix-free magma automorphisms (the hidden additive translations in (Z/31)²). Under this reorder the Cayley table is fully (Z/31)²-translation-invariant.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:15:52","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/961/3c1d2230e6d607f73abfa71c2eebd989d8b9366ea7b9f0ec007a81544de058b9.txt"},{"canonical_hash":"5f44e78d513f3d81773b40bb356c073357ccb23ac7f2f7fdab865d1855e6aaeb","size":961,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,2,5,17,14,11,8,26,23,20,461,458,455,452,449,446,443,440,437,434,431,428,425,422,419,416,413,410,407,404,401,1,417,435,453,27,3,414,432,450,24,6,411,429,447,21,18,408,426,444,462,15,405,423,441,459,12,402,420,438,456,9,775,760,745,823,808,793,778,763,748,826,811,796,781,766,751,829,814,799,784,769,754,832,817,802,787,772,757,835,820,805,790,204,129,147,165,183,201,126,144,162,180,198,123,141,159,177,195,213,138,156,174,192,210,135,153,171,189,207,132,150,168,186,339,357,375,393,318,336,354,372,390,315,333,351,369,387,312,330,348,366,384,309,327,345,363,381,399,324,342,360,378,396,321,663,681,699,717,735,660,678,696,714,732,657,675,693,711,729,654,672,690,708,726,651,669,687,705,723,741,666,684,702,720,738,929,13,463,448,433,418,403,16,22,451,436,421,406,19,25,454,439,424,409,7,28,457,442,427,412,4,10,460,445,430,415,662,659,656,653,650,740,737,734,731,728,725,722,719,716,713,710,707,704,701,698,695,692,689,686,683,680,677,674,671,668,665,228,246,264,282,300,225,243,261,279,297,222,240,258,276,294,219,237,255,273,291,216,234,252,270,288,306,231,249,267,285,303,927,852,870,888,906,924,849,867,885,903,921,846,864,882,900,918,843,861,879,897,915,840,858,876,894,912,837,855,873,891,909,229,307,292,277,262,247,232,217,295,280,265,250,235,220,298,283,268,253,238,223,301,286,271,256,241,226,304,289,274,259,244,773,770,767,764,761,758,755,752,749,746,743,833,830,827,824,821,818,815,812,809,806,803,800,797,794,791,788,785,782,779,776,638,635,632,629,626,623,620,617,614,611,608,605,602,599,596,593,590,587,584,581,578,575,572,569,566,563,560,557,647,644,641,338,335,332,329,326,323,320,317,314,311,308,398,395,392,389,386,383,380,377,374,371,368,365,362,359,356,353,350,347,344,341,926,923,920,917,914,911,908,905,902,899,896,893,890,887,884,881,878,875,872,869,866,863,860,857,854,851,848,845,842,839,836,928,913,898,883,868,853,838,916,901,886,871,856,841,919,904,889,874,859,844,922,907,892,877,862,847,925,910,895,880,865,850,205,190,175,160,145,130,208,193,178,163,148,133,211,196,181,166,151,136,214,199,184,169,154,139,124,202,187,172,157,142,127,48,66,84,102,120,45,63,81,99,117,42,60,78,96,114,39,57,75,93,111,36,54,72,90,108,33,51,69,87,105,30,484,469,547,532,517,502,487,472,550,535,520,505,490,475,553,538,523,508,493,478,556,541,526,511,496,481,466,544,529,514,499,203,200,197,194,191,188,185,182,179,176,173,170,167,164,161,158,155,152,149,146,143,140,137,134,131,128,125,122,212,209,206,227,224,221,218,215,305,302,299,296,293,290,287,284,281,278,275,272,269,266,263,260,257,254,251,248,245,242,239,236,233,230,340,325,310,388,373,358,343,328,313,391,376,361,346,331,316,394,379,364,349,334,319,397,382,367,352,337,322,400,385,370,355,483,501,519,537,555,480,498,516,534,552,477,495,513,531,549,474,492,510,528,546,471,489,507,525,543,468,486,504,522,540,465,960,951,946,935,957,952,944,959,931,932,947,940,937,934,930,933,950,955,948,945,958,936,954,956,941,953,943,939,949,938,942,49,34,112,97,82,67,52,37,115,100,85,70,55,40,118,103,88,73,58,43,121,106,91,76,61,46,31,109,94,79,64,774,792,810,828,753,771,789,807,825,750,768,786,804,822,747,765,783,801,819,744,762,780,798,816,834,759,777,795,813,831,756,664,742,727,712,697,682,667,652,730,715,700,685,670,655,733,718,703,688,673,658,736,721,706,691,676,661,739,724,709,694,679,640,625,610,595,580,565,643,628,613,598,583,568,646,631,616,601,586,571,649,634,619,604,589,574,559,637,622,607,592,577,562,47,44,41,38,35,32,29,119,116,113,110,107,104,101,98,95,92,89,86,83,80,77,74,71,68,65,62,59,56,53,50,482,479,476,473,470,467,464,554,551,548,545,542,539,536,533,530,527,524,521,518,515,512,509,506,503,500,497,494,491,488,485,639,564,582,600,618,636,561,579,597,615,633,558,576,594,612,630,648,573,591,609,627,645,570,588,606,624,642,567,585,603,621","comment":"Size-961 = 31² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 31) line family. The 992 = 32 × 31 size-31 sub-magmas are exactly the lines of AG(2, 31); every pair of distinct points lies on a unique line.\n\nConstruction parameter: ALL 32 parallel classes use the SAME α = 23. Each line is isomorphic to magma#fdf14b96 (= x ◇ y = 9x + 23y mod 31, the F_31 linear magma with α = 23 ∈ {15, 23, 27, 29} = primitive 10th roots of unity in F_31 = roots of Φ_10 mod 31).\n\nEquivalently, this is the medial direct product F_31(α=23) × F_31(α=23), a single F_31²-linear quasigroup with\n\n  (x₁, x₂) ◇ (y₁, y₂) = ((1 − 23)·x_i + 23·y_i mod 31)_(i=1,2)\n\nSibling magmas at size 961, all 4 constant-α direct products: magma#fc322ba7, magma#2b8e3c08, magma#ba90950a, plus this one (α=23).\n\nDisplay reorder coordinates each point as F_31² (a, b) at index 31·a + b. F_31 addition is computable in the magma itself via the identity\n\n  x + y = T(R_0⁻¹(x), L_0⁻¹(y))\n\nwhere R_0(x) = T[x, 0] (= ×(1 − α) in F_31) and L_0(x) = T[0, x] (= ×α). This lets us recover canonical → F_31² labels by BFS over the ⟨R_0, L_0⟩ action on canonical 1 (giving the horizontal axis F_31 × {0}), then on a chosen vertical generator (giving the vertical axis), then combining via the addition formula above. Under this reorder the Cayley table is fully (Z/31)²-translation-invariant AND every cell matches the medial-product formula exactly — visually a clean rainbow-diagonal pattern.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:18:41","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/961/5f44e78d513f3d81773b40bb356c073357ccb23ac7f2f7fdab865d1855e6aaeb.txt"},{"canonical_hash":"fc322ba743f69d20d52473266bda3e6e3c600bf85e9ecf01f012a16370d71310","size":961,"satisfies_255":true,"right_cancellative":true,"idempotent":true,"display_reorder":"0,5,761,499,276,778,48,870,523,800,664,429,142,216,941,571,97,330,621,477,454,687,179,255,205,402,606,902,727,826,75,1,329,498,453,47,254,799,605,141,825,570,34,620,275,686,869,204,663,901,215,74,96,760,476,777,178,552,401,428,726,940,925,516,35,817,129,558,638,674,192,889,92,748,765,540,416,958,317,441,272,593,843,22,293,857,651,233,114,464,166,389,714,960,345,357,358,339,335,340,349,351,341,347,344,352,338,361,348,363,346,353,337,359,362,356,336,364,355,350,354,343,342,360,3,729,374,181,479,99,218,666,872,278,7,828,608,257,456,332,943,431,525,780,733,77,904,207,689,623,573,144,802,50,501,922,955,711,413,386,537,163,792,491,745,111,89,230,886,648,189,854,701,290,635,19,555,840,126,590,814,269,62,438,513,314,923,90,841,712,887,591,387,190,270,164,702,439,492,636,315,112,556,956,231,127,414,649,815,538,855,63,763,291,514,746,20,370,866,937,683,723,302,425,617,398,31,549,567,175,852,774,138,473,602,757,796,123,251,71,44,242,450,898,495,660,326,201,366,613,770,247,656,719,563,753,446,862,394,134,67,322,298,171,822,894,933,27,469,40,197,421,848,119,521,679,545,598,238,371,568,72,938,823,243,724,139,899,426,603,661,399,797,202,550,252,867,176,45,684,775,451,303,474,496,618,758,327,32,124,914,282,529,148,103,460,211,703,11,784,806,222,306,693,378,832,737,54,670,947,627,155,612,81,505,876,405,577,483,261,908,916,485,878,584,949,739,695,808,705,105,284,263,407,83,629,56,380,224,13,462,531,910,579,507,157,672,834,308,786,213,150,372,662,452,73,798,475,824,551,619,725,868,328,900,46,95,604,776,569,400,304,939,203,497,244,253,759,140,177,33,427,685,929,804,625,906,782,945,259,9,668,481,731,52,575,209,735,403,458,830,874,101,376,503,146,691,79,527,334,610,280,220,183,2,430,180,762,217,206,277,572,607,49,331,728,524,478,76,665,688,6,143,256,500,942,373,779,98,903,871,622,827,801,455,917,264,580,879,84,158,950,57,835,696,225,787,706,433,151,285,911,486,408,508,585,630,643,740,381,309,809,14,214,106,532,369,601,682,122,424,43,30,897,174,325,137,865,756,722,250,616,241,548,494,851,200,472,936,795,301,70,397,449,566,659,773,926,749,294,36,541,652,130,959,115,639,442,167,193,594,715,93,23,517,766,858,818,417,234,559,318,465,675,273,390,890,844,913,53,147,626,210,80,783,404,305,260,831,281,669,102,184,732,504,805,576,692,907,736,528,946,459,611,10,875,221,482,377,928,392,467,236,860,25,596,444,931,543,751,892,677,561,820,519,717,169,117,654,296,846,245,320,419,768,65,195,641,132,38,4,829,905,375,258,690,480,333,574,219,432,803,873,781,502,8,78,730,609,208,182,457,624,100,944,145,667,526,51,279,734,918,788,644,581,434,382,85,286,810,951,487,185,836,509,533,226,631,265,707,741,880,152,310,159,912,15,58,409,107,697,586,368,547,121,199,29,794,324,396,755,658,615,600,493,423,471,896,300,136,448,721,772,240,681,850,42,935,173,69,864,565,249,924,440,816,842,637,856,888,113,764,388,957,515,271,128,21,673,650,91,463,539,713,316,64,592,557,292,191,232,747,165,415,927,168,235,295,595,319,542,94,676,131,518,391,116,859,845,443,418,750,194,560,37,716,466,653,24,274,930,767,891,640,819,921,700,412,18,162,125,744,268,229,512,188,954,289,385,554,791,589,110,61,885,313,853,710,634,536,839,490,813,88,437,647,367,135,198,771,323,849,657,172,522,564,895,546,447,28,239,395,41,614,68,422,248,299,120,720,793,680,754,934,599,863,470,365,893,246,468,562,420,861,520,66,597,170,642,932,655,39,752,847,393,678,321,237,821,769,26,718,196,445,118,133,544,297,920,109,17,312,743,633,511,489,288,436,790,699,60,161,882,267,535,187,812,384,646,588,411,884,154,709,228,838,953,87,553,915,223,583,530,694,506,104,833,406,212,55,484,12,948,909,807,156,283,307,82,149,379,877,461,738,578,704,671,262,785,628,919,186,311,645,510,883,435,227,59,86,266,108,811,742,587,488,153,789,837,160,582,534,16,383,632,410,287,708,698,952,881","comment":"Size-961 = 31² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 31) line family. The 992 = 32 × 31 size-31 sub-magmas are exactly the lines of AG(2, 31); every pair of distinct points lies on a unique line.\n\nConstruction parameter: ALL 32 parallel classes use the SAME α = 29. Each line is isomorphic to magma#7ee5b4b8 (= x ◇ y = 3x + 29y mod 31, the F_31 linear magma with α = 29 ∈ {15, 23, 27, 29} = primitive 10th roots of unity in F_31 = roots of Φ_10 mod 31).\n\nEquivalently, this is the medial direct product F_31(α=29) × F_31(α=29), a single F_31²-linear quasigroup with\n\n  (x₁, x₂) ◇ (y₁, y₂) = ((1 − 29)·x_i + 29·y_i mod 31)_(i=1,2)\n\nSibling magmas at size 961, all 4 constant-α direct products: magma#2b8e3c08, magma#5f44e78d, magma#ba90950a, plus this one (α=29).\n\nDisplay reorder coordinates each point as F_31² (a, b) at index 31·a + b. F_31 addition is computable in the magma itself via the identity\n\n  x + y = T(R_0⁻¹(x), L_0⁻¹(y))\n\nwhere R_0(x) = T[x, 0] (= ×(1 − α) in F_31) and L_0(x) = T[0, x] (= ×α). This lets us recover canonical → F_31² labels by BFS over the ⟨R_0, L_0⟩ action on canonical 1 (giving the horizontal axis F_31 × {0}), then on a chosen vertical generator (giving the vertical axis), then combining via the addition formula above. Under this reorder the Cayley table is fully (Z/31)²-translation-invariant AND every cell matches the medial-product formula exactly — visually a clean rainbow-diagonal pattern.\n\n[text written by Claude]","submitted_at":"2026-05-14 05:25:54","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/961/fc322ba743f69d20d52473266bda3e6e3c600bf85e9ecf01f012a16370d71310.txt"},{"canonical_hash":"39810531a48227e78f82ee0427bb626c32f550db9ac3f3987765ca9c639985ec","size":961,"satisfies_255":true,"right_cancellative":true,"idempotent":false,"display_reorder":"957,75,442,609,356,394,522,41,255,123,289,475,891,759,419,926,164,701,13,148,210,563,850,556,801,219,681,652,333,742,808,939,80,447,614,361,399,527,46,260,97,294,480,896,764,424,908,169,706,18,153,215,568,855,530,806,224,655,626,338,716,813,944,85,452,619,366,373,501,51,265,102,299,485,870,769,429,913,174,711,23,127,189,573,860,535,780,229,660,631,312,721,818,949,90,457,593,371,378,506,56,270,107,304,490,875,774,403,918,179,685,28,132,194,578,865,540,785,234,665,636,317,726,823,954,64,462,598,345,383,511,61,275,112,309,495,880,748,408,923,184,690,2,137,199,583,839,545,790,239,670,641,322,731,828,936,69,436,603,350,388,516,35,249,117,283,469,885,753,413,905,158,695,7,142,204,588,844,550,795,244,675,646,327,736,833,956,74,441,608,355,393,521,40,254,122,288,474,890,758,418,925,163,700,12,147,209,562,849,555,800,218,680,651,332,741,838,938,79,446,613,360,398,526,45,259,96,293,479,895,763,423,907,168,705,17,152,214,567,854,529,805,223,654,625,337,715,812,943,84,451,618,365,372,500,50,264,101,298,484,900,768,428,912,173,710,22,126,188,572,859,534,779,228,659,630,311,720,817,948,89,456,592,370,377,505,55,269,106,303,489,874,773,433,917,178,684,27,131,193,577,864,539,784,233,664,635,316,725,822,953,63,461,597,344,382,510,60,274,111,308,494,879,747,407,922,183,689,0,136,198,582,869,544,789,238,669,640,321,730,827,935,68,435,602,349,387,515,34,248,116,282,468,884,752,412,904,157,694,6,141,203,587,843,549,794,243,674,645,326,735,832,955,73,440,607,354,392,520,39,253,121,287,473,889,757,417,924,162,699,11,146,208,561,848,554,799,217,679,650,331,740,837,937,78,445,612,359,397,525,44,258,95,292,478,894,762,422,906,167,704,16,151,213,566,853,559,804,222,653,624,336,745,811,942,83,450,617,364,402,499,49,263,100,297,483,899,767,427,911,172,709,21,125,187,571,858,533,778,227,658,629,310,719,816,947,88,455,591,369,376,504,54,268,105,302,488,873,772,432,916,177,714,26,130,192,576,863,538,783,232,663,634,315,724,821,952,62,460,596,343,381,509,59,273,110,307,493,878,746,406,921,182,688,1,135,197,581,868,543,788,237,668,639,320,729,826,934,67,434,601,348,386,514,33,278,115,281,467,883,751,411,903,156,693,5,140,202,586,842,548,793,242,673,644,325,734,831,960,72,439,606,353,391,519,38,252,120,286,472,888,756,416,929,161,698,10,145,207,560,847,553,798,247,678,649,330,739,836,959,77,444,611,358,396,524,43,257,94,291,477,893,761,421,928,166,703,15,150,212,565,852,558,803,221,683,623,335,744,810,941,82,449,616,363,401,498,48,262,99,296,482,898,766,426,910,171,708,20,124,186,570,857,532,777,226,657,628,340,718,815,946,87,454,621,368,375,503,53,267,104,301,487,872,771,431,915,176,713,25,129,191,575,862,537,782,231,662,633,314,723,820,951,92,459,595,342,380,508,58,272,109,306,492,877,776,405,920,181,687,30,134,196,580,867,542,787,236,667,638,319,728,825,933,66,464,600,347,385,513,32,277,114,280,497,882,750,410,902,155,692,4,139,201,585,841,547,792,241,672,643,324,733,830,930,71,438,605,352,390,518,37,251,119,285,471,887,755,415,466,160,697,9,144,206,590,846,552,797,246,677,648,329,738,835,958,76,443,610,357,395,523,42,256,93,290,476,892,760,420,927,165,702,14,149,211,564,851,557,802,220,682,622,334,743,809,940,81,448,615,362,400,528,47,261,98,295,481,897,765,425,909,170,707,19,154,216,569,856,531,807,225,656,627,339,717,814,945,86,453,620,367,374,502,52,266,103,300,486,871,770,430,914,175,712,24,128,190,574,861,536,781,230,661,632,313,722,819,950,91,458,594,341,379,507,57,271,108,305,491,876,775,404,919,180,686,29,133,195,579,866,541,786,235,666,637,318,727,824,932,65,463,599,346,384,512,31,276,113,279,496,881,749,409,901,185,691,3,138,200,584,840,546,791,240,671,642,323,732,829,931,70,437,604,351,389,517,36,250,118,284,470,886,754,414,465,159,696,8,143,205,589,845,551,796,245,676,647,328,737,834","comment":null,"submitted_at":"2026-05-17 21:37:33","submitted_by":"b-reinke","url":"https://eq677-magmas.icarm.cloud/magmas/961/39810531a48227e78f82ee0427bb626c32f550db9ac3f3987765ca9c639985ec.txt"}],"size_commentary":[{"size":2,"comment":"No magma of size 2 satisfies Equation 677.\n\nProof. Equation 677, x = y ◇ (x ◇ ((y ◇ x) ◇ y)), implies that for each fixed y, the map z ↦ y ◇ z is a bijection: its inverse sends x to x ◇ ((y ◇ x) ◇ y). So every row of the Cayley table must be a permutation of the carrier. An exhaustive check of all 2² = 4 such 2×2 row-Latin tables shows that none satisfies Eq677.\n\n[text written by Claude]"},{"size":3,"comment":"No magma of size 3 satisfies Equation 677.\n\nProof. Equation 677 forces every row of the Cayley table to be a permutation (the map z ↦ y ◇ z has inverse x ↦ x ◇ ((y ◇ x) ◇ y)), so candidates lie in the (3!)³ = 216 row-Latin tables. Exhaustive check: none satisfies Eq677.\n\n[text written by Claude]"},{"size":4,"comment":"No magma of size 4 satisfies Equation 677.\n\nProof. Equation 677 forces every row of the Cayley table to be a permutation (the map z ↦ y ◇ z has inverse x ↦ x ◇ ((y ◇ x) ◇ y)), so candidates lie in the (4!)⁴ = 331,776 row-Latin tables. Exhaustive check: none satisfies Eq677.\n\n[text written by Claude]"},{"size":5,"comment":"Size 5 is the smallest size > 1 that admits an Equation 677 magma (sizes 2, 3, 4 admit none — see their respective size pages), and there is exactly one such magma up to isomorphism: magma#e549b5f8.\n\nProof. Equation 677 forces every row of the Cayley table to be a permutation (the map z ↦ y ◇ z has inverse x ↦ x ◇ ((y ◇ x) ◇ y)), so candidates lie in the (5!)⁵ = 24,883,200,000 row-Latin tables. Backtracking that checks each instance of Eq677 as soon as the four rows it references are assigned visits only 6,409 nodes and returns 6 labeled magmas. Computing each one's canonical form (lex-min over all 5! = 120 relabellings) yields the same form for all six, so they are pairwise isomorphic.\n\nOrbit–stabilizer then gives |Aut(M)| = 5! / 6 = 20: a transitive group of order 20 on 5 points is the Frobenius group AGL(1, 5) = F₅ ⋊ F₅* — the affine group on F₅, acting sharply 2-transitively.\n\n[text written by Claude]"},{"size":6,"comment":"No magma of size 6 satisfies Equation 677.\n\nVerified by exhaustive search. The implication 'Eq 677 ⇒ every row of the Cayley table is a permutation' (the left inverse of z ↦ y ◇ z is x ↦ x ◇ ((y ◇ x) ◇ y), making each row a left-quasigroup) reduces the search space from 6^36 to (6!)^6 = 1.4 × 10¹⁷, which is large but cleanly enumerable. Ibrahim Tencer reported on the Zulip thread (Dec 7, 2024) that an exhaustive Vampire search confirmed no Eq 677 model exists at sizes 2, 3, 4, or 6 — same conclusion now corroborated for sizes 2, 3, 4 by independent brute-force enumeration over the row-permutation search space.\n\n[text written by Claude]"},{"size":8,"comment":"No magma of size 8 satisfies Equation 677.\n\nJose Brox confirmed this with an exhaustive Mace4 search taking 41 minutes (reported on the Zulip thread, Dec 7, 2024; configuration: selection_order 2, selection_measure 3, skolems_last).\n\n[text written by Claude]"},{"size":10,"comment":"No magma of size 10 satisfies Equation 677.\n\nJose Brox confirmed this with an exhaustive Mace4 search taking 39 hours (Zulip, Jan 12 2025; configuration: selection_order 2, selection_measure 3, skolems_last). Later independently confirmed using CaDiCaL (a modern CDCL SAT solver) in about 6 hours.\n\nCombined with the same conclusion at sizes 2, 3, 4, 6, and 8 (Tencer, Brox), this completes the proof that no Eq 677 magma exists at any size in {2, 3, 4, 6, 8, 10}.\n\nSizes 12 and 14 are OPEN: a CaDiCaL SAT attack ran for ~1 year on size 12 without terminating, and a separate experiment covered sizes 12–16 for 244 days without termination. So while 16 is the smallest size > 1 currently KNOWN to admit an Eq 677 magma (e.g. linear over F_16 = GF(2⁴) — Φ_10 has primitive 10th roots there since 10 | 15), 12 and 14 remain undecided.\n\n[text written by Claude]"},{"size":15,"comment":"No Eq 677 magma of size 15 is currently known; the existence question is OPEN but several substantial partial results restrict where one could live.\n\nLinear constructions are ruled out: 15 is not a prime power, so there is no field F_15. The standard linear construction x ◇ y = (1−α)x + αy requires a finite field, and the ring Z/15Z (the only sensible 15-element ring) doesn't help either: (Z/15Z)* ≅ Z/2 × Z/4 ≅ Z/8 by CRT (since |F_3*| · |F_5*| = 2·4), and 10 ∤ 8, so Φ_10 has no roots in Z/15Z. (Also 15 is not a square, ruling out AG(2, q) line magmas, and 15 isn't a prime square so no Zassenhaus exceptional or order-15 Dickson near-field exists.)\n\nTranslation-invariant magmas of size 15 are provably empty: Jose Brox confirmed (Zulip, Jan 2025) that there are no translation-invariant Eq 677 models of the form x ◇ y = x · f(x⁻¹ y) up to size 17 included, for ANY group structure on the carrier. Since the only group of order 15 is C_15 (cyclic — by gcd(3, 5−1) = 1 and Schur–Zassenhaus, this is the unique group), this exhaustively rules out the translation-invariant case at size 15.\n\nGeneral (non-translation-invariant) exhaustive search is inconclusive: a CaDiCaL SAT solver ran for about 6 days searching for a size-15 magma satisfying Eq 677 anti Eq 255, then segfaulted without resolution (Zulip thread; the searcher commented that finding one was 'unlikely'). The pure Eq 677 search at size 15 has not been finished by any tool.\n\nSo size 15 sits in the OPEN-but-unlikely category alongside sizes 12 and 14: known constructions don't produce one, partial-search results restrict where one could be, but full non-existence has not been proven.\n\n[text written by Claude]"},{"size":21,"comment":"Size 21 = 3·7 currently has 6 magmas in the DB, all idempotent, right-cancellative, and satisfying Eq 255. They split into two distinct structural families.\n\n**Family A: Steiner-S(2, 5, 21) = PG(2, 4) line magmas (4 magmas).** Every pair of distinct elements generates a 5-element sub-magma (≅ unique size-5 Eq 677 magma magma#e549b5f8). The 21 size-5 sub-magmas are the lines of the projective plane PG(2, 4) (the unique S(2, 5, 21)); each point lies on 5 lines. The four entries differ in their automorphism group:\n  • magma#b1cfacfa: |Aut| = Z_21 cyclic (translation-invariant, f involution)\n  • magma#4bd29022: |Aut| = F_21 = Z_7 ⋊ Z_3 (non-abelian Frobenius)\n  • magma#50e6ad54: |Aut| = F_21 = Z_7 ⋊ Z_3 (another non-abelian Frobenius, non-iso magma)\n  • magma#b904cba0: |Aut| = 1 (trivial — most rigid)\n\n**Family B: Pencil-through-pivot magmas (2 magmas).** Different structure: 21 = 1 + 5·4 — one pivot element + 5 size-5 lines through the pivot, partitioning the other 20 elements into 5 groups of 4. There are only **5** size-5 sub-magmas (not 21), all containing the pivot; cross-petal pairs (between different lines) generate the FULL 21-element magma. Both entries have |Aut| = 20 with orbit structure (1, 20).\n  • magma#2eea123a\n  • magma#9bef57c1\n\nThis is the smallest 'pencil' construction in the DB. Compare with the analogous magma#875876e7 at size 76 = 1 + 5·15, where the petals are size 16 (much larger) and a full TD(5, 15) of transversal size-5 sub-magmas connects the petals. At size 21, the petals are themselves size 5 and there are no cross-petal transversals.\n\nAll 6 size-21 entries share the same idempotent + RC + Eq 255 properties, but realize substantially different magma structures. The fundamental dichotomy:\n  • Family A: rich sub-magma structure (21 size-5 sub-magmas = full PG(2, 4) line set), but only some have nice algebraic symmetries.\n  • Family B: minimal sub-magma structure (5 size-5 sub-magmas all through a single pivot), but more rigid combinatorial design.\n\n[text written by Claude]"},{"size":25,"comment":"Size 25 = 5² currently has 54 magmas in the DB, all idempotent right-cancellative and satisfying Eq 255. They split into 4 distinct structural families:\n\n**Family 1: AG(2, 5) line magmas (29 magmas).** Every pair of distinct elements generates a 5-element sub-magma (≅ unique size-5 Eq 677 magma magma#e549b5f8). The 30 such sub-magmas are exactly the 30 lines of the affine plane AG(2, 5), partitioned into 6 parallel classes of 5 disjoint lines each — a Steiner system S(2, 5, 25). Of the 29, only 1 (magma#053cceeb, the F_5 × F_5 direct product) is (Z/5)²-translation-invariant; the other 28 have rigid Aut groups (orders 24-120) with no regular abelian subgroup. The display reorders use an AG(2, 5) coordinate grid (rows = parallel-class C_h lines, columns = parallel-class C_v lines).\n\n**Family 2: F_5(2, 4) × F_5 fiber bundles (23 magmas).** Tao G × M construction: an F_5 base group acts on an F_5 fiber, giving a fiber-bundle magma with only 5 size-5 sub-magmas (the fibers themselves) — far fewer lines than Family 1's 30. All are commented as 'F_5(2, 4) base × F_5 fiber'.\n\n**Family 3: 'Half-AG(2, 5)' sporadic (1 magma):** magma#d732efd1. Has exactly 15 size-5 sub-magmas (half of Family 1's 30); the lines correspond to 3 of the 6 AG(2, 5) parallel classes, with the other 3 classes having their pairs generate the full magma. Commented as 'the first known sporadic non-product magma at size 25.'\n\n**Family 4: No-size-5 sporadic (1 magma):** magma#09d21ec3. Has NO size-5 sub-magmas — every pair of distinct elements generates the entire 25-element magma. The 'most rigid' size-25 magma; L_0 has cycle structure (1, 8³).\n\nAll 54 are idempotent and have a unique idempotent at each element (full idempotence). Size-5 sub-magmas, where they exist, are always isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma; α = 4 is the only primitive 10th root of unity mod 5).\n\n**Why size 25 is so rich:** AG(2, 5) admits many distinct 'line-by-line' assignments, and the cohomological/Tao extension constructions on F_5 × F_5 are particularly fertile here. Comparing to other Steiner-S(2, 5, n) sizes: size 21 has 4 entries (Steiner S(2, 5, 21) = PG(2, 4)), size 41 has 8, size 61 has 32, size 65 has 9, size 81 has 16, size 85 has 7, size 125 has 1.\n\n[text written by Claude]"},{"size":41,"comment":"Size 41: 12 distinct Eq 677 magmas in the DB, all fully idempotent and right-cancellative. The family splits cleanly along two axes: (1) translation symmetry over F_41 (universal), and (2) whether multiplicative symmetry is preserved.\n\nThe base field is F_41. Note 41 is prime with 41 ≡ 1 (mod 10), so F_41 contains primitive 10th roots of unity. The four roots of the cyclotomic polynomial Phi_10(x) = x^4 - x^3 + x^2 - x + 1 in F_41 are {4, 23, 25, 31}, all of multiplicative order 10. These are the four Phi_10 roots, and they play the role of \"viable slopes\" for linear F_41 magmas.\n\nFour iso classes are the **linear F_41 affine line magmas**: x * y = x + alpha (y - x) mod 41, one for each Phi_10 root alpha. Each has |Aut| = 1640 = 40 * 41 = |AGL(1, 41)|, and ZERO size-5 sub-magmas (the F_41 line has no proper non-trivial sub-magmas other than singletons). These are: magma#345a4ec9 (alpha = 4), magma#385ad443 (alpha = 23), magma#ef76453c (alpha = 25), magma#a7a4546c (alpha = 31).\n\nThe other eight iso classes are **Steiner-line magmas** on S(2, 5, 41) designs: every pair of distinct elements lies in exactly one size-5 sub-magma, with 82 = 41*40/(5*4) blocks total, and each block is isomorphic to magma#e549b5f8 (the unique size-5 Eq 677 magma = the F_5 affine line). They split by symmetry:\n\n* **One** Z_5-symmetric variant: magma#b7e8bf90, |Aut| = 205 = 5*41. Aut is the Frobenius-style group Z_41 ⋊ Z_5, where Z_5 acts by multiplication by a primitive 5th root of unity (= zeta_5 = 10 in F_41). In F_41-translation labeling, the operation is x*y = x + f(y - x) with f(y) = alpha(y) * y where alpha takes only the 4 Phi_10-root values, each on a size-10 set (= union of 2 cosets of <zeta_5>).\n\n* **Seven** translation-only variants, |Aut| = 41 each (just the Z_41 of translations). In F_41-translation labeling, slope alpha(y) = f(y)/y takes 12 distinct values: the 4 Phi_10 roots PLUS 8 \"extra\" non-root slopes {11, 13, 15, 17, 19, 27, 29, 38}. These 7 split by class-size multiset into two types:\n  - Type A (5 magmas: magma#d32b07ca, magma#c0b238e3, magma#10305dec, magma#8f879c02, magma#c754a6c0): each Phi_10 slope occurs on a size-2 subset; each non-Phi slope on a size-4 subset. Total 4*2 + 8*4 = 40.\n  - Type B (2 magmas: magma#e3521249, magma#8b36eeff): each Phi_10 slope occurs on a size-6 subset; each non-Phi slope on a size-2 subset. Total 4*6 + 8*2 = 40.\n\nA remarkable fact: ALL 8 Steiner-line magmas use the SAME set of 12 slope values across F_41* (the 4 Phi_10 roots plus the same 8 non-Phi roots). The 7 translation-only variants differ from each other in WHICH subset of F_41* gets which slope (= different difference-family choices for the cyclic (41, 5, 1)-BIBD plus different inner block-labelings).\n\nConstruction recipe: a Steiner-line magma at any prime p ≡ 1 (mod 10) arises from a cyclic S(2, 5, p) Steiner system together with a choice of \"F_5-line orientation\" on each block. The cyclic (41, 5, 1)-BIBD has 2 base blocks under Z_41 (Fisher's relation: 41*r/k = 82 = 41 * 2). Each labeled magma corresponds to (i) a base-block pair, and (ii) a Z_41-equivariant F_5-line labeling per block, with the global Eq 677 condition imposing compatibility constraints. The Z_5-symmetric variant (magma#b7e8bf90) chooses base blocks that are Z_5-stable; the translation-only variants do not.\n\nSmaller analogs: size 11 (linear F_11, |Aut| = 110, one iso class, no proper sub-magmas), size 31 (similar, F_31 with Phi_10 roots), size 21 (PG(2,4) Steiner-line + pencil families). Larger analogs at primes p ≡ 1 mod 10: 61, 71, 101 etc. would presumably exhibit similar linear-vs-Steiner splits but the database hasn't enumerated them.\n\n[text written by Claude]"},{"size":49,"comment":"Size 49 = 7^2. The smallest sizes admitting eq677 magmas are 5 and 7; over F_7 there are two eq677 magmas, x*y = 4x + y and x*y = 4x + 3y (written F_7(4,1) and F_7(4,3)). Order-49 magmas are built over this order-7 base structure, and the ones examined so far all have a single idempotent. Two structural families occur:\n\n1) Fiber bundles. These carry a congruence with 7 classes of size 7; the quotient is one of F_7(4,1) or F_7(4,3) and the classes are order-7 fibers. Both right-cancellative and non-right-cancellative examples exist (in the nRC case some right multiplications collapse a fiber). In (base, fiber) coordinates the Cayley table is a clean 7x7 block super-grid.\n\n2) Pencils. These are simple (no nontrivial congruence): two elements generate either a shared order-7 sub-magma or the entire magma. Each pencil has exactly 8 order-7 sub-magmas, all through one common element (the unique idempotent), partitioning the remaining 48 elements into 8 petals of 6 -- the incidence pattern of the 8 lines through a point of AG(2,7), which is also how the 8 one-dimensional F_7-subspaces of a linear F_49 magma sit. Strikingly, these pencils are NOT isomorphic to any linear magma over F_49 and are not affine over their lines: they are genuinely twisted. They sub-classify by the multiset of line types: 8xF_7(4,1) (6 magmas); 7xF_7(4,1) + 1xF_7(4,3) (6 magmas); 8xF_7(4,3) (6 magmas); 7xF_7(4,3) + 1xF_7(4,1) (6 magmas).\n\nA recent batch of new order-49 magmas (submitted by b-reinke) comprises 6 fiber bundles (4 RC over F_7(4,3)/F_7(4,1), 2 nRC over F_7(4,3)) and 24 pairwise non-isomorphic pencils. Their display reorders were (re)derived: bundles via (base, fiber) coordinates, pencils -- lacking any congruence -- by minimizing a Cayley-image smoothness measure. [text written by Claude]"},{"size":61,"comment":"Size 61: 36 distinct Eq 677 magmas in the DB, all fully idempotent and right-cancellative. 61 is prime with 61 ≡ 1 (mod 10), so F_61 admits primitive 10th roots of unity. The four roots of the cyclotomic polynomial Phi_10(x) = x^4 - x^3 + x^2 - x + 1 in F_61 are {3, 27, 41, 52} (each of multiplicative order 10).\n\nThe family splits into two structural classes plus a richer sub-classification by automorphism size:\n\n**4 Linear magmas** (F_61 affine line, x*y = x + alpha(y - x) = (1-alpha)x + alpha*y mod 61, one per Phi_10 root):\n  magma#f2d8c865 (alpha = 52, equivalently x ◇ y = 10x + 52y)\n  magma#d5df0d93 (alpha = 41, equivalently x ◇ y = 21x + 41y)\n  magma#82a4911c (alpha = 27, equivalently x ◇ y = 35x + 27y)\n  magma#e70931b6 (alpha = 3,  equivalently x ◇ y = 59x + 3y)\n  Each has |Aut| = 3660 = 60*61 = |AGL(1, 61)|. Zero size-5 sub-magmas (the F_61 line has no proper non-trivial sub-magmas).\n\n**32 Steiner-line magmas** on cyclic S(2, 5, 61) designs. Each has 183 = 61*60/(5*4) size-5 sub-magmas, each block is the F_5 affine line magma#e549b5f8, and every pair of distinct elements lies in exactly one block. They split by |Aut|:\n\n* 1 Z_15-symmetric variant: magma#0bcf3cca, |Aut| = 915 = 15*61. The order-15 subgroup of F_61* = (F_61*)^4 = {y : y^15 = 1} fixes the point 0 and acts by multiplication. In F_61 translation labeling, x*y = x + f(y - x) with f(y) = alpha(y)*y, where alpha takes ONLY the 4 Phi_10 roots, each on exactly one of the 4 (F_61*)^4-cosets. (See magma#0bcf3cca commentary for the explicit coset-to-root mapping.)\n\n* 1 Z_3-symmetric variant: magma#05fbff2c, |Aut| = 183 = 3*61. Stabilizer = order-3 subgroup {1, 13, 47}. In F_61 translation labeling, slope alpha is constant on the 20 Z_3-orbits of size 3, and takes 16 NON-Phi_10 slope values (avoiding {3, 27, 41, 52} entirely). The exact opposite of magma#0bcf3cca's Phi-only slope structure.\n\n* 30 translation-only variants: |Aut| = 61 (just Z_61). These split further by their *slope value set* in F_61 translation labeling:\n  - The \"Phi + inverse-paired tribe\": 3 magmas (magma#e87f6bb9, magma#2426bbe0, magma#ec9ec6f6) use the same 12-element slope value set V = {3, 7, 10, 21, 27, 30, 32, 35, 41, 52, 55, 59} = (4 Phi_10 roots) union (4 non-Phi inverse-pairs {7,35}, {10,55}, {21,32}, {30,59} in F_61*). They differ by class-size distribution: e87f6bb9 has Phi-sum=44 (Phi-classes of size 11), 2426bbe0/ec9ec6f6 have Phi-sum=28 (Phi-classes of size 7). Note magma#0bcf3cca uses just the 4-element subset {3, 27, 41, 52} of V.\n  - The other 27 magmas use larger slope-value sets, generally chaotic and unique per magma (|slope-values| ranges from 16 up to 38). A few pairs share slope-value sets (e.g. magma#2e8995b3 / magma#e1aef716, magma#b175c0f4 / magma#b8ecd854) - these are likely Galois-conjugate pairs.\n\nSlope-fingerprint distribution among the 30 translation-only magmas, by Phi-sum (= number of F_61* elements mapped to Phi_10-root slopes): Phi-sum=44 (1 magma), Phi-sum=28 (2), Phi-sum=6 (4), Phi-sum=4 (8), Phi-sum=2 (7), Phi-sum=0 (8 -- \"Phi-free\" translation-only variants, joining magma#05fbff2c structurally though without its Z_3 symmetry).\n\nCompare with size 41 (40 = 8*5 vs 60 = 4*15 has fewer divisors): size 41 has only 1 multi-stabilizer variant (Z_5, |Aut|=205) plus 7 translation-only Steiner-line magmas, and all 8 share a single 12-value slope set. Size 61 has both Z_15 and Z_3 multi-stabilizer variants and 26 distinct slope sets among 32 Steiner-line magmas, reflecting 60's richer divisor structure (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60).\n\nSmaller analogs at p ≡ 1 (mod 10): size 11 (just F_11 linear, 1 iso class). Larger: size 71 has |F_71*| = 70 = 2*5*7 with only Z_5 and Z_7 multi-stabilizer subgroups (no Z_15 analog).\n\n[text written by Claude]"},{"size":65,"comment":"Size 65: 17 distinct Eq 677 magmas in the DB. Unlike sizes 41 and 61, 65 = 5*13 is composite. Crucially, the cyclotomic Phi_10(x) factors as (x+1)^4 mod 5 (single root with multiplicity 4) and is irreducible of degree 4 mod 13. By CRT, Phi_10 has NO roots in Z_65, so there is no \"linear F_65 affine line\" magma at this size. All 17 size-65 Eq 677 magmas are non-linear constructions.\n\nThe 17 magmas split by idempotency:\n\n**9 fully idempotent magmas** -- Steiner-line over cyclic S(2, 5, 65). Each has 208 = 65*64/(5*4) size-5 sub-magmas (every block isomorphic to the F_5 affine line magma#e549b5f8). All 9 are translation-invariant over Z_65 = Z_5 x Z_13 (so |Aut| is a multiple of 65). They sub-classify by automorphism size and slope pattern:\n\n* 1 Z_4-symmetric variant: magma#eff27734, |Aut| = 260 = 4 * 65. Point-stabilizer is Z_4 = <34> = {1, 34, 51, 44} in Z_65*. In Z_65 translation labeling, slope alpha(y) = f(y)/y takes ONLY 4 values {3, 22, 35, 51}, each on a size-12 Z_4-coset. (Compare with magma#b7e8bf90 at size 41, magma#0bcf3cca at size 61: all are the \"most symmetric Steiner-line\" variants at their sizes.)\n\n* 8 translation-only variants: |Aut| = 65 (just Z_65). All 8 use the SAME 12-element slope value set on Z_65*: V = {3, 15, 21, 22, 31, 32, 34, 35, 44, 45, 51, 63}. Inside V:\n  - 9 units form 4 inverse pairs {3,22}, {21,31}, {32,63}, {34,44} plus 1 self-inverse (51, since 51^2 = 1 mod 65)\n  - 3 non-units {15, 35, 45} (all multiples of 5, hence non-invertible mod 65)\n  The Z_4-symmetric magma#eff27734 uses the 4-element subset {3, 22, 35, 51} of V.\n  \n  The 8 translation-only magmas split by slope-class-size pattern:\n  - Type A (5 magmas: magma#a09c4223, magma#86e94818, magma#4d60c34f, magma#bcf3ee89, magma#84076266): class sizes (6, 6, 6, 4, 4, 4, 4, 4, 4, 2, 2, 2) - sum 48\n  - Type B (2 magmas: magma#d8ba33b5, magma#2db4eae0): (8, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2)\n  - Type C (1 magma: magma#62917c53): (9, 9, 9, 8, 2, 2, 2, 2, 2, 1, 1, 1)\n\n**8 non-idempotent magmas** -- F_5 x F_13 product-type constructions (already commented from a prior session):\n* magma#5e80e1c2dc82 (1 magma): pure direct product F_5 * F_13 of linear magmas\n* magma#b8dd5d8f5072, magma#b841b444f6b6, magma#f6a46900b44d, magma#22cb8afe1ff0, magma#3a1e3dea0200 (5 magmas): \"F_5(2,4) base x F_13 fiber\" bundles (5 fibers of 13)\n* magma#3e7f78778326 (1 magma): F_5 base x F_13 fiber with within-fiber smoothing\n* magma#17d8eb76b6bf (1 magma): contains a F_5(2,4) sub-magma + 5 fibers of 12 remaining elements\n\nNote the structural contrast: prime sizes (41, 61) admit linear F_p magmas AND Steiner-line magmas; composite sizes (65) admit ONLY Steiner-line idempotent magmas + non-idempotent fiber-bundle constructions.\n\nCompare with size 41 (|Aut|=205 multi-stab + 7 translation-only Steiner-line on a 12-element slope set), size 61 (|Aut|=915 Z_15-stab + |Aut|=183 Z_3-stab + 30 translation-only on 26 different slope sets). Size 65 has only 1 multi-stab (Z_4) and only 12 slope values across all 9 idempotent magmas -- but distributed across only 4 distinct slope-pattern types (eff27734 + Types A, B, C). The smaller variety at size 65 reflects 64 = phi(65) = 4*12 = order(Z_65*) being more constrained.\n\nOpen question: what does the \"Phi_10-roots-don't-exist-mod-N\" constraint translate to in the algebraic structure of the magma? The 12-element slope set V suggests there's still some algebraic-number-theory residue, perhaps tied to Z_5-roots of Phi_2 = (x+1) lifting to mixed elements in Z_5 x Z_13.\n\n[text written by Claude]"},{"size":81,"comment":"Size 81 = 3⁴ admits several distinct families of Eq 677 magmas, distinguished by the additive carrier and the directional / fiber structure.\n\nCurrently 24 size-81 magmas are in the DB. All satisfy Eq 255. 19 are idempotent; 5 are non-idempotent (and all 5 of those are extensions of the unique size-9 Eq 677 magma magma#2925dc18, 'x ◇ y = x + 3y mod 9').\n\nIdempotent families:\n\n1. Linear over Z/81Z (cyclic ring, not the field): magma#b9170dc7 with x ◇ y = 21x + 16y (mod 81). One idempotent entry. (Z/81Z is a ring; the genuinely-field-based magmas are Family 2.)\n\n2. F_81 = (Z/3)⁴ with order-10 directional δ — 'b-reinke template' (4 magmas). Carrier is the additive group (Z/3)⁴ ≅ F_81 = GF(81). Operation x ◇ y = x + δ(y − x) where δ has cycle structure (10⁸, 1): 8 orbits of length 10 plus a fixed point at 0, with δ acting on each of the 8 cosets of the order-10 subgroup H ⊂ F_81* as multiplication by some δ_i ∈ H. |Aut| = 81 × 40 = 3240. Examples: magma#a1ef80ed, magma#cdf12d20, magma#b89c1afe, magma#632999fe.\n\n3. Z_81 (cyclic) with involution f and Steiner S(2, 5, 81) (16 magmas). Carrier is Z_81 cyclic (not (Z/3)⁴). Operation x ◇ y = x + f(y − x) where f is a fixed-point-free INVOLUTION (cycle structure (1, 2⁴⁰)). Every pair of distinct elements generates a 5-element sub-magma; the 324 sub-magmas form a 2-(81, 5, 1) Steiner system. |Aut| = 81 (just the additive translations of Z_81). Examples: magma#8c8fe34b, magma#c5da3284, magma#0d529c59 + 13 others.\n\nNon-idempotent families (extensions of the unique size-9 Eq 677 magma magma#2925dc18):\n\n4. F_9 × F_9 direct product: 1 magma, magma#761fd630. The size-9 sub-magmas are exactly the 10 projective lines through origin in F_9² (9 'finite-slope' lines plus the 'vertical' line). |Aut| is large.\n\n5. Size-9 fiber bundle over a size-9 base: 1 magma, magma#0dd86070. The 81 elements partition (in canonical labels) into 9 consecutive blocks {9k, …, 9k+8}; the block partition is a magma congruence and the quotient is the size-9 magma magma#2925dc18. The unique size-9 sub-magma {72…80} is the canonical section. |Aut| = 9 (just the additive translations within the fiber).\n\n6. Non-fiber-bundle extension of size-9: 1 magma, magma#67110840. Has the same unique size-9 sub-magma at {72…80} but NO non-trivial congruence — no projection M → F_9 exists. |Aut| = 72 = AGL(1, F_9), the full Aut of the size-9 sub-magma lifted to M.\n\nDisplay reorders for all 16 Family-3 magmas have been set to the orbit of 0 under an order-81 magma automorphism (the hidden Z_81 additive translation), exposing the cyclic translation symmetry. For magma#0dd86070 the canonical labeling already exposes the fiber-bundle structure (visible as a clean 9×9 checkerboard).\n\n[text written by Claude]"},{"size":85,"comment":"Size 85 = 5·17 currently has 7 magmas in the DB, all sharing a single structural template: **Z_85 cyclic + involution + Steiner system S(2, 5, 85)**. All are idempotent, right-cancellative, and satisfy Eq 255.\n\nCommon structure:\n  • Additive carrier: the cyclic group Z_85 (= Z_5 × Z_17 by CRT). The magma is fully Z_85-translation-invariant: there is an order-85 fix-free magma automorphism τ acting as 'translation by 1' in the hidden Z_85 structure.\n  • Operation: x ◇ y = x + f(y − x), where f: Z_85 → Z_85 is a fixed-point-free involution (f² = id, f(0) = 0, 42 transpositions). L_0 has cycle structure (1, 2⁴²); R_0 has cycle structure (1, 4²¹).\n  • Sub-magma design: every pair of distinct elements generates a 5-element sub-magma isomorphic to the unique size-5 Eq 677 magma over F_5. There are 357 such sub-magmas (= C(85, 2)/C(5, 2)), each point on exactly 21, forming a **Steiner system S(2, 5, 85)**. (Necessary condition for S(2, 5, v): v ≡ 1 or 5 mod 20; here 85 ≡ 5 ✓.)\n\nSeven entries (differ in which specific involution f is chosen):\n  • magma#31ae2815\n  • magma#10e5c920\n  • magma#5d5c0411\n  • magma#84944e78\n  • magma#d02731a8\n  • magma#6282dd11\n  • magma#4b5e27f5\n\nSame family as the 16 size-81 Family-4 magmas (Z_81 + involution + S(2, 5, 81); see magma#c5da3284 and siblings), with 81 ≡ 1 mod 20 the next smaller admissible size. The template generalizes to any n ≡ 1 or 5 mod 20 admitting both:\n  • A fixed-point-free involution f on Z_n satisfying Eq 677.\n  • A Steiner system S(2, 5, n) compatible with f's transpositions inside each line.\n\nOther DB sizes where this Steiner-system + involution template is represented: 21, 25, 41, 61, 65, 81, 125. Notably size 61 has 32 such magmas (all already commented), size 81 has 16, size 41 has 8, size 65 has 9, size 25 has 29.\n\nDisplay reorders for all 7 size-85 entries have been set to the orbit grid (i ↦ τⁱ(0)) using the hidden Z_85 additive translation, exposing the cyclic translation symmetry as clean diagonal banding in the rendered Cayley table.\n\n[text written by Claude]"},{"size":121,"comment":"Size 121 = 11² is among the most populated sizes in the DB (65 magmas as of writing). All 65 are idempotent and satisfy Equation 255. The cleanest sorting is by **# size-11 sub-magmas** (= # parallel classes of AG(2, 11) closed under the operation):\n\n| sub-11 | classes | # | RC | family |\n|---|---|---|---|---|\n| 0 | 0 | 8 | mixed | F_121 / Zassenhaus / order-k multiplier |\n| 12 | 11 fibers + 1 transversal | 1 | LC only | magma#ee53a960 fiber-bundle |\n| 22 | 2 | 8 | yes | \"2-class\" twisted AG(2, 11) |\n| 44 | 4 | 2 | no | \"4-class\" twisted AG(2, 11) |\n| 88 | 8 | 4 | no | \"8-class\" twisted AG(2, 11) |\n| 132 | all 12 | 42 | yes | full AG(2, 11) line family |\n\n**Within sub-11 = 0**, the 8 magmas split by L_0/R_0 cycle:\n- **1 + 15·8** (multiplier order 8, NEW family of 5): magma#70e5572a, magma#873c2695, magma#58669675, magma#af70b7bb, magma#fdc7e335. Uses (F_121*)^15 (order-8 subgroup) as multiplier; OUTSIDE Pace Nielsen's Type-1/Type-2 (which require multiplier order 10 or roots of Phi_2_5).\n- **1 + 6·20** (multiplier order 20, 1 magma): magma#74c24c4d.\n- **1 + 4·30** (multiplier order 30, 1 magma): magma#5ebfbb80, the **Zassenhaus exceptional near-field**. Multiplicative group Z_5 × SL(2, 3); Aut sharply 2-transitive of order 14,520; also satisfies Eq 3345.\n- **Asymmetric L_0/R_0** (NON-RC, 1 magma): magma#3f8367e9.\n\n**Construction families:**\n\n1. **Direct products F_11 × F_11** (sub-11 = 132, 4 entries): (x_1, x_2) ◇ (y_1, y_2) componentwise. α ∈ {2, 6, 7, 8}: magma#d4b8c23f, magma#199764ee, magma#65eed598, magma#c3819eed.\n\n2. **Full AG(2, 11) line family** (sub-11 = 132, 42 magmas). All 12 parallel classes preserved as F_11-line sub-magmas; non-isomorphic Phi_10-slope assignments give different iso classes (e.g. 12+0, 10+2, 8+4, 6+6 splits). Example: magma#83a10ff4, magma#270b7c37 (10+2 split).\n\n3. **\"k-class\" twisted AG(2, 11)** (NEW). Exactly k ∈ {2, 4, 8} of 12 parallel classes preserved. k=2: 8 RC iso classes including magma#6bab1ff9. k=4 and k=8: 2 + 4 non-RC iso classes; see magma#014291bf and magma#c8dcedeb.\n\n4. **Zassenhaus near-field II** (sub-11 = 0, magma#5ebfbb80; see above).\n\n5. **\"Order-8 multiplier\" family** (NEW, sub-11 = 0, 5 magmas; see above).\n\n6. **\"Order-20 multiplier\"** (sub-11 = 0, 1 magma): magma#74c24c4d.\n\n7. **Twisted product fiber bundle** (sub-11 = 12, magma#ee53a960). 11 fibers + 1 transversal; LC but not RC.\n\n8. **Non-RC outlier** (sub-11 = 0, magma#3f8367e9).\n\n**Display convention**: magmas with sub-11 ≥ 22 use an F_11 × F_11 grid reorder where positions 11·r + c correspond to the intersection of P1-row r and P2-column c (using 2 preserved parallel classes as axes). The 5 \"order-8\" magmas use an F_11 × F_11 ADDITIVE grid (commuting order-11 translations as axes).\n\n**Lower bound on iso classes**: at least 13,794 distinct Eq 677 magmas of size 121 exist (Burnside count over the AG(2, 11) line construction, varying Phi_10-slope assignments to the 12 parallel classes). The 65 currently in the DB are a small sample of this combinatorial space.\n\n[text written by Claude]"},{"size":127,"comment":"Size 127 is prime, with multiplicative group F_127* of order 126 = 2·3²·7. Since 10 does not divide 126, F_127 contains no primitive 10th roots of unity, and the polynomial Φ_10(α) = α⁴ − α³ + α² − α + 1 has no roots in F_127.\n\nConsequence: there is no simple-linear idempotent Eq 677 magma on F_127. (A single-multiplier x ◇ y = (1 − α)x + α y satisfies Eq 677 iff Φ_10(α) ≡ 0, which has no solution here.)\n\nThe Tao Type II piecewise-linear construction rescues this. Splitting f according to whether y − x is a QR or NQR mod 127 — i.e. taking x ◇ y = x + f(y − x) with f(d) = α_QR · d on QR and f(d) = α_NQR · d on NQR — allows Eq 677 even at primes where no single α works.\n\nThe unique DB example at this size is magma#cf044a9b, with (α_QR, α_NQR) = (58, 29). (Note 58 = 2·29 and 2 is a QR mod 127, so the two multipliers are related by a QR scalar.) It is idempotent, right-cancellative, and satisfies Eq 255.\n\n[text written by Claude]"},{"size":181,"comment":"Size 181 is prime, so every Eq 677 magma here lives on a cyclic additive group of order 181 (or fails to even be translation-invariant, see below). The DB currently lists 16 magmas: 8 simple-linear and 8 Tao-Type-II piecewise-linear.\n\nAll 16 satisfy Eq 255. 12 are idempotent; 4 are non-idempotent.\n\n1. Simple linear (single multiplier). x ◇ y = α x + β y on F_181 for fixed α, β. Eight DB entries (all dwrensha submissions).\n\n  1a. Idempotent (α + β = 1, equivalently x ◇ y = x + α(y − x)). Eq 677 forces Φ_10(α) ≡ α⁴ − α³ + α² − α + 1 ≡ 0 (mod 181), giving four valid α ∈ {46, 56, 122, 139} (the four primitive 10th roots of unity in F_181). All four are in the DB:\n    • magma#355635ab (α = 139)\n    • magma#e8378e60 (α = 122)\n    • magma#5c952978 (α = 56)\n    • magma#d836a209 (α = 46)\n\n  1b. Non-idempotent (α + β ≠ 1). Four DB entries — magma#5c97e821, magma#6960b95b, magma#df073ec9, magma#45b4632c — with various (α, β). These are NOT translation-invariant under the additive group of F_181 (the obstruction (α + β − 1)·a ≡ 0 mod 181 forces a = 0); their natural symmetry is multiplicative scaling x ↦ λx for λ ∈ F_181*.\n\n2. Tao Type II piecewise-linear (two multipliers, keyed to QR/NQR). x ◇ y = x + f(y − x) on F_181, where f(d) = α_QR · d when d is a quadratic residue mod 181 and f(d) = α_NQR · d when d is a non-residue (and f(0) = 0). All 8 b-reinke size-181 magmas have this form. (α_QR, α_NQR) pairs found:\n\n  • magma#2c0a619d (RC):  (122, 46)\n  • magma#7580f29f (RC):  (139, 122)\n  • magma#8c3de954 (RC):  (56, 139)\n  • magma#f14f808f (RC):  (139, 46)\n  • magma#70249bf6 (RC):  (56, 122)\n  • magma#ddf8aaa4 (RC):  (56, 46)\n  • magma#2f965789 (non-RC): (139, 176)\n  • magma#3beeddee (non-RC): (48, 139)\n\nThe α-values appearing across the piecewise family are {46, 48, 56, 122, 139, 176}. The four α with Φ_10(α) ≡ 0 mod 181 (46, 56, 122, 139) also appear singly in family 1a; α = 48 and α = 176 only arise as one half of a piecewise pair.\n\nDisplay reorders for all 8 piecewise magmas have been set to the orbit of 0 under an order-181 fix-free magma automorphism (the hidden additive translation by 1 in F_181). After the reorder, the Cayley table is fully translation-invariant: every row is a horizontal shift of row 0 = the function f, and the rendered image shows clean diagonal banding across the entire 181×181 grid.\n\n[text written by Claude]"},{"size":343,"comment":"Size 343 = 7³ currently has 5 magmas in the DB, falling into two distinct families.\n\nFamily A: Dickson-near-field-style construction on F_343 = GF(7³) (1 magma, right-cancellative, idempotent). magma#ff552011. Translation-invariant on (Z/7)³ — the additive group of GF(7³) — with three commuting order-7 fix-free magma automorphisms exhibiting the (Z/7)³ structure. L_0 has cycle structure (1, 18¹⁹) and R_0 has (1, 19¹⁸), with ord(L_0) · ord(R_0) = 18·19 = 342 = |F_343*|. L_0 is axis-additive on each F_7-axis but NOT globally F_7-linear (only 7.3% of cells match the F_7-linear formula) — the structural fingerprint of near-field multiplication. Since 7³ is NOT in the Zassenhaus exceptional list {5², 7², 11², 23², 29², 59²}, this is presumably a Dickson near-field construction with the order-3 Frobenius x ↦ x⁷.\n\nWhy no simple-linear or AG-line magma exists at this size: F_343 has primitive 10th roots of unity iff 10 | 342; since 342 = 2·3²·19 is not divisible by 10, Φ_10(α) has no roots in F_343. (Also 7³ ≠ q² so AG(2, q) line magmas don't apply.) The non-distributive Dickson multiplication is required to satisfy Eq 677.\n\nFamily B: Direct products of a non-right-cancellative size-49 factor with a linear F_7 factor (4 magmas, all non-right-cancellative, non-idempotent except for one idempotent fixed point, all satisfying Eq 255). These are all dwrensha submissions of the form (nRC-49) × F_7(α, ω):\n\n  • magma#d25da012 — (nRC-49 b91b0b41) × F_7(4, 1)\n  • magma#102a77e6 — (nRC-49 b91b0b41) × F_7(4, 3)\n  • magma#1ed733cf — (nRC-49 d50b3565) × F_7(4, 1)\n  • magma#97279551 — (nRC-49 d50b3565) × F_7(4, 3)\n\nThe two non-RC size-49 factors (magma#b91b0b41 and magma#d50b3565) sit in the DB at size 49 (Zassenhaus exceptional near-field size 7² territory). Each is then multiplied by one of two non-isomorphic linear F_7(α=4) magmas (distinguished by their parameter ω = 1 or 3).\n\nAll 5 size-343 magmas satisfy Eq 255. Notably, the right-cancellative entry is the only idempotent one (Family A), while the non-RC entries (Family B) have exactly one idempotent element each.\n\n[text written by Claude]"},{"size":361,"comment":"Size 361 = 19² admits Eq 677 magmas via near-field-style constructions. Currently 3 magmas in the DB, all idempotent right-cancellative, all satisfying Eq 255, all b-reinke submissions.\n\nAll 3 share the same structural template:\n  • Carrier: F_361 = GF(19²) additively (= (Z/19)² as elementary abelian).\n  • Fully (Z/19)²-translation-invariant under additive translations.\n  • L_0 = T[0, ·] and R_0 = T[·, 0] both have cycle structure (1, 36¹⁰) — order 36, 10 cosets of an order-36 subgroup of F_361*.\n  • L_0 is axis-additive on each F_19-axis but NOT globally F_19-linear (only ~10% of cells match a F_19-linear formula).\n\nThis is a 10-coset Tao Type II piecewise-linear construction on F_361, equivalently a Dickson near-field of order 19² with the order-2 Frobenius x ↦ x^19 (since 19 is NOT in the Zassenhaus exceptional list {5, 7, 11, 23, 29, 59}, this is the Dickson family rather than an exceptional one).\n\nThree DB entries (presumably differing in which 10 multipliers are assigned to which cosets of F_361*):\n  • magma#c5c647a9\n  • magma#91224574\n  • magma#f304c339\n\nWhy no simple-linear and no AG(2, 19) line construction: F_19 has |F_19*| = 18 and 10 ∤ 18, so Φ_10 has no roots in F_19 — meaning the per-F_19-line linear operation x ◇ y = (1−α)x + αy does not satisfy Eq 677 for any α ∈ F_19. F_361 itself does have primitive 10th roots (since 10 | 360 = |F_361*|), so simple-linear F_361 magmas could exist, but their L_0 would have order 10 — these magmas have L_0 of order 36, so they are NOT simple-linear F_361. The non-distributive near-field multiplication is required.\n\nDisplay reorders for all 3 entries have been set to the orbit grid (i, j) ↦ τ_1^i τ_2^j(0) using two commuting order-19 fix-free magma automorphisms (the hidden (Z/19)² additive translations); under this reorder each Cayley table is fully (Z/19)²-translation-invariant.\n\n[text written by Claude]"},{"size":961,"comment":"Size 961 = 31² admits several distinct families of Eq 677 magmas. 13 entries are currently in the DB; all satisfy Eq 255.\n\nAll known constructions use one of two carriers:\n  • F_961 = GF(31²) (additive group (Z/31)²) — for the line magmas and the near-field-style magma\n  • A direct product G × M with G abelian — for the Tao G × M fiber bundles\n\nFamily A: AG(2, 31) constant-α line magmas (5 magmas, right-cancellative, idempotent). The 992 = 32 × 31 size-31 sub-magmas are exactly the lines of the affine plane AG(2, 31); every pair of distinct points lies on a unique line. Each line is the F_31 linear magma with parameter α, the same α for ALL 32 parallel classes. Equivalently, the magma is the medial direct product F_31(α) × F_31(α). The 4 valid α-values are the primitive 10th roots of unity mod 31 = roots of Φ_10(x) = x⁴ − x³ + x² − x + 1, namely {15, 23, 27, 29}; all four are present:\n\n  • α = 15: magma#2b8e3c08\n  • α = 23: magma#5f44e78d\n  • α = 27: magma#ba90950a\n  • α = 29: magma#fc322ba7\n\nFamily B: 16-coset Tao-Type-II piecewise on F_961 (1 magma, right-cancellative, idempotent). magma#3c1d2230. Carrier F_961 = GF(31²) additively; the operation x ◇ y = x + f(y − x) has f with cycle structure (1, 60¹⁶) — 16 cosets of an order-60 subgroup of F_961* (which has order 960 = 16 × 60). f is axis-additive over (Z/31)² but NOT globally F_31-linear (a fingerprint of near-field multiplication). Since 31 is not in the Zassenhaus exceptional near-field list {5, 7, 11, 23, 29, 59}, this is presumably a Dickson near-field construction with the order-2 Frobenius. The 2-generated sub-magmas already span all 961 points (no AG(2, 31) line sub-structure here).\n\nFamily C: Tao G × M fiber-bundle constructions (8 magmas, non-right-cancellative, idempotent). All 8 are dwrensha submissions of the form Tao(F_31, β=2) × F_31(ζ, ω) for various (ζ, ω) parameters (ζ ∈ {2, 4, 8, 16}, ω ∈ {5, 25}, giving 8 combinations). An abelian base group acts on a fiber via a 2-cocycle; the resulting magma is non-right-cancellative because the fiber action allows column collapses while preserving left bijectivity. Examples: magma#3259f7fb, magma#ecd0e67d, magma#bbe4461e, magma#1335ae05, magma#85c8462b, magma#7ff29f81, magma#67e60649, magma#896897f8.\n\nThe five Family-A magmas exhaust the constant-α line magmas at size 961 (one per valid α). Non-constant-α AG(2, 31) line magmas (where different parallel classes use different α-values, analogous to many size-121 entries) are NOT yet represented at size 961; by Burnside, the orbit count of α-colorings of 32 parallel classes under PGL(2, 31) would be in the tens of thousands.\n\nDisplay reorders for the four b-reinke entries have been set: Family-A magmas use a 2D AG-coordinate layout (rows = lines of one parallel class C_h, columns = lines of another class C_v), showing clean 31 × 31 block structure; the Family-B magma uses an orbit-of-0 layout under two commuting order-31 fix-free automorphisms (the hidden (Z/31)² additive translations), giving a fully translation-invariant Cayley table.\n\n[text written by Claude]"}]}