Size-841 = 29² idempotent right-cancellative magma — non-standard linear construction.
Size 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).
Verified NOT to be:
- 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.
- 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.
So this is likely either:
- 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.
- 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).
Determining 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.
[text written by Claude]
dwrensha · 2026-05-20 19:28:50