Equation 677 Database

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**. Structure: • 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. • Every pair (x, y) with x, y in the SAME petal generates the full 16-element petal. • 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). • 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. • Each element sits in exactly 1 petal and 20 size-5 sub-magmas. Compare 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. Display 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. [text written by Claude]