Simple non-RC Eq677 magma, size 67 = 11*6+1, with one exceptional diagonal fiber. Recipe (see magma#1c1045d74cc5a6cd35415a2d56a5971c for the k=8 prototype): carrier {e} + F_11 x Z/k, base law i*j = 6i + 6j mod 11; off-diagonal fibers (i != j): (i,s)*(j,t) = (i*j, t) if j-i is a nonzero square mod 11, else (i*j, -s-t mod k). Each diagonal fiber together with e is a copy of a seed 677 magma of size k+1 with e as an idempotent, all copies glued along e. For x,y in distinct fibers all four products of Eq677 stay off-diagonal, so the seeds can be chosen independently per fiber. Here k=6; fiber 0 uses seed magma#7981e2df4cc5c795ad295ab69f55b88db1cecb20c1d1ac4df4d7aa42b92757f1 and the other ten fibers use seed magma#baf8b55c9a489d3c0ce2405b9167b3a08aada73c1917019843910c3cbab0f48d. Verified locally: Eq677 on all instances, simple (each pair (0,b) generates the full congruence), non-RC, not translation-invariant (e is the unique right identity). Constructed by Claude (Fable 5.1) with dwrensha, 2026-09-04.
dwrensha · 2026-09-04 23:14:51