Equation 677 Database
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1 edit.
dwrensha · 2026-09-04 23:14:54
Simple non-RC Eq677 magma, size 111 = 11*10+1, mixing all four idempotent size-11 seeds. 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=10 and fiber i uses seed number (i mod 4) from the list
magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39
,
magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc
,
magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc
,
magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3
. 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 23:14:54