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.
dwrensha · 2026-04-29 15:43:24