Size-63 (= 9 × 7) right-cancellative fiber bundle: F_9(3,7) base × F_7(4,3) fiber, in the "twisted" Family B variant. The 63 elements partition into 9 fibers of 7 (a non-trivial congruence with F_9 quotient over the extension field F_9 = F_3²), but only ONE fiber is itself a sub-magma — the fiber at the F_9-idempotent coset, isomorphic to F_7(4,3). The other 8 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent. The database contains 3 inequivalent (non-isomorphic) Family B twists with this same F_9(3,7) × F_7(4,3) skeleton: e8303565, aa98186d, and a24a85fe — they share the same fiber-bundle structure but differ by non-trivial cocycle twists across fibers.
dwrensha · 2026-04-29 15:45:54
Size-63 (= 9 × 7) right-cancellative fiber bundle: F_9(3, 7) base × F_7(4, 3) fiber, in the "twisted" Family B variant. The 63 elements partition into 9 fibers of 7 (a non-trivial congruence with F_9 quotient over the extension field F_9 = F_3²), but only ONE fiber is itself a sub-magma — the fiber at the F_9-idempotent coset, isomorphic to F_7(4, 3). The other 8 fibers are non-closed congruence classes. Quasigroup (LC + RC) with a unique idempotent.
dwrensha · 2026-04-29 15:47:03
dwrensha · 2026-04-29 15:45:54