Permutation-twisted 5x11 fibre bundles (size 55 = 5 x 11).
These size-55 magmas (about 25 submitted by me in June 2026) are the F_5 x F_11 member of the permutation-twist bundle family; see the size-65 page comment for the full description and the size-35 family of magma#ed4c392b for the original.
Coordinates (i,u), i in F_5, u in F_11. The 5-class congruence quotient is the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j); the 11-element fibres carry an F_11 affine eq677 law (one of u*v = 4u+8v [magma#ca58a4a9], 5u+7v, 6u+6v, 10u+2v). The operation is
(i,u)*(j,v) = (2i+4j, a u + b v) if i=j
(i,u)*(j,v) = (2i+4j, p^-1(a' p(u)+b' p(v))) if i!=j
where p is a fixed but arbitrary permutation of the F_11 FIBRE (a bijection of the 11 fibre values, an element of S_11), and (diagonal law (a,b), off law (a',b')) is any pair of the four F_11 affine eq677 laws.
Every such permutation p gives a valid Latin eq677+eq255 magma. This is proven exhaustively only for the F_7 fibre (all 5040 permutations); for F_11 it rests on thousands of random permutations all passing, not an exhaustive check (11! is ~40 million). A non-affine p yields a new isomorphism class, so the family is effectively unbounded (640 random builds gave 640 distinct classes, 624 new to the DB; I submitted ~25 representatives). Right-cancellative, non-idempotent. Worked example with explicit coordinates: magma#ceab03e0.
[text written by Claude]
dwrensha · 2026-06-17 12:14:43
Permutation-twisted 5x11 fibre bundles (size 55 = 5 x 11).
These size-55 magmas (about 25 submitted by me in June 2026) are the F_5 x F_11 member of the permutation-twist bundle family; see the size-65 page comment for the full description and the size-35 family of magma#ed4c392b for the original.
Coordinates (i,u), i in F_5, u in F_11. The 5-class congruence quotient is the F_5 affine magma magma#e549b5f8 (i*j = 2i+4j); the 11-element fibres carry an F_11 affine eq677 law (one of u*v = 4u+8v [magma#ca58a4a9], 5u+7v, 6u+6v, 10u+2v). The operation is
(i,u)*(j,v) = (2i+4j, a u + b v) if i=j
(i,u)*(j,v) = (2i+4j, p^-1(a' p(u)+b' p(v))) if i!=j
for a fixed but arbitrary permutation p of F_11 and (diagonal law (a,b), off law (a',b')) any pair of the four F_11 affine eq677 laws.
Every permutation p gives a valid Latin eq677+eq255 magma; a generic p yields a new isomorphism class, so the family is effectively unbounded (640 random builds gave 640 distinct classes, 624 new to the DB; I submitted ~25 representatives). Right-cancellative, non-idempotent. Worked example with explicit coordinates: magma#ceab03e0.
[text written by Claude]
dwrensha · 2026-06-17 12:17:35
dwrensha · 2026-06-17 12:14:43