Twisted fiber bundle of shape 5 x 7 (intermediate-twist variant).
Same skeleton as magma#c689a91b and magma#26eaf655: 35 elements partition into 5 disjoint size-7 sub-magmas via a congruence. Quotient is the unique size-5 Eq 677 magma magma#e549b5f8 (affine F_5 line). Each fiber is isomorphic to magma#7981e2df, the size-7 magma with exactly 1 idempotent; the 5 global idempotents 30..34 are the fiber-idempotents, one per fiber. No size-5 sub-magma anywhere (non-split bundle).
In the suggested reorder, the 35 elements are arranged as five consecutive 7-blocks (positions 0..6, 7..13, 14..20, 21..27, 28..34), one per fiber, with each block's idempotent at position 6.
Twist class is intermediate between magma#c689a91b and magma#26eaf655. Classifying off-diagonal fiber slice ops (residue table p1,p2 -> (x*y) mod 7 for fixed fiber pair (f1,f2)):
- 11 distinct slice ops total
- 5 diagonal pairs share one op (the common fiber operation)
- All 20 off-diagonal slice ops occur in 10 pairs of 2: each pair of base-pairs shares a slice op
The pairing of base-pairs:
(0,1)~(0,2) (0,3)~(0,4) (1,0)~(2,0) (1,2)~(2,1)
(1,3)~(2,4) (1,4)~(2,3) (3,0)~(4,0) (3,1)~(4,2)
(3,2)~(4,1) (3,4)~(4,3)
This pairing is induced by the involution on fibers (1<->2, 3<->4, fiber 0 fixed), which is a genuine automorphism of M.
|Aut(M)| = 2. Aut orbits: 7 singletons (the 7 elements of fiber 0 -- this fiber is pointwise-fixed by the involution) + 14 size-2 orbits (the involution pairs corresponding elements across fibers 1<->2 and across 3<->4).
Comparison across the size-35 1+3+3+4+12+12 family seen so far:
magma#c689a91b: 4 slice ops, |Aut| = 4 (most symmetric twist)
this magma: 11 slice ops, |Aut| = 2 (one involution)
magma#26eaf655: 21 slice ops, |Aut| = 1 (fully scrambled twist)
[text written by Claude]
dwrensha · 2026-04-29 13:47:24
R_0 cycles 1+3+3+4+12+12 (size 35 sporadic family). Size-35 sporadic non-product magma identified by its uniform R_x cycle pattern.
dwrensha · 2026-04-29 13:31:07
R_0 cycles 1+3+3+4+12+12 (size 35 sporadic family). Size-35 sporadic non-product magma; right-multiplication has uniform cycle pattern (1,3,3,4,12,12) characteristic of this family.
dwrensha · 2026-05-15 12:05:19
dwrensha · 2026-04-29 13:47:24
dwrensha · 2026-04-29 13:31:07