775-element magma on (Z_31 x Z_5) x Z_5: the difference-indexed fibre-5 tower over the order-155 cocycle model magma#b9f3f9a00db96eeb71be02e052d84d7a.
Element encoding: i = 25*x + 5*r + s with x in Z_31, r, s in Z_5 (equivalently i = 5*i155 + s over the base encoding i155 = 5*x + r).
Operation:
((x,r),s) * ((y,t),u) = ((5x - 4y + 1 mod 31,
2r - t + h(y - x) mod 5),
2s - u + h(y - x) mod 5)
with the cocycle h = [1, 1, 4, 3, 0, 1, 3, 0, 0, 1, 2, 3, 1, 2, 0, 2, 1, 1, 2, 1, 1, 3, 0, 4, 4, 4, 2, 0, 1, 1, 1] indexed by (y - x) mod 31; the second fibre uses the lifted cocycle h' = h o pr_1 (it reads only the Z_31 difference of the base).
Invariants (verified exhaustively on the raw table): satisfies Equation 677 at all 775^2 pairs; satisfies Equation 255 at every point; idempotent-free (0 idempotents); rows and columns bijective (left and right cancellative); translation group transitive; diagonal-orbit lengths {50: 775}.
Provenance: melvyn lab, magma-677-255 session 15 (difference-indexed fibre extension probe, self-test T3: the affine tower over M155 passes every FE chain), re-verified exhaustively session 27.
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