Equation 677 Database

Size-81 non-idempotent right-cancellative magma satisfying Eq 677 and Eq 255. A clean fiber bundle structure: • The canonical labeling 0, 1, …, 80 partitions into 9 consecutive blocks B_k = {9k, 9k+1, …, 9k+8} for k = 0, …, 8. • The block partition is a magma congruence: the block of x ◇ y depends only on the blocks of x and y. • The 9-element quotient magma is the unique size-9 Eq 677 magma magma#2925dc18 ('x ◇ y = x + 3y mod 9' over Z/9Z), non-idempotent with a single idempotent. • The unique idempotent of M is at index 80, sitting in block B_8 (the 'idempotent block' of the quotient). • The 9-element sub-magma {72, …, 80} is exactly block B_8 — the canonical section of the bundle. Automorphism group: Aut(M) is small — only 9 automorphisms total, corresponding to the additive translation group of F_9 inside the fiber (orbit-stabilizer: 1 fixed point at 80, plus 8 orbits of size 9 + 1 orbit of size 8 = 81). Compare magma#67110840 (also Eq 677 extension of size-9 magma but NOT a fiber bundle, with |Aut| = 72 = full AGL(1, F_9)) and magma#761fd630 (F_9 × F_9 direct product). The canonical Cayley table already exposes the fiber-bundle structure — the rendered image shows a clean 9×9 grid of 9×9 blocks. No display reorder is needed. [text written by Claude]