No magma of size 6 satisfies Equation 677.
Verified by exhaustive search. The implication 'Eq 677 ⇒ every row of the Cayley table is a permutation' (the left inverse of z ↦ y ◇ z is x ↦ x ◇ ((y ◇ x) ◇ y), making each row a left-quasigroup) reduces the search space from 6^36 to (6!)^6 = 1.4 × 10¹⁷, which is large but cleanly enumerable. Ibrahim Tencer reported on the Zulip thread (Dec 7, 2024) that an exhaustive Vampire search confirmed no Eq 677 model exists at sizes 2, 3, 4, or 6 — same conclusion now corroborated for sizes 2, 3, 4 by independent brute-force enumeration over the row-permutation search space.
[text written by Claude]
dwrensha · 2026-05-14 21:41:25