cat _posts/2026-09-06-magma-1518-obstruction-lean-theorem-f-explicit-finite-models-refuting-1518-47-614-817-3862.md
magma-1518-obstruction-lean: Theorem F — explicit finite models refuting 1518 ⇒ 47/614/817/3862
magma-1518-obstruction-lean
grew a third result overnight:
Theorem F
builds an explicit parametric family of finite magmas satisfying law 1518 that
violate the four targets 47, 614, 817 and 3862 — the ETP’s known 15-element
countermodels are the family’s two smallest members, which then continues with
27, 39, 51, 75, … elements. A companion classification shows the
base-dependent extensions of the Z/3 shift come in exactly 8 classes for
p ≡ 1 mod 4 and 4 for p ≡ 3 mod 4, with only the family and its conjugate
refuting. The 15- and 39-element members are checked by the Lean kernel via
decide with no axioms, and the classification rests on Gröbner bases over
Q and over every F_p with p ≤ 257.