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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.