The Alpöge–Fable counterexample to the Jacobian Conjecture: verification, geometry, dynamics, and an equivariant program for the plane case

Independent exact-arithmetic verification of the July 19, 2026 counterexample to the Jacobian Conjecture announced by L. Alpöge (with Claude Fable), together with new results: a cubic resolvent proving geometric degree 3; the exact image ℂ³∖M and its stability under iteration; the identity disc = −(54a)²·D linking the fiber discriminant to the Jelonek quartic, giving full S₃ monodromy; a two-region description of the real form; the degree sequence 7, 43, 265, 1633, 10063, 62011 of iterates suggesting dynamical degree 3+√10; an explicit injective non-surjective endomorphism of the Weyl algebra A₃; and an unconditional no-go theorem for the first class of a mirror-equivariant approach to the still-open two-dimensional case. All claims reproducible via the included scripts. Not peer-reviewed.

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