The minimal equivariant counterexample to the Jacobian conjecture
Year: 2026
Type: preprint
Abstract: Machine-certified classification of C*-equivariant Keller maps on C3. We prove that Alpöge's degree-7 counterexample to the Jacobian conjecture is degree-minimal within its full equivariant class: every C*-equivariant Keller map of total degree at most 6 for weights (−1,1,2) is a polynomial automorphism. The same rigidity holds through degree 6 for weight systems (−1,1,3) and (−1,1,4). For every k ≥ 2 and weights (−1,1,k) we prove the quotient identity det Dφ = −Ek det JF, machine-checked in Lean 4 uniformly in k, which drives the equivariant degree search across the family. All computations are exact (rational arithmetic). Gröbner-basis certificates (msolve, cross-checked in Singular) accompany the paper.
Author: Austermann, Sloan
Institution: Omni Sciences (United States)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204074399
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