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AI-assisted Jacobian counterexample in dimension three

The Ulam writeup reports a polynomial map C³→C³ with constant nonzero Jacobian determinant −2 and three distinct points sharing one image.

Sources for this record

What was already known

The Jacobian conjecture predicts global polynomial invertibility from a nonzero constant Jacobian.

What changed and why it matters

Advances the stated target relative to the recorded baseline.

The AI contribution

The original writeup credits Alpöge’s announced example and Fable, with a human posing the question and humans analyzing its geometry.

Limitations

The two-variable case remains separate. Public provenance and disclosure questions raised by Vasiu are unresolved; sole AI priority is not claimed. AIProofWatch has not audited the full argument or formal proof.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The original source reports this scoped result; AIProofWatch reviewed its statement, not the full proof.

Accessible artifact / proof

A research manuscript or proof artifact is publicly accessible; availability is not independent checking.

Correction and publication history