Problem detail · source-aware
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Adjamagbo's positive-characteristic refinement of the Jacobian conjecture asks that a polynomial endomorphism with unit Jacobian determinant whose induced function-field extension has degree prime to the characteristic be an automorphism. It is false: an explicit $F: \mathbb{A}_k^3 \to \mathbb{A}_k^3$ over any field of characteristic $2$ has Jacobian determinant identically $1$ and function-field degree $3$, yet is not injective.
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The AI usage section states that the text is the result of a discussion with ChatGPT 5.6 Sol, with conversation transcripts available on request, and that the proof itself was verified as correct by the named author.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The counterexample is a three-line explicit polynomial map; the non-injectivity is witnessed by three distinct source points and the Jacobian determinant is a direct computation, both checkable by hand. Single-author arXiv note, not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
the counterexample to the original Jacobian conjecture does not specialize to characteristic 2; this is a modification that does
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.