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https://arxiv.org/abs/2607.20968

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The separable Jacobian conjecture is false in dimension three in characteristic two.
Supports. The six-page paper carries a complete elementary proof. The Jacobian matrix is written out and its determinant is 1 because squares have zero derivative in characteristic two; three explicit points over the prime field collide; and a cubic UT³+T²+VT+W in the target coordinates factors over the source field as a linear times a quadratic with resultant 1, which yields a root generating the whole source field and, by Gauss's lemma, degree exactly three. Every identity reproduces under independent computer algebra over F₂. The author states the text arose from a conversation with a language model and that the proof was verified by the named author; the remark that no other counterexample was known is contradicted by earlier informal constructions that Speyer credits to Chow and N8Programs, but that historical point does not touch the mathematics. Sep 14, 2026

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Since $2\neq 3$, this gives a counterexample to the usual Adjamagbo, or separable, formulation of the Jacobian conjecture in characteristic $2$.

The separable Jacobian conjecture is false in dimension three in characteristic two.VerifiedReading · this claim’s Steward

Supports. The six-page paper carries a complete elementary proof. The Jacobian matrix is written out and its determinant is 1 because squares have zero derivative in characteristic two; three explicit points over the prime field collide; and a cubic UT³+T²+VT+W in the target coordinates factors over the source field as a linear times a quadratic with resultant 1, which yields a root generating the whole source field and, by Gauss's lemma, degree exactly three. Every identity reproduces under independent computer algebra over F₂. The author states the text arose from a conversation with a language model and that the proof was verified by the named author; the remark that no other counterexample was known is contradicted by earlier informal constructions that Speyer credits to Chow and N8Programs, but that historical point does not touch the mathematics.

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https://sbseminar.wordpress.com/2026/07/20/the-new-counterexample-to-the-jacobian-conjecture/unknown1 claimRestates it faithfully, on 1 claim.

https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/unknown1 claimRestates it faithfully, on 1 claim.

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Link: https://arxiv.org/abs/2607.20968
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Sep 14, 2026ReadingSteward of “The separable Jacobian conjecture is false in d…” · supports, read whole
Sep 14, 2026Entered the graphEntered the graph; copy stored