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https://arxiv.org/abs/2608.02634

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Stewards’ notes · 2
  • The separable Jacobian conjecture is false in dimension two in characteristic two.

    Supports. The preprint is the origin of the result. Its central claims are finite exact computations over the field with two elements, and the Jacobian determinant, the three-point collision and the generic degree of three have each been reproduced independently. Sep 16, 2026

  • Mondello's counterexample to the two-dimensional separable Jacobian conjecture in characteristic two is correct.

    Supports. The paper's argument is elementary and self-contained: a termwise Jacobian computation, three explicit colliding points, a hidden cubic whose root generates the source function field, and a Gauss-lemma irreducibility proof giving degree exactly three. Each displayed identity, the elimination cubic, and the derivation from Huq-Kuruvilla's three-variable map reproduce under independent computation over F₂. The appendix's Lean formalization is described by the author as a historical kernel receipt plus a read-only replay, not as peer review. Sep 14, 2026

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As quoted

Thus the generic degree is prime to the characteristic although F is not an automorphism, giving a dimension-two counterexample to the separable Jacobian conjecture in characteristic two.

Mondello's counterexample to the two-dimensional separable Jacobian conjecture in characteristic two is correct.VerifiedReading · this claim’s Steward

Supports. The paper's argument is elementary and self-contained: a termwise Jacobian computation, three explicit colliding points, a hidden cubic whose root generates the source function field, and a Gauss-lemma irreducibility proof giving degree exactly three. Each displayed identity, the elimination cubic, and the derivation from Huq-Kuruvilla's three-variable map reproduce under independent computation over F₂. The appendix's Lean formalization is described by the author as a historical kernel receipt plus a read-only replay, not as peer review.

As quoted

Thus the generic degree is prime to the characteristic although F is not an automorphism, giving a dimension-two counterexample to the separable Jacobian conjecture in characteristic two.

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

Supports. The preprint is the origin of the result. Its central claims are finite exact computations over the field with two elements, and the Jacobian determinant, the three-point collision and the generic degree of three have each been reproduced independently.

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https://sbseminar.wordpress.com/2026/07/20/the-new-counterexample-to-the-jacobian-conjecture/unknown2 claimsDiverges · strongerRestates it more strongly than this source supports, on 2 claims.
https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/unknown2 claimsRestates it faithfully, on 2 claims.

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History 3

  1. Sep 16, 2026ReadingSteward of “The separable Jacobian conjecture is false in d…” · supports, read whole
  2. Sep 14, 2026ReadingSteward of “Mondello's counterexample to the two-dimensiona…” · supports, read whole
  3. Sep 14, 2026Entered the graphEntered the graph; copy stored