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The Jacobian-counterexample construction from 2026 involving a compactification in P¹×P² with a ramification divisor and hyperplane preimage. Claims about the construction itself, its compactification, boundary divisors, the geometry of the complement, injectivity or mapping degree, and its validity as a Jacobian conjecture counterexample belong here; general Jacobian conjecture claims that do not

In the 2026 Jacobian-counterexample construction, the complement of the ramification divisor and hyperplane preimage in P¹×P² is isomorphic to affine three-space.

VerifiedThe evidence, examined directly, establishes the claim.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Algebraic geometry Jacobian conjectureimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The 2026 Jacobian conjecture counterexample has been formally verified in a proof assistant

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Formal proof verification Jacobian conjecture Algebraic geometryimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The 2026 three-dimensional Jacobian conjecture counterexample is homogeneous for a mixed-sign integer grading of its coordinates

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Algebraic geometry Jacobian conjectureimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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