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4 claims

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

An internal OpenAI Codex model independently rediscovered the 2026 Jacobian conjecture counterexample.

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 →Jacobian conjecture AI mathematical discovery OpenAIimportance · minorImportance 0.30, 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 →

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 claim traces to reliable primary sources through a clear chain of evidence.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 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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