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3 claims

Vitushkin's 1999 construction of rational functions (in the analytic capacity / removable sets setting), treated as a precedent. Claims about the construction itself, or that other constructions — e.g. putative Jacobian conjecture counterexamples — derive from, parallel, or generalize it, belong here; general analytic capacity or rational approximation claims do not.

The 2026 Jacobian conjecture counterexample closely parallels Vitushkin's 1999 rational construction lifted to three dimensions

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 →Jacobian conjecture Algebraic geometry Alpöge's ℂ³ mapimportance · 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 →

Vitushkin's construction method faces an obstruction in two dimensions that the three-dimensional polynomial counterexample circumvents

SupportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Algebraic geometry Jacobian conjecture Alpöge's ℂ³ mapimportance · 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 →

Vitushkin's 1999 paper constructs a non-injective rational self-map of C² with constant nonzero Jacobian

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 0.15, 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 →

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