Claims

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3 results

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.

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

SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.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 0.35, 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 closely parallels Vitushkin's 1999 rational construction lifted to three dimensions

VerifiedThe evidence, examined directly, establishes the claim.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 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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