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The construction attributed to Gao using a tangent-sweep method to produce polynomial maps with constant (non-zero) Jacobian determinant that are claimed counterexamples, with arbitrarily large geometric degree, in every dimension greater than two. Claims about the construction, its degree, injectivity, or validity in a given dimension belong here; general Jacobian conjecture claims that do not co

Gao's tangent-sweep construction produces constant-Jacobian counterexamples of arbitrarily large geometric degree in every dimension greater than two

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 →Jacobian conjecture Algebraic geometryimportance · 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 →

Gao's explicit four- and five-dimensional Keller maps F4, F5, F6, F7 have constant Jacobian determinant and generic fiber sizes 5, 10, 6 and 12

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 conjectureimportance · settledImportance 0.20, 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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