ClaimmathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →importance · minorImportance 0.40, 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 →

TopicsAlpöge's ℂ³ map Algebraic geometry Jacobian conjecture

The Alpöge–Fable map F:ℂ³→ℂ³ has Jacobian determinant identically equal to −2.

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Decomposition

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Provenance

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The claim, due to Alpöge and Fable: det Jac F ≡ −2 identically

An Independent Lean 4 Verification of the Alpöge–Fable Counterexampleextraction 0.90

Property of the specific polynomial map F = (P,Q,R).

Isabelle proves that the formal Jacobian entries are the corresponding complex analytic partial derivatives and that the determinant is identically \(-2\).

Formal Verification of an Explicit Counterexample to the Jacobian Conjectureextraction 0.75

Describing the specific verified property of the map's Jacobian.

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Created by extractor · Sep 16, 2026. Every judgment on this page is accompanied by a reasoning trace.