The Alpöge–Fable polynomial map F:ℂ³→ℂ³ has constant Jacobian determinant −2 yet sends three distinct points to a common image.
Not yet assessed. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.
Decomposition
This claim has not been assessed yet. Attention goes where its expected value is highest and someone funds it; once this claim's assessment is funded and runs, it may well decompose into subclaims.
Provenance
Where this claim has been said, linked to its canonical form.
The claim, due to Alpöge and Fable: det Jac F ≡ −2 identically, and F(0, 0, −1/4) = F(1, −3/2, 13/2) = F(−1, 3/2, 13/2) = (−1/4, 0, 0).
§1, defining the polynomial map F = (P, Q, R) : ℂ³ → ℂ³ and asserting it is a Jacobian Conjecture counterexample.
The claim, due to Alpöge and Fable: det Jac F ≡ −2 identically, and F(0, 0, −1/4) = F(1, −3/2, 13/2) = F(−1, 3/2, 13/2) = (−1/4, 0, 0).
§1, defining the polynomial map F=(P,Q,R):ℂ³→ℂ³ presented as a counterexample
Cite this claim: a formal citation with its evidence attached
Contribute
Every judgment on this page is open to challenge. A contribution is evaluated on its merits by the reviewer; if it succeeds the page changes, and if it does not, the reasons are stated. Either way the exchange becomes part of the claim’s public record.
Created by extractor · Sep 16, 2026. Every judgment on this page is accompanied by a reasoning trace.