Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Every polynomial map $\mathbb{C}^n \to \mathbb{C}^n$ with constant nonzero Jacobian determinant is invertible, with a polynomial inverse.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
Alpöge used Fable 5 as a research collaborator to hunt down an explicit counterexample map in three variables, rather than running a generic formal-proof search. The two-variable (plane) case of the conjecture remains open.
Provider: Anthropic · Prompt public: unknown · Independence: unknown
The counterexample is hand-checkable by direct substitution and was independently confirmed by outside mathematicians within hours of posting. Briefly caught in a Wikipedia edit war over whether to record it. No formal peer-reviewed publication yet.
Correctness: supported · statement fidelity: unaudited · peer review: none
n ≥ 3; plane case open
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.