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The Jacobian Conjecture after the Three-Dimensional Counterexample: Exact Validation, a General Seed Family, the Geometry of Non-Properness, and Two-Dimensional Equivariant Rigidity
On 2026-07-20, Levent Alpöge announced (crediting the language model Claude Fable 5 and a question posed by Akhil) an explicit polynomial map F from C^3 to C^3 with constant Jacobian determinant -2 and a repeated value, refuting the Jacobian conjecture for every N ≥ 3. We report an exact-arithmet
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