trailThe 2026 Jacobian conjecture counterexample introduces no essentially new techniques beyond Vitushkin's 1999 work
Vitushkin lineage· for
Vitushkin's 1999 paper constructs a non-injective rational self-map of C² with constant nonzero Jacobian
atomic
The 2026 Jacobian conjecture counterexample closely parallels Vitushkin's 1999 rational construction lifted to three dimensions
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
The polynomial step· against
Vitushkin's construction method faces an obstruction in two dimensions that the three-dimensional polynomial counterexample circumvents
Every polynomial Keller map of the complex plane that is equivariant for a nontrivial multiplicative-group action is a polynomial automorphism
The 2026 three-dimensional Jacobian conjecture counterexample is homogeneous for a mixed-sign integer grading of its coordinates
assumed
A counterexample to the Jacobian conjecture in three variables was announced in July 2026 and independently verified
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The 2026 Jacobian conjecture counterexample introduces no essentially new techniques beyond Vitushkin's 1999 work
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