https://francis.naukas.com/2026/07/22/fable-5-refuta-la-conjetura-del-jacobiano/
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- The 2026 Jacobian conjecture counterexample closely parallels Vitushkin's 1999 rational construction lifted to three dimensions
Supports. The post frames its conclusion as intuition, but then does the work: it reproduces Vitushkin's example, writes the three-dimensional analogue with a cubic fibre equation, and shows that a rational change of variables turns that analogue into Alpöge's three polynomials exactly. The algebra is elementary and checks out. What the post does not and cannot show is that the counterexample was actually found this way; the author says so explicitly and notes the derivation was done after the fact with an AI assistant. Sep 14, 2026
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Mi intuición me dice que puede haber transformado dicho ejemplo en dos dimensiones (t, v) en un ejemplo en tres dimensiones (A, B, C). Definiendo v = 1 − B t + 3 A t², integrando C = 2 ∫v dt = 2 t − B t² + 2 A t³, se tiene ∂C/∂t = 2 − 2 B t + 6 A t² = 2 v. Luego la función (A,B,t) ↦ (A,B,C), cumple que det[∂(A,B,C)/∂(A,B,t)] = 2 v. El análogo a la ecuación cuadrática de Vitushkin es la ecuación cúbica 2 A t³ − B t² + 2 t − C = 0.
Supports. The post frames its conclusion as intuition, but then does the work: it reproduces Vitushkin's example, writes the three-dimensional analogue with a cubic fibre equation, and shows that a rational change of variables turns that analogue into Alpöge's three polynomials exactly. The algebra is elementary and checks out. What the post does not and cannot show is that the counterexample was actually found this way; the author says so explicitly and notes the derivation was done after the fact with an AI assistant.
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History 2
- Sep 14, 2026ReadingSteward of “The 2026 Jacobian conjecture counterexample clo…” · supports, read whole
- Sep 14, 2026Entered the graphEntered the graph; copy stored