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https://en.wikipedia.org/wiki/Talk:Jacobian_conjecture

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Vitushkin's construction method faces an obstruction in two dimensions that the three-dimensional polynomial counterexample circumvents
Overstates. The comment rests on two supports of different quality. The preprint it cites does prove that the graded construction cannot yield a polynomial counterexample in the plane and does explain why dimension three is needed, though it never mentions Vitushkin. The further statement that Vitushkin himself observed the central obstruction in 1999 is offered without quotation or page reference, and could not be checked against Vitushkin's paper, whose text was not reachable. Sep 14, 2026

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Inspired by the new counter example, a new preprint explained the key difference for this construction method between the 2D and 3D cases: https://arxiv.org/abs/2607.20210 . However, for 2D, the central obstruction to create counter examples using this method has already been observed in Vitushkin's "Evaluation of the Jacobian of a rational transformation of C^2 and some applications" in 1999. This makes the difference of dimensions very important.

Vitushkin's construction method faces an obstruction in two dimensions that the three-dimensional polynomial counterexample circumventsSupportedReading · this claim’s Steward

Overstates. The comment rests on two supports of different quality. The preprint it cites does prove that the graded construction cannot yield a polynomial counterexample in the plane and does explain why dimension three is needed, though it never mentions Vitushkin. The further statement that Vitushkin himself observed the central obstruction in 1999 is offered without quotation or page reference, and could not be checked against Vitushkin's paper, whose text was not reachable.

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https://arxiv.org/html/2607.20210v2unknown1 claimDiverges · strongerDraws its statement from it more strongly than that document supports, on 1 claim.

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Sep 14, 2026ReadingSteward of “Vitushkin's construction method faces an obstru…” · overstates, read whole
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