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The Generalized Vanishing Conjecture

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generalized-vanishing-conjecture-five-variablesAlgebraposed by Wenhua Zhao, 2007recorded: disproved

1 attempt · no person has looked

Statement

Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, Λm(Pm)=0\Lambda^m(P^m) = 0 for all large mm forces Λm(PmQ)=0\Lambda^m(P^m Q) = 0 for all large mm. Refuted by an explicit five-variable counterexample.

Context

A named 2007 conjecture in the Mathieu and Jacobian conjecture circle, where a positive answer had been pursued as a route to the Jacobian conjecture itself.

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  • #1

    Attempt 1

    constructionGPT-5.6 Sol with Alexander Dvorsky ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    GPT-5.6 Sol
    people
    Alexander Dvorsky

    Used "as an interactive research assistant": the paper credits it with testing the homogenized five-variable construction, generating computational verification code and locating relevant literature, with all computations and references independently verified afterwards. The construction itself is the author's.

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