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The Generalized Vanishing Conjecture

Algebra · posed by Wenhua Zhao, 2007 · disproved

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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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Alexander Dvorsky, using GPT-5.6 Sol

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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    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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