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Two-Variable Factorial Conjecture

Algebra · posed by Arno van den Essen, David Wright, Wenhua Zhao, 2011 · candidate

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Statement

Let L(xayb)=a! b!\mathcal{L}(x^{a}y^{b})=a!\,b! on C[x,y]\mathbb{C}[x,y]. The Factorial Conjecture asks whether L(fm)=0\mathcal{L}(f^{m})=0 for every m≥1m\geq 1 forces f=0f=0. The homogeneous two-variable case was settled by Liu and Sun; the inhomogeneous problem does not reduce to it, because radial integration couples the homogeneous layers through Gamma factors. A claimed proof settles the full two-variable case affirmatively.

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

  1. proof attempt · #1

    Christopher D. Long, using GPT-5.6 Sol, Claude Opus 5

    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.

    AI involvement
    ai co developed
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    Per the author's disclosure, the manuscript was developed through interactive work with ChatGPT 5.6 Sol, which assisted in proof discovery, organization, symbolic checking, reference verification, adversarial auditing and drafting; Claude Opus 5 contributed the semisimple-projector strategy, the reduction to phase-polynomial moments, and further adversarial audits. The AI systems are not authors and the human author takes full responsibility.

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