Algebraic and complex geometry·OpenAI Math·Result 053

A counterexample to Pixton completeness in Chow

One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.

Latest paper

A high-arity counterexample to Pixton completeness in Chow

24 September 2026 · PDF

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What OpenAI claims

Constructs a tautological relation on a moduli space of stable pointed curves that vanishes in rational Chow, hence in rational cohomology, but lies outside Pixton's original relation span. This disproves the Chow and rational-cohomological forms of his original completeness conjecture.

Paper

  1. A high-arity counterexample to Pixton completeness in Chow

    · Preprint, not peer reviewed · PDF

    We disprove the Chow and rational-cohomological forms of Pixton's completeness conjecture for his original relation system. We construct a formal tautological class outside the original Pixton relation span whose image is zero in the Chow ring and in rational cohomology. The example has genus 1060 and 3(1060 choose 3) markings.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.

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