∑math20

Algebraic and complex geometry · Result 053

A counterexample to Pixton completeness in Chow

1 paper

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.

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Papers 1

First page of A high-arity counterexample to Pixton completeness in Chow

A high-arity counterexample to Pixton completeness in Chow

OpenAI · September 24, 2026

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 \(10^{60}\) and \(3\binom{10^{60}}3\) markings.

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@misc{OAI:A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026,
  author = {{OpenAI}},
  title = {{A high-arity counterexample to Pixton completeness in Chow}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026/paper.pdf}{OAI:A-high-arity-counterexample-to-Pixton-completeness-in-Chow-September-24-2026}},
  year = {2026}
}

Formal verification

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