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.
Manuscript
A high-arity counterexample to Pixton completeness in Chow
September 24, 2026 · source · cite as \cite{OAI:A-high-arity-counterexample-to-Pixton-completeness-in-Chow-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.
Result 053 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md