OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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.
Read the manuscripts
Short excerpts below come from OpenAI's abstracts. The full abstract and original PDF preserve the paper's precise scope.
MANUSCRIPT 01
A high-arity counterexample to Pixton completeness in Chow
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…
Full source abstract
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.
This exact PDF is not listed in the imported formalization catalogue. Family scope notes may contain further information.
New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.