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 embeds the animation.
In one line: OpenAI reports a counterexample to Pixton completeness in Chow (algebraic and complex geometry) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More, is on YouTube.
Chapter 74 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 25:29 · watch from there on YouTube →
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
A high-arity counterexample to Pixton completeness in Chow
OpenAI's 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 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.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- 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.
- Where is the proof?
- In the paper, A high-arity counterexample to Pixton completeness in Chow (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 74).
Also in
- Chapter 9 of 9 in Shafarevich Conjecture, Zariski's Cancellation Problem and 7 More · starts at 2:49 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · Compilation · 29:20 · chapter 74 from 25:29 · description, sources and chapters →
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