A counterexample to Pixton's original completeness conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

A
D
V
E
R
T

I
S
E
M
E
N
T

A counterexample to Pixton's original completeness conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

thinking... about 3 hours remaining

If this game doesn't work on your computer, we can't help you. No Lean version yet. Some unformalized games could have issues!

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	shapes made of equations	Levels:	1
Category:	Algebraic and complex geometry	Lean version:	not yet
Rate this game! 4.8 out of 5 (7,469 votes)

>>> How to Play <<<

A counterexample to Pixton completeness in Chow. 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.

>>> Level Select <<<

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

released 2026-09-24 | 3 theorems · 23 lemmas · 30 proofs · 27,307 words | PLAY LEVEL 1 » (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 $10^{60}$ and $3\binom{10^{60}}3$ markings.

More Algebraic and complex geometry Games!
A stable-coordinate counterexample in four variables	A counterexample to Griffiths' positivity conjecture	Kobayashi's canonical-ampleness conjecture	Tangent-bundle splittings and universal covers
Counterexamples to Kuznetsov's rationality conjecture	Toda's Gepner conjecture and large-volume stability	Termination of fourfold minimal model programs HOT!	Campana's abelianity conjecture and special varieties

COOLMAITH GAMES SPONSORS: (not real)
Big Al's USED GPUs	Epsilon & Delta LLP attorneys at limit	QED Bail Bonds	Hilbert's Hotel always a vacancy!

Cool Links: openai/math Lean Mathlib arXiv the real Coolmath Games

You are visitor number 000719

Thanks for visiting CoolmAIth Games
© 1997-2026 CoolmAIth Games. A parody. Not affiliated with Coolmath.com LLC or OpenAI.
Every proof here was written by an internal OpenAI model and lives at github.com/openai/math.
Best viewed in Netscape Navigator 4.0 at 800x600