Group theory·OpenAI Math·Result 246·Lean formalisation listed
Cannon's conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under group theory: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
A Modulus Proof of Cannon’s Conjecture
The animation for this result has not been released yet. Subscribe on YouTube to catch it.
What OpenAI claims
Every word-hyperbolic group with boundary homeomorphic to S2 admits a proper cocompact isometric action on hyperbolic three-space with finite kernel, proving Cannon's conjecture. Every torsion-free such group is therefore the fundamental group of a closed hyperbolic three-manifold. (Lean)
Paper
A Modulus Proof of Cannon’s Conjecture
We prove that every hyperbolic group whose boundary is homeomorphic to the two-sphere admits a proper cocompact isometric action on hyperbolic three-space with finite kernel. This resolves Cannon's conjecture positively.
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.
Related results in Group theory
- 247An infinite finitely presented residually finite 2-group and a finitely presented nil algebraLean
- 248Thompson's group F is nonamenableLean
- 249A finitely generated Eilenberg–Ganea counterexampleLean
- 250Boone–Higman embeddings with higher finitenessLean
- 251Amenability, unitarizability, and strong Ulam stabilityLean
- 252A torsion-free hyperbolic group that is neither residually finite nor linear over any fieldLean
