{"id":"openai-math/A-Modulus-Proof-of-Cannons-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Modulus-Proof-of-Cannons-Conjecture-September-23-2026","tags":["geometric-group-theory","hyperbolic-groups","topology"],"score":0,"title":"A Modulus Proof of Cannon’s Conjecture","domain":"Group theory","family":"246","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://proofsandprompts.com/2026/10/08/100-reactions-to-100-solutions/#:~:text=several%20of%20the%20problems%20or%20their%20variations%20were%20ones%20I%20had%20been%20working%20on","date":"2026-10-08","kind":"web","site":"Proofs and Prompts","text":"several of the problems or their variations were ones I had been working on right up until the day before, or were closely related to them. The Cannon conjecture is one example. But my research program around it has never been solely about proving the conjecture. I wanted to understand why it…","added":"2026-11-04","title":"100+ reactions to 100+ solutions","author":"Harry Hyungryul Baik"}],"formalized":false,"family_title":"Cannon's conjecture"}