{"id":"openai-math/A-counterexample-to-Naimarks-problem-in-ZFC","pdf":"https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026/naimark-counterexample-zfc.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-counterexample-to-Naimarks-problem-in-ZFC-September-24-2026","tags":["operator-algebras","c-star-algebras","representation-theory","set-theory"],"score":0,"title":"A counterexample to Naimark's problem in ZFC","domain":"Operator algebras","family":"297","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We construct in ZFC a unital infinite-dimensional simple complex C ∗ -algebra with a faithful tracial state whose nonzero irreducible representations are all unitarily equivalent. This gives a negative answer to Naimark's problem without additional set-theoretic assumptions.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://mathoverflow.net/a/515860","date":"2026-10-08","kind":"web","site":"mathoverflow.net","text":"Maybe one of the less earth-shaking results, but close to my heart: \"297. A ZFC counterexample to Naimark's problem \". It's been known since 2004 that the existence of a counterexample is consistent with ZFC, and I think it's probably fair to say that the conventional wisdom was that a positive…","added":"2026-10-24","title":"Answer to: Which of the results released by OpenAI went against the conventional mathematical wisdom?","author":"Nik Weaver"}],"formalized":false,"family_title":"A ZFC counterexample to Naimark's problem"}