OpenAI · 287-01 · 2026-09-23 · Operator algebras
An isomorphism of the free group factors
preprints/An-isomorphism-of-the-free-group-factors-September-23-2026
Family 287. All nonabelian free group factors are isomorphic.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Resolves the free group factor isomorphism problem: , and hence all interpolated free group factors, including , are isomorphic. Their common factor has fundamental group .
We solve the free group factor isomorphism problem affirmatively by proving that and are isomorphic as tracial von Neumann algebras. The classical free group factor alternative then implies that all interpolated free group factors, including , are isomorphic and have fundamental group .
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 287: Isomorphism of the free group factors. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.