Resolves the free group factor isomorphism problem: L(\mathbb F_2)\cong L(\mathbb F_3), and hence all interpolated free group factors, including L(\mathbb F_\infty), are isomorphic. Their common factor has fundamental group \mathbb R_{\gt 0}. (Lean)
Manuscript
An isomorphism of the free group factors
September 23, 2026 · source · cite as \cite{OAI:An-isomorphism-of-the-free-group-factors-September-23-2026}
We solve the free group factor isomorphism problem affirmatively by proving that L(\mathbb F_2) and L(\mathbb F_3) are isomorphic as tracial von Neumann algebras. The classical free group factor alternative then implies that all interpolated free group factors, including L(\mathbb F_\infty), are isomorphic and have fundamental group \mathbb R_{\gt 0}.
Result 287 · Operator algebras. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md