Operator algebras·OpenAI Math·Result 287·Lean formalisation listed

Isomorphism of the free group factors

One of the 372 results in OpenAI's public mathematics catalogue, filed under operator algebras: 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

An isomorphism of the free group factors

23 September 2026 · PDF

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What OpenAI claims

Resolves the free group factor isomorphism problem: L(𝔽2) ≅ L(𝔽3), and hence all interpolated free group factors, including L(𝔽∞), are isomorphic. Their common factor has fundamental group ℝ> 0. (Lean)

Paper

  1. An isomorphism of the free group factors

    · Preprint, not peer reviewed · PDF

    We solve the free group factor isomorphism problem affirmatively by proving that L(𝔽2) and L(𝔽3) are isomorphic as tracial von Neumann algebras. The classical free group factor alternative then implies that all interpolated free group factors, including L(𝔽∞), are isomorphic and have fundamental group ℝ> 0.

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.

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