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 embeds the animation.
Also known as free group factor isomorphism problem; L(F2) isomorphic to L(F3); Murray–von Neumann free group factors
In one line: OpenAI reports a result titled ‘Isomorphism of the free group factors’ (operator algebras) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Free Group Factor Problem: OpenAI Claims L(F2) = L(F3), is on YouTube.
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
An isomorphism of the free group factors
OpenAI's abstract 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.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- 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)
- Where is the proof?
- In the paper, An isomorphism of the free group factors (PDF).
- Is there a video?
- Yes, on YouTube (0:21).
Also in
- Chapter 63 of 84 in Every OpenAI Math Result, Part 4 of 4: L = BPL, Integer Multiplication and 82 More · starts at 21:33 · watch from there on YouTube →
The video
Free Group Factor Problem: OpenAI Claims L(F2) = L(F3) · Short · 0:21 · description, sources and transcript →
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