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The free group factor isomorphism problem

Claims that $L(\mathbb F_2)\cong L(\mathbb F_3)$ , by an explicit iterative construction inside $L(\mathbb F_{n+1})$ of a freely generating Haar $n$ -tuple, built from small trace-preserving automorphisms driven by a polynomial flow. With the classical interpolated-factor dichotomy, all $L(\mathbb F_r)$ , $1<r\le\infty$ , are isomorphic and their fundamental group is $\mathbb R_{>0}$ . It also shows free entropy dimension depends on the generating tuple. It does not identify $L(\mathbb F_2)$ with other non-free group factors.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The free group factor isomorphism problem · Free group factor isomorphism problem

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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VibeMathed record: The free group factor isomorphism problem

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorems 1.1 and 1.2 of the TeX source read against the posed problem; a trace-preserving normal *-isomorphism $L(\mathbb F_n)\cong L(\mathbb F_{n+1})$ for $n\ge3$ , hence $L(\mathbb F_2)\cong L(\mathbb F_3)$ , answering it affirmatively with the Radulescu-Dykema dichotomy. Lean-checked on the release's own Comparator challenge InterpolatedFactors (OAI.FreeGroupFactorMain.Interpolation.allInterpolatedIsomorphic) together with its solution module, both present at the pinned commit; the challenge is not listed in the release's formalization catalogue, the statement was read here but not independently audited, and the development was not rebuilt here.