Source authenticated

Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra?

Claims a negative answer for $\delta$ , $\delta_0$ , $\delta^*$ and $\delta^\star$ : each takes every integer value $n\ge2$ on finite self-adjoint generating tuples of the single factor $L(\mathbb F_2)$ , obtained by transporting semicircular and group-algebra tuples through the new isomorphisms. It does not compute free entropy dimension for other algebras or address the microstates-free equality questions.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. 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: Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra? · Invariance of free entropy dimension

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra?

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Corollary (dependence on von Neumann generators) of the TeX source read against Voiculescu's question; for every $n\ge2$ it gives generating tuples of $L(\mathbb F_2)$ with $\delta=\delta_0=n$ and others with $\delta^*=\delta^\star=n$ , a negative answer for all four dimensions. It is a short transport argument that depends entirely on the unrefereed isomorphism theorem. The Lean comparator for the family does not state this corollary.

Source ↗

The free group factor isomorphism problem

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Voiculescu, Free entropy (2002)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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A second route via the generator problem (OpenAI math release)

paper · pending

paper link supplied by the VibeMathed registry.

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Lineage and corrections

A second route via the generator problem (OpenAI math release) evidence for this event

This event attributed to Unreleased internal OpenAI model

Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra? parent of this event

Voiculescu, Free entropy (2002) evidence for this event

VibeMathed record: Voiculescu's question: is free entropy dimension an invariant of the generated von Neumann algebra? evidence for this event

The free group factor isomorphism problem evidence for this event

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