CATALOGUE 287
All nonabelian free group factors are isomorphic
This single-paper catalogue follows the construction of small perturbations of free Haar generators and a generating limit, then the amplification step yielding $L(\mathbb F_2)\cong L(\mathbb F_3)$. It also covers the consequences for countably infinite rank, fundamental groups, and the dependence of free entropy dimensions on generators.
1. Paper in this catalogue
These summaries give the principal scope; consult the cited original results for the complete hypotheses and statements.
Page counts include references. On narrow screens, scroll the table sideways.
| # | Manuscript and overview | Principal claim | Role and available overview |
|---|---|---|---|
| 01 | An isomorphism of the free group factors →Short name: An isomorphism of the free group factorsSeptember 23, 2026 · 23 pagesOriginal paper (GitHub) ↗ | Consecutive ranks n≥3, ranks two and three, and all interpolated parameters 1<r≤∞ are isomorphic. Fundamental groups are R>0; four free entropy dimensions depend on generators. Theorems 1.1–1.2 · pp. 1–2; Corollaries 6.1, 7.1 · pp. 21–22 ↗ | Small cocycle → tracial flow → generating limit with adaptive error budgets; followed by amplification, dichotomy, and transport of tuples. Bilingual account and self-check prepared. Read the proof overview → |
2. External inputs
The passage to rank two uses Dykema's amplification formula; inclusion of the infinite parameter uses the classical dichotomy. For entropy dimensions, semicircular tuples and algebraic group-algebra generators are transported separately. The article's inputs and applications distinguish statement-and-application checks from complete proof verification.
3. Sources and checking scope
The official overview title is All nonabelian free group factors are isomorphic; CONTENTS uses Isomorphism of the free group factors. Entry 287 belongs to Operator algebras and appears on overview print/PDF p.31. The source commit is 1581d4cbdd69a0faf34b2089614fe2a814316a6a; the included manuscript is by OpenAI, dated September 23, 2026, and has 23 pages.
OpenAI Research Catalog · Catalogue 287, Operator algebras · p. 31
The author of this account read the central passages of §§2–7 and performed a self-check, not an independent review. Complete proofs of external inputs and further dependencies were not verified. Rădulescu's dichotomy was checked through Goldbring–Pi's explicit restatement; the Brannan et al. input was checked in author preprint v2 §5. See the source reading guide and unresolved scope.