What was already known
Brown, Ozawa and Pestov posed forms of the question of an infinite simple property-(T) hyperlinear or sofic group. The cited sources and a bounded priority search found no earlier witness.
AI involvement
Claude agents developed the Toeplitz crossed-product witness, prose argument and Lean formalization under Sauers’s direction. Agent review does not count as human checking.
The cited repository explicitly traces the retained witness and its proof to Claude agent work under the user's direction.
- Supporting source (github.com) — Pestov91 result and group construction section
Importance
Provides one explicit witness to the sofic and hyperlinear forms of a longstanding group-theory question.
Limitations
The witness is not claimed to be finitely presented. The reported machine checks cover the project’s formal definitions and one witness; no human expert proof review is documented, and the priority search is bounded.
Technical verification
The project reports Comparator matching, Lean kernel acceptance, NanoDa replay and standard-axiom closure for both existential declarations. The checks apply to its formal definitions of property (T), soficity and hyperlinearity and one Toeplitz witness; the historical priority search remains bounded.
Formal checking
statement/definition comparison, kernel proof checking, independent exported-proof replay and axiom audit. Pestov91.exists_infinite_simple_propertyT_hyperlinear and Pestov91.exists_infinite_simple_propertyT_sofic for the pinned Toeplitz witness
- Checker
- Palomar Comparator, Lean kernel and NanoDa
- Scope
- A group built as EL₃(LC(X,F₂)⋊ℤ), with X a binary Toeplitz subshift, is infinite and simple, has Kazhdan property (T), and is locally embeddable into finite groups. It is therefore sofic and hyperlinear. The Lean project compares two existential statements using this same witness.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The cited source credits the mathematical argument and exposition to Claude and reports no human expert explanation of the central witness. Few is the missing-evidence default, not a finding that Sauers cannot understand it.
Correction and publication history
The sofic and hyperlinear statements use the same Toeplitz witness and are assessed together.
Read this published revision