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Ten Advances in Mathematics and Theoretical Computer Science

OpenAI

OpenAI gives a finitely presented group that lacks finite permutation approximations, establishing the existence of non-sofic groups. Its construction combines a Kun–Thom criterion with an expander-matching argument involving binary Leavitt algebra and Thompson’s group V.

Sources for this record

What was already known

Whether any countable non-sofic group existed was open. Kun and Kun–Thom supplied earlier ingredients; later authors used the criterion for different non-sofic families.

AI involvement AI-led

OpenAI attributes the construction and Lean formalization to Astra. Human staff chose the problem and prepared the manuscript; later mathematicians studied and reused parts of its criterion.

OpenAI’s original disclosure assigns the argument and subsequent Lean formalization to Astra; human manuscript preparation is separately credited.

Importance Major

The explicit witness answers a central existence question in group theory.

Limitations

The project reports a Lean certificate for the finite-presentation and non-soficity claim. Human reviews noted convention and parameter bookkeeping issues and did not document a complete independent proof check.

Technical verification Formal (Lean 4.32.0 with Mathlib and Comparator + human)

The project reports a complete Lean certificate for the stated formal theorem. Human assessments have narrower scope; semantic matching and any manuscript gaps remain separately noted.

Independent checking

chapter-specific mathematical review of the published argument, with the limited coverage summarized in the audit

Checker
Chapter 3 human reviewers in the Sienicki et al. review corpus
Scope
non-sofic construction conventions and auxiliary-parameter hierarchy
Basis
Reported by the linked checker
Evidence source

Formal checking

Lean 4.32.0 formal certificate in NonSoficGroup.lean; comparator target for SoficGroups.SourceTopLevelCompressionFinal.exists_finitelyPresented_nonsofic_group; manifest reports zero sorry and only standard axioms

Checker
OpenAI ten-proofs project, Lean kernel and Comparator configuration
Scope
finitely presented non-sofic group
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Full

Fournier-Facio and Kun–Thom engage with and reuse the proof criterion, supporting human understanding of its expander-matching mechanism; this is not a complete check of the original manuscript.

Correction and publication history