What was already known
Group algebras over characteristic-zero fields and those of sofic groups were known directly finite. The unrestricted positive-characteristic scalar question remained open; a matrix defect alone would not settle it.
AI involvement
OpenAI attributes the manuscript and Lean artifact to an internal model. No named human checker or explanation of the finite-incidence scalar construction is documented.
The OpenAI-authored release attributes this mathematical construction to an internal model; individual-session autonomy is undocumented.
- Supporting source (github.com) — Scoped original claim, comparison or checking evidence
Importance
The scalar witness negates unrestricted Kaplansky direct finiteness and also yields a nonsurjunctive cellular automaton for the constructed group.
Limitations
The verified scope uses odd-prime torsion and an unspecified finite characteristic-two field. The separate torsion-free companion is paper-only and is outside this Formal assessment. The prescription was proved to terminate but was not executed.
Technical verification
The reported Lean theorem checks the characteristic-two scalar witness for a finitely presented group with odd-prime torsion. The torsion-free October companion has no cited complete check and is outside this rating.
Formal checking
Source-reported Lean proof of the finite-presentation scalar counterexample; the torsion-free strengthening is outside this theorem.
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- Finite characteristic-two field, finitely presented odd-prime-torsion group and scalar ab=1 with ba≠1
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the finite-incidence scalar construction is documented; Few is the evidence default.
Correction and publication history
The scalar one-sided inverse result is distinct from published zero-divisor, odd-characteristic surjunctivity and determinant witnesses.
Read this published revision