What is recorded here?
The manuscript claims a finitely presented torsion-free group G and elements a,b,c in F2[G] with ab=1, ac=0 and c nonzero. These identities would force ba!=1, disproving direct finiteness in this positive-characteristic setting. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The known characteristic-zero theorem is unchanged. The available family scope note describes other characteristic-two and odd-characteristic constructions, not this selected torsion-free paper; that Lean coverage cannot be transferred to this target. The August nonsofic-group package needs explicit overlap review. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.
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People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed The recorded author list is incomplete.
OpenAI research model · OpenAI · Unreleased internal frontier model; exact identifier not disclosed
Source-reported mathematical argument generation; human preparation/editing roles retained separately where disclosed. Source-reported attribution; provider attestation is unavailable.
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English catalogue narrative
OpenAI: A claimed torsion-free group-algebra counterexample to direct finiteness
The manuscript claims a finitely presented torsion-free group G and elements a,b,c in F2[G] with ab=1, ac=0 and c nonzero. These identities would force ba!=1, disproving direct finiteness in this positive-characteristic setting. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.
Scientific scope
The known characteristic-zero theorem is unchanged. The available family scope note describes other characteristic-two and odd-characteristic constructions, not this selected torsion-free paper; that Lean coverage cannot be transferred to this target. The August nonsofic-group package needs explicit overlap review. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed
OpenAI research model / OpenAI / Unreleased internal frontier model; exact identifier not disclosed: Source-reported mathematical argument generation; human preparation/editing roles retained separately where disclosed (source reported).