What was already known
Boone and Higman had characterized decidable word problem using an intermediate simple group inside a finitely presented group; whether the simple overgroup itself could always be finitely presented remained open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the Boone–Higman conjecture by making the simple overgroup finitely presented.
Limitations
This record assesses the equivalence in the first manuscript. The family also contains separate higher-finiteness and universal-group results.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note explicitly covers both directions of the Boone–Higman equivalence.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A finitely generated group has decidable word problem if and only if it embeds in a finitely presented simple group.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision