What was already known
Boone and Higman asked for a finitely presented simple overgroup. The published Boone–Higman record concerns that weaker conclusion; this manuscript also uses earlier human embedding theorems.
AI involvement
OpenAI credits its internal model with this manuscript family. The construction uses earlier human embedding theorems as inputs; no human-origin step in the new higher-finiteness argument is documented.
Institutional AI authorship and the release’s production account support AI-led mathematical work; autonomous generation of each lemma is not established.
Importance
Strengthens the Boone–Higman result to higher finiteness for every eligible group.
Limitations
The source-reported Lean theorem matches the stated embedding, but its build and the correspondence of formal definitions to the manuscript were not independently established in the review.
Technical verification
The Lean documentation explicitly states the higher-finiteness strengthening and a comparator for exactly this embedding claim. The formalized statement includes decidable word problem, a nontrivial simple target, type F_infinity and an injective homomorphism.
Formal checking
Formal theorem matched to SimpleOvergroups comparator and scope documentation
- Checker
- Lean 4/mathlib SimpleOvergroups development
- Scope
- Every finitely generated decidable-word-problem group embeds in a nontrivial simple F_infinity group
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The release names no human interpreter of the model’s ring-encoding, homological and stabilizer argument; Few is the evidence default.
Correction and publication history
If correct, strengthens the Boone–Higman result to higher finiteness for every eligible group.
Read this published revision