lean artifact · pending
Artifact ↗Source authenticated
Simple overgroups of type F-infinity for groups with solvable word problem (higher-finiteness Boone-Higman)
Theorem 1.1: every finitely generated group with decidable word problem embeds in a nontrivial simple group of type ; with the classical converse, these are exactly the finitely generated subgroups of simple groups of type . This implies the Boone-Higman conjecture. The classifying space may be infinite-dimensional; no torsion-freeness, finite cohomological dimension or type is claimed.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Simple overgroups of type F-infinity for groups with solvable word problem (higher-finiteness Boone-Higman) · Simple F-infinity overgroups
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Belk-Bleak-Matucci-Zaremsky, Progress around the Boone-Higman conjecture evidence for this event
This event attributed to Unreleased internal OpenAI model
Companion: Simple F-infinity overgroups of groups with decidable word problem evidence for this event
Theorem 1.1: every finitely generated group with decidable word problem embeds in a nontrivial simple group of type ; with the classical converse, these are exactly the finitely generated subgroups of simple groups of type . This implies the Boone-Higman conjecture. The classifying space may be infinite-dimensional; no torsion-freeness, finite cohomological dimension or type is claimed. parent of this event
Comparator statement: SimpleOvergroups.lean evidence for this event
VibeMathed record: Simple overgroups of type F-infinity for groups with solvable word problem (higher-finiteness Boone-Higman) evidence for this event
Lean proof (OAI.SimpleFInftyOvergroups.main) evidence for this event
Simple overgroups of type F-infinity for groups with solvable word problem (higher-finiteness Boone-Higman) parent of this event
The Boone-Higman conjecture: groups with solvable word problem embed in finitely presented simple groups evidence for this event
Act on this frontier