lean artifact · pending
Artifact ↗Source authenticated
The Boone-Higman conjecture: groups with solvable word problem embed in finitely presented simple groups
Theorem 1.1: a finitely generated group has decidable word problem if and only if it embeds in a finitely presented simple group. The route is Theorem 1.2: every such group embeds in a finitely presented group with a faithful two-transitive action on a countable set with finitely generated point stabilizers, built as a mapping torus of an affine Steinberg group over finitely presented -algebras, which Zaremsky's criterion for twisted Brin-Thompson groups turns into a finitely presented simple overgroup. The higher-finiteness strengthening is the companion's separate entry; no explicit bound on the size of the presentation is given.
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: The Boone-Higman conjecture: groups with solvable word problem embed in finitely presented simple groups · Boone-Higman conjecture
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
Theorem 1.1: a finitely generated group has decidable word problem if and only if it embeds in a finitely presented simple group. The route is Theorem 1.2: every such group embeds in a finitely presented group with a faithful two-transitive action on a countable set with finitely generated point stabilizers, built as a mapping torus of an affine Steinberg group over finitely presented -algebras, which Zaremsky's criterion for twisted Brin-Thompson groups turns into a finitely presented simple overgroup. The higher-finiteness strengthening is the companion's separate entry; no explicit bound on the size of the presentation is given. parent of this event
The Boone-Higman conjecture: groups with solvable word problem embed in finitely presented simple groups parent of this event
Companion: A universal group of type F-infinity 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
Comparator statement: BooneHigman.lean evidence for this event
Lean proof (OAI.FiniteAlgebraicEnvelopes.main) evidence for this event
The Boone-Higman conjecture: groups with solvable word problem embed in finitely presented simple groups evidence for this event
VibeMathed record: The Boone-Higman conjecture: groups with solvable word problem embed in finitely presented simple groups evidence for this event
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