lean artifact · pending
Artifact ↗Source authenticated
A universal group of type F-infinity containing every finitely presented group (F-infinity Higman embedding)
Theorem 1.1 constructs one group of type containing every finitely presented group; by Higman's theorem its finitely generated subgroups are exactly the finitely generated recursively presented groups (Corollary 1.2). No word-problem hypothesis is imposed. The classifying space need not be finite-dimensional, so type is not claimed, and is not claimed simple.
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: A universal group of type F-infinity containing every finitely presented group (F-infinity Higman embedding) · Universal group of type F-infinity
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
Companion: A universal group of type F-infinity evidence for this event
This event attributed to Unreleased internal OpenAI model
VibeMathed record: A universal group of type F-infinity containing every finitely presented group (F-infinity Higman embedding) evidence for this event
Fournier-Facio and Zaremsky, Finiteness properties and Higman's rope trick evidence for this event
Lean proof (OAI.UniversalFInfinity.universal_group_of_type_FInfinity) evidence for this event
A universal group of type F-infinity containing every finitely presented group (F-infinity Higman embedding) parent of this event
Comparator statement: UniversalFInfinity.lean evidence for this event
Theorem 1.1 constructs one group of type containing every finitely presented group; by Higman's theorem its finitely generated subgroups are exactly the finitely generated recursively presented groups (Corollary 1.2). No word-problem hypothesis is imposed. The classifying space need not be finite-dimensional, so type is not claimed, and is not claimed simple. parent of this event
Act on this frontier