lean artifact · pending
Artifact ↗Source authenticated
Is there an infinite finitely presented simple amenable group?
Theorem 1.1: there exists an infinite finitely presented simple amenable group. It is an alternating subgroup of a polygon exchange group (piecewise translations of finitely many squares over a real quadratic ring, with two inclined edge directions besides the coordinate ones). Finite presentation comes from propagating relations over a fixed finite generating set with a homological argument in the style of Szymik-Wahl; amenability from correlated random polygonal partitions giving almost-invariant measures. No explicit bound on the sizes of the generating set or relators 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: Is there an infinite finitely presented simple amenable group? · Finitely presented simple amenable group
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
Compute record
No linked compute attempts recorded.
Lineage and corrections
Lean: OAI/GroupTheory/SimpleAmenable/Main.lean (main) evidence for this event
VibeMathed record: Is there an infinite finitely presented simple amenable group? evidence for this event
Zaremsky, Some open problems (July 2026), Problem 10 evidence for this event
This event attributed to Unreleased internal OpenAI model
Is there an infinite finitely presented simple amenable group? evidence for this event
Button, Largeness of LERF and 1-relator groups (GGD 2010), where the question is recorded evidence for this event
Is there an infinite finitely presented simple amenable group? parent of this event
Theorem 1.1: there exists an infinite finitely presented simple amenable group. It is an alternating subgroup of a polygon exchange group (piecewise translations of finitely many squares over a real quadratic ring, with two inclined edge directions besides the coordinate ones). Finite presentation comes from propagating relations over a fixed finite generating set with a homological argument in the style of Szymik-Wahl; amenability from correlated random polygonal partitions giving almost-invariant measures. No explicit bound on the sizes of the generating set or relators is given. parent of this event
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