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Artifact ↗Source authenticated
Are all word-hyperbolic groups residually finite?
Theorem 1.1: there is a torsion-free word-hyperbolic group , the fundamental group of a finite Euclidean triangle complex, that is not residually finite; one member of a fixed finite family of nontrivial elements lies in the finite residual, without identifying which. Corollary 1.2: every finite-dimensional representation of over every commutative field kills the finite residual, so is linear over no field. With Kapovich-Wise this gives a nontrivial hyperbolic group with no nontrivial finite quotient and a hyperbolic group that is not virtually torsion-free (curator's reading of the paper's stated consequences). It says nothing about skew fields or infinite-dimensional representations, and does not settle whether all hyperbolic groups are sofic.
Exact FrontierDelta
Prior state unknown→disproved
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: Are all word-hyperbolic groups residually finite? · Residual finiteness of hyperbolic groups
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
Comparator statement: TorsionFreeHyperbolic.lean evidence for this event
Lean proof (OAI.Release075.main) evidence for this event
This event attributed to Unreleased internal OpenAI model
Are all word-hyperbolic groups residually finite? evidence for this event
Are all word-hyperbolic groups residually finite? parent of this event
Theorem 1.1: there is a torsion-free word-hyperbolic group , the fundamental group of a finite Euclidean triangle complex, that is not residually finite; one member of a fixed finite family of nontrivial elements lies in the finite residual, without identifying which. Corollary 1.2: every finite-dimensional representation of over every commutative field kills the finite residual, so is linear over no field. With Kapovich-Wise this gives a nontrivial hyperbolic group with no nontrivial finite quotient and a hyperbolic group that is not virtually torsion-free (curator's reading of the paper's stated consequences). It says nothing about skew fields or infinite-dimensional representations, and does not settle whether all hyperbolic groups are sofic. parent of this event
VibeMathed record: Are all word-hyperbolic groups residually finite? evidence for this event
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