lean artifact · pending
Artifact ↗Source authenticated
The CAT(0) conjecture for Artin groups
Theorem 1.1: there is an explicit Artin matrix on 116 generators, with off-diagonal labels in , whose Artin group admits no proper cocompact isometric action on any nonempty proper CAT(0) space, in any dimension. The group contains the triangle Artin group with three braid relations, extended by three 40-strand braid blocks and two commuting generators making a simultaneous centralizer; stable translation lengths force six Euclidean sectors of angle less than around a cycle, which a winding-number argument rules out. It does not decide which Artin groups are CAT(0).
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: The CAT(0) conjecture for Artin groups · CAT(0) conjecture for Artin 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
Compute record
No linked compute attempts recorded.
Lineage and corrections
Charney, Problems related to Artin groups (Problem 1) evidence for this event
This event attributed to Unreleased internal OpenAI model
The CAT(0) conjecture for Artin groups parent of this event
VibeMathed record: The CAT(0) conjecture for Artin groups evidence for this event
Lean Comparator challenge ArtinCAT0 (OpenAI math release) evidence for this event
Theorem 1.1: there is an explicit Artin matrix on 116 generators, with off-diagonal labels in , whose Artin group admits no proper cocompact isometric action on any nonempty proper CAT(0) space, in any dimension. The group contains the triangle Artin group with three braid relations, extended by three 40-strand braid blocks and two commuting generators making a simultaneous centralizer; stable translation lengths force six Euclidean sectors of angle less than around a cycle, which a winding-number argument rules out. It does not decide which Artin groups are CAT(0). parent of this event
The CAT(0) conjecture for Artin groups evidence for this event
Haettel 2022, XXL type Artin groups are CAT(0) evidence for this event
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