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CAT(0) action counterexample library
Family 257: A hyperbolic group without a geometric CAT(0) action. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Record a hyperbolic group with a finite classifying space that lacks a proper cocompact action on any proper complete CAT(0) space.
Applicability and commercial boundary
Hyperbolicity does not automatically imply this action property; the example does not invalidate restricted CAT(0) algorithms.
Initial business decision
Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.
Next verification action
Extract the presentation and exact obstruction.
Evidence scope
The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.