What was already known
Linear disk filling characterizes word hyperbolicity, but a geometric CAT(0) realization did not follow. Earlier Brady–Crisp examples excluded actions only on two-dimensional CAT(0) targets; the unrestricted dimension question remained open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Gives a dimension-independent obstruction to geometric CAT(0) realization of a hyperbolic group.
Limitations
The Lean scope does not include the manuscript’s stronger two-dimensional witness or its exclusion of finite locally CAT(0) homotopy models.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note states the finite aspherical linear-filling witness and excludes every proper complete CAT(0) geometric action of its fundamental group.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- There is a finite connected aspherical complex with a linear combinatorial disk-filling bound whose word-hyperbolic fundamental group has no proper cocompact isometric action on any nonempty proper complete CAT(0) space.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision