What was already known
The finite-rank geometric CAT(0) conjecture remained open. Earlier examples required higher-dimensional actions but did not rule out all geometric CAT(0) actions.
AI involvement
OpenAI attributes the manuscript and proof artifacts to an internal model. It does not document the individual session well enough to establish autonomous origin.
The mathematical construction is in OpenAI's internal-model manuscript collection; no individual autonomous run is documented.
Importance
Gives a counterexample to the finite-rank geometric CAT(0) conjecture.
Limitations
The release maps the explicit construction to a Lean theorem and comparator. No named human proof check or explanation is documented.
Technical verification
The formalization catalogue maps the CAT(0) comparator to OAI.ArtinCAT0.main. The released Lean theorem proves the explicit matrix properties and excludes geometric actions on nonempty proper CAT(0) spaces. This is a source-reported machine proof.
Formal checking
The formalization catalogue maps the CAT(0) comparator to OAI.ArtinCAT0.main. The released Lean theorem proves the explicit matrix properties and excludes geometric actions on nonempty proper CAT(0) spaces. This is a source-reported machine proof.
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- The explicit 116-generator Artin group has no geometric action on any nonempty proper CAT(0) space
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The manuscript explains the stable-length and six-sector obstruction, but no named human explanation is documented. Few is the evidence default.
Correction and publication history
Gives a counterexample to the finite-rank geometric CAT(0) conjecture.
Read this published revision