Not evaluated
A hyperbolic group with no geometric CAT(0) action (family 257)
The gist
OpenAI claims, in an announcement of October 6, 2026, a hyperbolic group with no geometric CAT(0) action.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-257-hyperbolic-group-no-geometric-cat-0-action-r1
@misc{discoveria-oai-fam-257-hyperbolic-group-no-geometric-cat-0-action-r1,
author = {{DiscoverIA}},
title = {A hyperbolic group with no geometric CAT(0) action (family 257)},
howpublished = {DiscoverIA registry, entry oai-fam-257-hyperbolic-group-no-geometric-cat-0-action},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-257-hyperbolic-group-no-geometric-cat-0-action#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript held, being hyperbolic would not be enough for a group to act geometrically on a CAT(0) space. A CAT(0) space is a space whose triangles are at least as thin as in an ordinary flat plane; a geometric action is an action by isometries that is proper and cocompact. A hyperbolic group is a group whose triangles, measured with the distance of the group, are uniformly thin.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by the claimant and marked “review: status: unchecked” in formalization.yaml. No third-party check has been read. It is not known what part of the proof the Lean covers exactly.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 257.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · A-hyperbolic-group-with…link only, reading not recorded
- Lean proofgithub.com · 257.mdpage read word for word
- Lean proofgithub.com · HyperbolicObstruction.leanlink only, reading not recorded
Method
One manuscript, “A hyperbolic group with no geometric CAT(0) action”, dated September 25, 2026. A Comparator statement is described in lean/docs/257.md, with the file lean/ComparatorChallenges/HyperbolicObstruction.lean. The family is present in the `sources` of formalization.yaml; history.md reports no revision. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Group theory)
- In openai/math
- family 257, section “Group theory”, 1 manuscript dated Sep 25, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 251 of 372, by family number
- Not evaluated : Artin's K(π,1) conjecture and CAT(0) obstructions (family 254)
- Not evaluated : Quasi-isometric rigidity of virtually polycyclic groups (family 255)
- Not evaluated : Howie's conjecture on equations over groups (family 256)
- Not evaluated : A hyperbolic group with no geometric CAT(0) action (family 257)
- Not evaluated : Gersten's conjecture for one-relator groups (family 258)
- Not evaluated : A group without fixed price (family 259)
- Not evaluated : Spacetime Penrose inequalities and rigidity (family 260)
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