Not evaluated
A three-manifold with no conjugate points and no nonpositively curved metric (family 358)
The gist
OpenAI claims a three-manifold without conjugate points and without a nonpositively curved metric, announced on October 6, 2026, in a manuscript dated September 24, 2026.
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-358-three-manifold-no-conjugate-points-no-r1
@misc{discoveria-oai-fam-358-three-manifold-no-conjugate-points-no-r1,
author = {{DiscoverIA}},
title = {A three-manifold with no conjugate points and no nonpositively curved metric (family 358)},
howpublished = {DiscoverIA registry, entry oai-fam-358-three-manifold-no-conjugate-points-no},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-358-three-manifold-no-conjugate-points-no#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript held, such an example would exist in dimension three, which would be an existence result in differential geometry. Conjugate points are a notion tied to geodesics, the locally shortest paths, and the metric is the way of measuring lengths and angles.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, with the mention “review: status: unchecked” in formalization.yaml. No third-party verification has been read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 358.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-Three-Manifold-Without…link only, reading not recorded
- Lean proofgithub.com · 358.mdpage read word for word
- Lean proofgithub.com · ConjugatePoints.leanlink only, reading not recorded
Method
The manuscript “A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric”, dated September 24, 2026, is the only one in family 358. A Comparator statement accompanies it (lean/ComparatorChallenges/ConjugatePoints.lean, described in lean/docs/358.md); the family is present in the sources of formalization.yaml. 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 (Differential geometry)
- In openai/math
- family 358, section “Differential geometry”, 1 manuscript dated Sep 24, 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 352 of 372, by family number
- Not evaluated : Unique tangent flows at the first surface singularity (family 355)
- Not evaluated : Gigli's characterization of Alexandrov curvature (family 356)
- Not evaluated : Bi-Lipschitz coordinates at every regular RCD point (family 357)
- Not evaluated : A three-manifold with no conjugate points and no nonpositively curved metric (family 358)
- Not evaluated : Negative Kähler curvature without bounded holomorphic coordinates (family 359)
- Not evaluated : Villani’s convexity conjecture and regular optimal transport (family 360)
- Not evaluated : Global smoothness for relativistic Vlasov–Maxwell (family 362)
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