Not evaluated
Gigli's characterization of Alexandrov curvature (family 356)
The gist
On October 6, 2026, OpenAI announced two differential geometry manuscripts on Alexandrov spaces and RCD spaces, from an unreleased internal model.
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-356-giglis-characterization-alexandrov-curvature-r1
@misc{discoveria-oai-fam-356-giglis-characterization-alexandrov-curvature-r1,
author = {{DiscoverIA}},
title = {Gigli's characterization of Alexandrov curvature (family 356)},
howpublished = {DiscoverIA registry, entry oai-fam-356-giglis-characterization-alexandrov-curvature},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-356-giglis-characterization-alexandrov-curvature#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 these manuscripts were correct, one would concern a characterisation of the curvature of Alexandrov spaces in the sense of distributions, the other weak Hessian bounds along every geodesic in RCD spaces. The repository files this family under differential geometry.
What remains unclear
The Lean is supplied by OpenAI itself; its formalization.yaml file carries “review: status: unchecked”, and no third-party verification is recorded. The sources read do not say whether the first manuscript claims a new result or restates the one by Gigli named in its title.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 356.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 · Giglis-distributional…link only, reading not recorded
- Repositorygithub.com · Weak-Hessian-bounds-along…link only, reading not recorded
- Lean proofgithub.com · 356.mdpage read word for word
- Lean proofgithub.com · WeakHessian.leanlink only, reading not recorded
Method
The openai/math repository contains two manuscripts dated September 24, 2026, in the “Differential geometry” section: “Gigli’s distributional curvature characterization of Alexandrov spaces” and “Weak Hessian bounds along every geodesic in RCD spaces”. The file lean/docs/356.md goes with 1 Comparator statement, in lean/ComparatorChallenges/WeakHessian.lean. history.md reports no revision of these manuscripts. 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 356, section “Differential geometry”, 2 manuscripts 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
- 5 : 1 read word for word, 4 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 350 of 372, by family number
- Not evaluated : The sharp dimension threshold for affine Bernstein rigidity (family 353)
- Not evaluated : Isoperimetric regions in the cubic three-torus (family 354)
- 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)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.