Not evaluated
Villani’s convexity conjecture and regular optimal transport (family 360)
The gist
On October 6, 2026, OpenAI announced two manuscripts under the “Weak MTW” assumption, linked to Villani's convexity conjecture and to regular optimal transport.
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-360-villanis-convexity-conjecture-regular-r1
@misc{discoveria-oai-fam-360-villanis-convexity-conjecture-regular-r1,
author = {{DiscoverIA}},
title = {Villani’s convexity conjecture and regular optimal transport (family 360)},
howpublished = {DiscoverIA registry, entry oai-fam-360-villanis-convexity-conjecture-regular},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-360-villanis-convexity-conjecture-regular#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 manuscripts were correct, they would bring new results under “Weak MTW”: one on global support and convex injectivity domains, the other on uniform bi-Holder transport. The repository files this family under differential geometry.
What remains unclear
The Lean code (Lean is a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and no third-party verification is recorded; formalization.yaml carries the entry “review: status: unchecked”. The sources read do not say how each of the two manuscripts relates to Villani's conjecture.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 360.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 · Global-Support-and-Convex…link only, reading not recorded
- Repositorygithub.com · Uniform-Bi-Holder…link only, reading not recorded
- Lean proofgithub.com · 360.mdpage read word for word
- Lean proofgithub.com · BiholderTransport.leanlink only, reading not recorded
- Lean proofgithub.com · WeakMTWGlobalSupport.leanlink only, reading not recorded
Method
The openai/math repository contains two manuscripts dated September 25, 2026 (family 360, section “Differential geometry” of overview.tex): “Global Support and Convex Injectivity Domains under Weak MTW” and “Uniform Bi-Holder Transport from Weak MTW”. The file lean/docs/360.md, which “describes the scope of the Lean formalization”, comes with 2 Comparator statements: lean/ComparatorChallenges/BiholderTransport.lean and lean/ComparatorChallenges/WeakMTWGlobalSupport.lean. The recorded note is: family present in the `sources` of formalization.yaml; history.md reports no revision; commit fd4aeeb of October 7, 2026. 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).
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 360, section “Differential geometry”, 2 manuscripts 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
- 6 : 1 read word for word, 5 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 354 of 372, by family number
- 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)
- Not evaluated : Boltzmann nonuniqueness with exact local conservation (family 363)
- Not evaluated : Kinetic limits and fluctuations over the Boltzmann lifespan (family 364)
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