Not evaluated
Sharp one-third stability of optimal transport maps (family 374)
The gist
In its release of October 6, 2026, OpenAI claims, using an unreleased internal model, a “sharp one-third” stability result for “Brenier maps”, the subject of a manuscript.
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-374-sharp-one-third-stability-optimal-transport-r1
@misc{discoveria-oai-fam-374-sharp-one-third-stability-optimal-transport-r1,
author = {{DiscoverIA}},
title = {Sharp one-third stability of optimal transport maps (family 374)},
howpublished = {DiscoverIA registry, entry oai-fam-374-sharp-one-third-stability-optimal-transport},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-374-sharp-one-third-stability-optimal-transport#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The manuscript belongs to partial differential equations. It concerns the stability of what it calls “Brenier Maps”. Its family speaks of “optimal transport maps”: optimal transport maps move one distribution of matter onto another at the lowest cost.
What remains unclear
The sources read do not say what the “one-third” refers to, nor what “sharp” guarantees. The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it “unchecked”. No third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 374.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 · Sharp-One-Third-Stability…link only, reading not recorded
- Lean proofgithub.com · 374.mdpage read word for word
- Lean proofgithub.com · Brenier.leanlink only, reading not recorded
Method
The openai/math repository contains the manuscript “Sharp One-Third Stability of Brenier Maps”, dated September 25, 2026 and filed under “Partial differential equations” in overview.tex. The file lean/docs/374.md describes the Lean formalisation, with one Comparator statement (lean/ComparatorChallenges/Brenier.lean). The family is absent from the “sources” of formalization.yaml; history.md reports no revision of this manuscript. 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 (Partial differential equations)
- In openai/math
- family 374, section “Partial differential equations”, 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 367 of 372, by family number
- Not evaluated : Stable blowup for a defocusing Schrödinger equation (family 371)
- Not evaluated : Global uniqueness in smooth isotropic elasticity (family 372)
- Not evaluated : Nonattainment in three-marginal Coulomb transport (family 373)
- Not evaluated : Sharp one-third stability of optimal transport maps (family 374)
- Not evaluated : De Giorgi's conjecture in dimension eight (family 375)
- Not evaluated : Universal computation in forced Navier–Stokes flows (family 376)
- Not evaluated : Interior C^(1,α) regularity for infinity-harmonic functions (family 377)
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