Not evaluated
Fourier restriction for positively curved surfaces (family 077)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, two manuscripts on Fourier restriction for positively curved surfaces.
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-077-fourier-restriction-positively-curved-r1
@misc{discoveria-oai-fam-077-fourier-restriction-positively-curved-r1,
author = {{DiscoverIA}},
title = {Fourier restriction for positively curved surfaces (family 077)},
howpublished = {DiscoverIA registry, entry oai-fam-077-fourier-restriction-positively-curved},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-077-fourier-restriction-positively-curved#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Fourier restriction studies what can be said about the Fourier transform of a function (its decomposition into pure waves) when it is looked at only on a curved surface. If the manuscripts were correct, they would bring new results for the sphere and for positively curved surfaces in three dimensions, according to their titles.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The sources read do not say where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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 · Elliptic-capacity…link only, reading not recorded
- Repositorygithub.com · Diagonal-Fourier…link only, reading not recorded
Method
The openai/math repository contains two manuscripts, both dated September 24, 2026: “Elliptic capacity propagation and Fourier restriction to the sphere” and “Diagonal Fourier extension for positively curved surfaces in three dimensions”. The absence of Lean is inferred from the absence of a lean/docs/077.md file; 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Real and complex analysis)
- In openai/math
- family 077, section “Real and complex analysis”, 2 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 74 of 372, by family number
- Not evaluated : Kakeya in three and four dimensions (family 074)
- Not evaluated : The L log L Fourier-convergence conjecture (family 075)
- Not evaluated : Ultraflat real Littlewood polynomials (family 076)
- Not evaluated : Fourier restriction for positively curved surfaces (family 077)
- Not evaluated : The three-dimensional Bochner–Riesz conjecture (family 078)
- Not evaluated : Sogge's local smoothing conjecture in dimension three (family 079)
- Not evaluated : The Sobolev endpoint in Carleson's Schrödinger convergence problem (family 080)
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