Not evaluated
The Sobolev endpoint in Carleson's Schrödinger convergence problem (family 080)
The gist
On October 6, 2026, OpenAI published two manuscripts, from an unreleased internal model, on the Sobolev endpoint in Carleson’s Schrödinger convergence problem.
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-080-sobolev-endpoint-carlesons-schrodinger-r1
@misc{discoveria-oai-fam-080-sobolev-endpoint-carlesons-schrodinger-r1,
author = {{DiscoverIA}},
title = {The Sobolev endpoint in Carleson's Schrödinger convergence problem (family 080)},
howpublished = {DiscoverIA registry, entry oai-fam-080-sobolev-endpoint-carlesons-schrodinger},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-080-sobolev-endpoint-carlesons-schrodinger#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Carleson’s problem asks how much smoothness (measured by a Sobolev index) it suffices to require of the initial data of a Schrödinger equation for its solution to converge to it at almost every point as time tends to zero. If the manuscripts were correct, they would deal, going by their titles, with the endpoint case of this index, in the plane and then in higher dimensions.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied and no independent 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 · Endpoint-convergence-for…link only, reading not recorded
- Repositorygithub.com · Endpoint-pointwise…link only, reading not recorded
Method
The manuscripts “Endpoint convergence for the planar Schrodinger equation” and “Endpoint pointwise convergence for the Schrodinger equation in higher dimensions” are dated September 24, 2026 and filed under the “Real and complex analysis” section of the openai/math repository. There is no lean/docs/080.md file, and history.md reports no revision. 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 080, 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 77 of 372, by family number
- 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)
- Not evaluated : The David–Semmes Riesz-transform problem in higher codimension (family 081)
- Not evaluated : Maximal and variational bounds for the triangular Hilbert transform (family 082)
- Not evaluated : Stein's conjecture for Hilbert transforms along Lipschitz directions (family 083)
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