Not evaluated
The L log L Fourier-convergence conjecture (family 075)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on almost-everywhere convergence of Fourier series for functions in the class L log L.
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-075-l-l-fourier-convergence-conjecture-r1
@misc{discoveria-oai-fam-075-l-l-fourier-convergence-conjecture-r1,
author = {{DiscoverIA}},
title = {The L log L Fourier-convergence conjecture (family 075)},
howpublished = {DiscoverIA registry, entry oai-fam-075-l-l-fourier-convergence-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-075-l-l-fourier-convergence-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript were correct, it would establish, going by its title, that the Fourier series of a function in the class L log L (the decomposition of the function into simple waves) converges almost everywhere, that is everywhere except on a negligible set of points. The repository files this family under the section “Real and complex analysis”.
What remains unclear
No check of the Lean supplied by OpenAI (a language in which a computer checks every step of a proof) by a third party, nor any other 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 · 075.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 · Almost-everywhere-Fourier…link only, reading not recorded
- Lean proofgithub.com · 075.mdpage read word for word
- Lean proofgithub.com · FourierLLogL.leanlink only, reading not recorded
Method
The manuscript in the openai/math repository is titled “Almost-everywhere Fourier convergence in L log L” and is dated September 23, 2026. OpenAI supplies lean/docs/075.md and one Lean file, lean/ComparatorChallenges/FourierLLogL.lean (one Comparator statement); formalization.yaml carries “review: status: unchecked” and lists the family in its sources. history.md reports no revision of the 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 (Real and complex analysis)
- In openai/math
- family 075, section “Real and complex analysis”, 1 manuscript dated Sep 23, 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 72 of 372, by family number
- Not evaluated : Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)
- Not evaluated : The Falconer distance conjecture (family 073)
- 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)
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