Not evaluated
Sogge's local smoothing conjecture in dimension three (family 079)
The gist
On October 6, 2026, OpenAI announced a manuscript on Sogge's local smoothing conjecture in dimension three, from an unreleased internal model.
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-079-sogges-local-smoothing-conjecture-dimension-r1
@misc{discoveria-oai-fam-079-sogges-local-smoothing-conjecture-dimension-r1,
author = {{DiscoverIA}},
title = {Sogge's local smoothing conjecture in dimension three (family 079)},
howpublished = {DiscoverIA registry, entry oai-fam-079-sogges-local-smoothing-conjecture-dimension},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-079-sogges-local-smoothing-conjecture-dimension#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 manuscript were correct, it would establish Sogge's conjecture for the wave equation (which describes how a wave propagates) in dimension three, in the so-called “critical” case according to its title.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) 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 · Critical-local-smoothing…link only, reading not recorded
Method
The manuscript “Critical local smoothing for the three-dimensional wave equation” is dated September 24, 2026; family 079 has only this one, and history.md reports no revision of it. 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 079, section “Real and complex analysis”, 1 manuscript dated Sep 24, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 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 76 of 372, by family number
- 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)
- 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)
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