Not evaluated
Sharp one-dimensional Lieb–Thirring inequalities (family 262)
The gist
On October 6, 2026, OpenAI published 3 manuscripts on sharp one-dimensional Lieb–Thirring inequalities, two of them on the case of matrix potentials.
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-262-sharp-one-dimensional-liebthirring-r1
@misc{discoveria-oai-fam-262-sharp-one-dimensional-liebthirring-r1,
author = {{DiscoverIA}},
title = {Sharp one-dimensional Lieb–Thirring inequalities (family 262)},
howpublished = {DiscoverIA registry, entry oai-fam-262-sharp-one-dimensional-liebthirring},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-262-sharp-one-dimensional-liebthirring#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A Lieb–Thirring inequality bounds the sum of powers of the negative eigenvalues of an operator by the integral of a power of the negative part of its potential. If these manuscripts held, they would announce “sharp”, that is optimal, constants for this inequality in one dimension. One manuscript would address matrix potentials, another the cases where the inequality becomes an equality.
What remains unclear
No third party is recorded as a checker, and the Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, marked “unchecked”. The sources read do not give the value of the announced constants, nor how the 3 manuscripts fit together.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 262.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 · Equality-cases-in-the…link only, reading not recorded
- Repositorygithub.com · Sharp-one-dimensional…link only, reading not recorded
- Repositorygithub.com · Sharp-One-Dimensional…link only, reading not recorded
- Lean proofgithub.com · 262.mdpage read word for word
- Lean proofgithub.com · LiebThirring.leanlink only, reading not recorded
Method
OpenAI publishes 3 manuscripts for family 262 in its openai/math repository. The first, “Sharp one-dimensional Lieb–Thirring constants”, is dated September 23, 2026. The second, dated October 5, 2026, is “Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials”. The third, dated the same day, is “Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality”. Lean supplied: lean/docs/262.md and lean/ComparatorChallenges/LiebThirring.lean (1 Comparator statement). The family is present in the `sources` of formalization.yaml. 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 (Mathematical physics)
- In openai/math
- family 262, section “Mathematical physics”, 3 manuscripts 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
- 6 : 1 read word for word, 5 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 256 of 372, by family number
- Not evaluated : A group without fixed price (family 259)
- Not evaluated : Spacetime Penrose inequalities and rigidity (family 260)
- Not evaluated : Localization and delocalization in the Anderson model (family 261)
- Not evaluated : Sharp one-dimensional Lieb–Thirring inequalities (family 262)
- Not evaluated : The ionization and generalized ionization conjectures (family 263)
- Not evaluated : Strong cosmic censorship near two-ended Kerr data (family 264)
- Not evaluated : The two-dimensional gapped area law (family 265)
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