Not evaluated
Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures (family 093)
The gist
On October 6, 2026, OpenAI announced a dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures, 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-093-dimension-free-logarithmic-sobolev-r1
@misc{discoveria-oai-fam-093-dimension-free-logarithmic-sobolev-r1,
author = {{DiscoverIA}},
title = {Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures (family 093)},
howpublished = {DiscoverIA registry, entry oai-fam-093-dimension-free-logarithmic-sobolev},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-093-dimension-free-logarithmic-sobolev#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 bring, according to its title, a logarithmic Sobolev inequality whose constant would not depend on the dimension. This kind of inequality compares the entropy of a function with the size of its variations. The measures concerned are log-concave (their density has a concave logarithm) and subgaussian (their tails are at most as heavy as those of a normal distribution).
What remains unclear
No Lean proof (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 give only the manuscript's title, not its exact statement.
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 · A-dimension-free…link only, reading not recorded
Method
The openai/math repository contains one manuscript dated September 23, 2026, “A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures”. It is filed under the section “Convex and metric geometry” (overview.tex). The file lean/docs/093.md does not exist, and OpenAI's README states that not all manuscripts have a Lean formalisation. According to history.md, no revision of this manuscript is reported. 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 (Convex and metric geometry)
- In openai/math
- family 093, section “Convex and metric geometry”, 1 manuscript dated Sep 23, 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 90 of 372, by family number
- Not evaluated : Universal optimality of the triangular lattice (family 090)
- Not evaluated : The logarithmic Brunn–Minkowski conjecture (family 091)
- Not evaluated : The optimal order of convex-body covering density (family 092)
- Not evaluated : Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures (family 093)
- Not evaluated : Subpolynomial dimension reduction in L_p (family 094)
- Not evaluated : Hyperbolicity cones without semidefinite lifts (family 095)
- Not evaluated : The Gaussian propeller conjecture (family 096)
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