Not evaluated
The sharp simplex conjecture for isotropic constants (family 101)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on an entropy bound and the simplex inequality for isotropic constants.
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-101-sharp-simplex-conjecture-isotropic-constants-r1
@misc{discoveria-oai-fam-101-sharp-simplex-conjecture-isotropic-constants-r1,
author = {{DiscoverIA}},
title = {The sharp simplex conjecture for isotropic constants (family 101)},
howpublished = {DiscoverIA registry, entry oai-fam-101-sharp-simplex-conjecture-isotropic-constants},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-101-sharp-simplex-conjecture-isotropic-constants#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 bring, according to its title, a so-called “sharp” entropy bound (announced as optimal) and the simplex inequality for isotropic constants. An isotropic constant is a number attached to a convex body that describes how its volume is spread.
What remains unclear
No Lean file (Lean is a language in which a computer checks every step of a proof) is supplied, and no third-party evaluation is recorded. It is not known whether specialists have reviewed the manuscript.
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-sharp-entropy-bound-and…link only, reading not recorded
Method
According to CONTENTS.md, family 101 comprises one manuscript: “A sharp entropy bound and the simplex inequality for isotropic constants”. It is dated October 5, 2026 and filed under the section “Convex and metric geometry” of overview.tex. history.md reports no revision of this 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: “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 101, section “Convex and metric geometry”, 1 manuscript dated Oct 5, 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 98 of 372, by family number
- Not evaluated : A negative answer to the Lang–Plaut problem (family 098)
- Not evaluated : The sharp distortion of edit distance into ℓ_1 (family 099)
- Not evaluated : A counterexample to Bang's cylinder-covering bound (family 100)
- Not evaluated : The sharp simplex conjecture for isotropic constants (family 101)
- Not evaluated : Claimed proof of the Unique Games Conjecture (family 102)
- Not evaluated : Derandomization of logarithmic space: L=RL=BPL (family 103)
- Not evaluated : Quasipolynomial algorithms for mean-payoff, stochastic and parity games (family 104)
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