Not evaluated
Uniform sparsest cut: hardness and semidefinite gaps (family 117)
The gist
On October 6, 2026, OpenAI announced two manuscripts on uniform sparsest cut: constant-factor hardness and integrality gaps.
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-117-uniform-sparsest-cut-hardness-semidefinite-r1
@misc{discoveria-oai-fam-117-uniform-sparsest-cut-hardness-semidefinite-r1,
author = {{DiscoverIA}},
title = {Uniform sparsest cut: hardness and semidefinite gaps (family 117)},
howpublished = {DiscoverIA registry, entry oai-fam-117-uniform-sparsest-cut-hardness-semidefinite},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-117-uniform-sparsest-cut-hardness-semidefinite#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 constant-factor hardness result would say that approximating the best cut to within a constant factor is hard for an efficient algorithm. An integrality gap is the gap between the problem and a relaxed version that is easier to compute. If the manuscripts were correct, they would bring both kinds of result on this problem.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself and marked “unchecked” in formalization.yaml. No third-party verification is recorded, and the sources read do not say under which assumptions the hardness is stated. A single Comparator statement accompanies the 2 manuscripts, and the sources read do not say what it covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 117.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 · Constant-factor-hardness…link only, reading not recorded
- Repositorygithub.com · Near-square-root…link only, reading not recorded
- Lean proofgithub.com · 117.mdpage read word for word
- Lean proofgithub.com · UniformSparsestCut.leanlink only, reading not recorded
Method
The openai/math repository contains 2 manuscripts dated September 24, 2026. The first is titled “Constant-factor hardness of uniform sparsest cut”. The second is titled “Near-square-root logarithmic integrality gaps for uniform sparsest cut”. OpenAI attaches lean/docs/117.md and lean/ComparatorChallenges/UniformSparsestCut.lean. According to history.md, no revision is reported for these manuscripts. 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
- Theoretical computer science
- In openai/math
- family 117, section “Theoretical computer science”, 2 manuscripts dated Sep 24, 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
- 5 : 1 read word for word, 4 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 114 of 372, by family number
- Not evaluated : Approximate counting of common integer polymatroid bases (family 114)
- Not evaluated : Sampling and counting contingency tables with arbitrary margins (family 115)
- Not evaluated : Uniform identity testing for noncommutative formulas (family 116)
- Not evaluated : Uniform sparsest cut: hardness and semidefinite gaps (family 117)
- Not evaluated : Unbounded bin-packing gaps and the modified integer round-up conjecture (family 118)
- Not evaluated : The Courtade–Kumar and Hellinger conjectures (family 119)
- Not evaluated : Almost-linear-time exact matching in general graphs (family 120)
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