Not evaluated
Exponential semidefinite complexity of perfect matching (family 126)
The gist
On October 6, 2026, OpenAI announced an exponential PSD rank for positively shifted matching matrices, 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-126-exponential-semidefinite-complexity-perfect-r1
@misc{discoveria-oai-fam-126-exponential-semidefinite-complexity-perfect-r1,
author = {{DiscoverIA}},
title = {Exponential semidefinite complexity of perfect matching (family 126)},
howpublished = {DiscoverIA registry, entry oai-fam-126-exponential-semidefinite-complexity-perfect},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-126-exponential-semidefinite-complexity-perfect#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, an exponential PSD rank for positively shifted matching matrices. The PSD rank of a matrix with non-negative entries is the smallest size of positive semidefinite matrices, one per row and one per column, whose inner product gives each entry. An exponential rank grows very fast as the size parameter increases.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file formalization.yaml marks it “unchecked”. No third-party verification is recorded, and the sources read do not specify the scope of the Lean relative to the manuscript.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 126.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 · Exponential-PSD-rank-of…link only, reading not recorded
- Lean proofgithub.com · 126.mdpage read word for word
- Lean proofgithub.com · MatchingAffineLift.leanlink only, reading not recorded
- Lean proofgithub.com · MatchingPSD.leanlink only, reading not recorded
Method
The openai/math repository contains one manuscript, “Exponential PSD rank of positively shifted matching matrices”, dated October 5, 2026. The file lean/docs/126.md describes the scope of the Lean formalisation, with 2 Comparator statements. The files are lean/ComparatorChallenges/MatchingAffineLift.lean and lean/ComparatorChallenges/MatchingPSD.lean. In formalization.yaml, the family is not among the listed sources; 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: “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 126, section “Theoretical computer science”, 1 manuscript dated Oct 5, 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 122 of 372, by family number
- Not evaluated : Superpolynomial lower bounds and quasipolynomial reconstruction from deletion traces (family 122)
- Not evaluated : Polynomial-time scheduling on three identical machines (family 124)
- Not evaluated : The approximation threshold for metric k-median (family 125)
- Not evaluated : Exponential semidefinite complexity of perfect matching (family 126)
- Not evaluated : The asymptotic Gotsman–Linial conjecture (family 127)
- Not evaluated : A factor-two approximation for shortest common superstring (family 128)
- Not evaluated : Exponential state costs for two-way automata (family 129)
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