Not evaluated
A cubic permanent–determinant lower bound (family 108)
The gist
In its release of October 6, 2026, OpenAI announces, using an unreleased internal model, a cubic lower bound for the border determinantal complexity of the permanent.
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-108-cubic-permanentdeterminant-lower-bound-r1
@misc{discoveria-oai-fam-108-cubic-permanentdeterminant-lower-bound-r1,
author = {{DiscoverIA}},
title = {A cubic permanent–determinant lower bound (family 108)},
howpublished = {DiscoverIA registry, entry oai-fam-108-cubic-permanentdeterminant-lower-bound},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-108-cubic-permanentdeterminant-lower-bound#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The permanent of a matrix is computed like its determinant, but without the alternating signs. If the bound held, it would be a cubic lower bound for the border determinantal complexity of the permanent. This complexity measures the size of matrix needed for determinants to reproduce the permanent, exactly or as a limit.
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 marks it as unchecked. No third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 108.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-cubic-lower-bound-for…link only, reading not recorded
- Lean proofgithub.com · 108.mdpage read word for word
- Lean proofgithub.com · PermanentCubic.leanlink only, reading not recorded
- Lean proofgithub.com · SmoothInitialForm.leanlink only, reading not recorded
Method
The openai/math repository contains the manuscript “A cubic lower bound for border determinantal complexity of the permanent”, dated September 24, 2026, and the file lean/docs/108.md, which describes the Lean formalisation with two Comparator statements (lean/ComparatorChallenges/PermanentCubic.lean and lean/ComparatorChallenges/SmoothInitialForm.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 108, section “Theoretical computer science”, 1 manuscript 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 105 of 372, by family number
- Not evaluated : The 2-to-1 Games Conjecture with perfect completeness (family 105)
- Not evaluated : Hardness of coloring three-colorable graphs (family 106)
- Not evaluated : Matrix multiplication exponent at most 9/4 (family 107)
- Not evaluated : A cubic permanent–determinant lower bound (family 108)
- Not evaluated : Integer multiplication below n log n (family 109)
- Not evaluated : Optimal-order randomized k-server on arbitrary metrics (family 110)
- Not evaluated : One-sample matroid prophet inequalities against an almighty adversary (family 111)
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