Not evaluated
Uniform identity testing for noncommutative formulas (family 116)
The gist
In its release of October 6, 2026, OpenAI claims results on matrix “hitting points” for noncommutative formulas.
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-116-uniform-identity-testing-noncommutative-r1
@misc{discoveria-oai-fam-116-uniform-identity-testing-noncommutative-r1,
author = {{DiscoverIA}},
title = {Uniform identity testing for noncommutative formulas (family 116)},
howpublished = {DiscoverIA registry, entry oai-fam-116-uniform-identity-testing-noncommutative},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-116-uniform-identity-testing-noncommutative#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 manuscripts held, a single rational matrix point would suffice to detect that a noncommutative formula is nonzero, and polynomial-size lists would suffice for noncommutative rational formulas. A hitting point is a set of values that does not make any nonzero formula of a given size vanish; here the values are matrices. In a noncommutative formula, the order of the factors matters.
What remains unclear
No independent assessment is recorded. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI and marked “review: status: unchecked” in formalization.yaml.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 116.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 · Uniform-Matrix-Hitting…link only, reading not recorded
- Repositorygithub.com · One-Rational-Matrix…link only, reading not recorded
- Repositorygithub.com · Polynomial-Hitting-Lists…link only, reading not recorded
- Lean proofgithub.com · 116.mdpage read word for word
- Lean proofgithub.com · FormulaHitting.leanlink only, reading not recorded
- Lean proofgithub.com · RationalHitting.leanlink only, reading not recorded
Method
Two OpenAI manuscripts are dated September 24, 2026: “One Rational Matrix Hitting Point for Noncommutative Formulas” and “Polynomial Hitting Lists for Noncommutative Rational Formulas”. A third, “Uniform Matrix Hitting Points in Every Positive Characteristic”, is dated October 4, 2026. The repository also holds lean/docs/116.md (2 Comparator statements), lean/ComparatorChallenges/FormulaHitting.lean and lean/ComparatorChallenges/RationalHitting.lean. 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 116, section “Theoretical computer science”, 3 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
- 7 : 1 read word for word, 6 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 113 of 372, by family number
- Not evaluated : Approximate counting and the perfect-matching entropy conjecture (family 113)
- 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)
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