Not evaluated
The complexity of Weisfeiler–Leman refinement (family 133)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, four manuscripts on the complexity of Weisfeiler–Leman refinement, with Lean files.
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-133-complexity-weisfeilerleman-refinement-r1
@misc{discoveria-oai-fam-133-complexity-weisfeilerleman-refinement-r1,
author = {{DiscoverIA}},
title = {The complexity of Weisfeiler–Leman refinement (family 133)},
howpublished = {DiscoverIA registry, entry oai-fam-133-complexity-weisfeilerleman-refinement},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-133-complexity-weisfeilerleman-refinement#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 were correct, they would provide, according to their titles, results on the running time needed to identify a graph by Weisfeiler–Leman refinement. This refinement is a procedure that labels the vertices of a graph according to their neighbourhood. One manuscript announces unconditional time lower bounds, that is, bounds that rest on no unproven assumption.
What remains unclear
The Lean files (Lean is a language in which a computer checks every step of a proof) are supplied by OpenAI itself, and the repository marks them “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 · 133.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 · Parity-lifts-and-bounded…link only, reading not recorded
- Repositorygithub.com · The-complexity-of…link only, reading not recorded
- Repositorygithub.com · Unconditional-time-lower…link only, reading not recorded
- Repositorygithub.com · Variable-dimension…link only, reading not recorded
- Lean proofgithub.com · 133.mdpage read word for word
- Lean proofgithub.com · ParityLifts.leanlink only, reading not recorded
- Lean proofgithub.com · VariableWL.leanlink only, reading not recorded
- Lean proofgithub.com · WLIdentification.leanlink only, reading not recorded
- Lean proofgithub.com · WeisfeilerLeman.leanlink only, reading not recorded
Method
The four manuscripts of family 133 are dated September 25, 2026. One is titled “The complexity of identifying a graph by Weisfeiler–Leman refinement”, another “Unconditional time lower bounds for Weisfeiler–Leman equivalence”. A third is titled “Parity lifts and bounded-treewidth witnesses for Weisfeiler–Leman equivalence”. The fourth is titled “Variable-dimension Weisfeiler–Leman equivalence on general and subcubic graphs”. The file lean/docs/133.md describes the scope of the formalisation, with four Comparator statements. Two files are lean/ComparatorChallenges/ParityLifts.lean and lean/ComparatorChallenges/VariableWL.lean. The other two are lean/ComparatorChallenges/WLIdentification.lean and lean/ComparatorChallenges/WeisfeilerLeman.lean. The family is not among the sources of formalization.yaml; history.md reports no revision. 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 133, section “Theoretical computer science”, 4 manuscripts dated Sep 25, 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
- 10 : 1 read word for word, 9 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 129 of 372, by family number
- Not evaluated : Fourier transforms below n log n (family 130)
- Not evaluated : Polynomial mixing of graph switches with prescribed degrees (family 131)
- Not evaluated : A counterexample to the quadratic sensitivity conjecture (family 132)
- Not evaluated : The complexity of Weisfeiler–Leman refinement (family 133)
- Not evaluated : Generalized star height at most three (family 134)
- Not evaluated : Sharp homogeneous depth-five complexity of matrix products (family 135)
- Not evaluated : The quasilinear PCP-for-PPAD conjecture (family 136)
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