Not evaluated
Polynomial mixing of graph switches with prescribed degrees (family 131)
The gist
On October 6, 2026, OpenAI released a manuscript claiming polynomial mixing of the “switch chain” for every graphical degree sequence.
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-131-polynomial-mixing-graph-switches-prescribed-r1
@misc{discoveria-oai-fam-131-polynomial-mixing-graph-switches-prescribed-r1,
author = {{DiscoverIA}},
title = {Polynomial mixing of graph switches with prescribed degrees (family 131)},
howpublished = {DiscoverIA registry, entry oai-fam-131-polynomial-mixing-graph-switches-prescribed},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-131-polynomial-mixing-graph-switches-prescribed#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The “switch chain” modifies a graph step by step by swapping the endpoints of two edges, which keeps the number of neighbours of every vertex unchanged. If the manuscript held, it would mix in a polynomial number of steps (bounded by a polynomial in the size of the graph), for every degree sequence that some graph can realise (a “graphical” sequence). It would then resemble a random draw among graphs with the same degrees.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and the repository marks its review “unchecked”. No third-party verification is recorded. The manuscript comes from an internal model that OpenAI has not released.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 131.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 · Polynomial-Mixing-of-the…link only, reading not recorded
- Lean proofgithub.com · 131.mdpage read word for word
- Lean proofgithub.com · SwitchChain.leanlink only, reading not recorded
Method
In the openai/math release, family 131 has a single manuscript, dated September 25, 2026: “Polynomial mixing of the switch chain for every graphical degree sequence”. It is filed under the section “Theoretical computer science” of overview.tex; history.md reports no revision. OpenAI adds a Lean Comparator file, lean/ComparatorChallenges/SwitchChain.lean (1 statement), described in lean/docs/131.md. 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 131, section “Theoretical computer science”, 1 manuscript 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
- 4 : 1 read word for word, 3 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 127 of 372, by family number
- Not evaluated : A factor-two approximation for shortest common superstring (family 128)
- Not evaluated : Exponential state costs for two-way automata (family 129)
- 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)
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