Not evaluated
GOE universality for random regular graphs with weak disorder (family 219)
The gist
In its release of October 6, 2026, OpenAI announces two universality manuscripts on random regular graphs: one of GOE type, the other with weak Anderson disorder.
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-219-goe-universality-random-regular-graphs-weak-r1
@misc{discoveria-oai-fam-219-goe-universality-random-regular-graphs-weak-r1,
author = {{DiscoverIA}},
title = {GOE universality for random regular graphs with weak disorder (family 219)},
howpublished = {DiscoverIA registry, entry oai-fam-219-goe-universality-random-regular-graphs-weak},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-219-goe-universality-random-regular-graphs-weak#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
In a random regular graph, every node has the same number of neighbours; the GOE is a family of random symmetric matrices with normally distributed entries. If the first manuscript held, the local statistics of the eigenvalues of these fixed-degree graphs, away from the edges of the spectrum (bulk), would follow those of the GOE. The second manuscript concerns fixed energy, with weak Anderson disorder (a random potential on the nodes).
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party assessment is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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 · Fixed-energy-universality…link only, reading not recorded
- Repositorygithub.com · GOE-bulk-universality-for…link only, reading not recorded
Method
The openai/math repository contains “GOE bulk universality for fixed-degree random regular graphs”, dated September 23, 2026. It also contains “Fixed-energy universality for weak Anderson disorder on random regular graphs”, dated October 5, 2026. It contains no file lean/docs/219.md, and history.md reports no revision of these manuscripts. 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Probability and statistical mechanics)
- In openai/math
- family 219, section “Probability and statistical mechanics”, 2 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 213 of 372, by family number
- Not evaluated : Critical logarithmic corrections and BKT scaling for the planar XY model (family 216)
- Not evaluated : The low-temperature Sherrington–Kirkpatrick fluctuation law (family 217)
- Not evaluated : Conformal universality for weakly interacting and disordered Ising models (family 218)
- Not evaluated : GOE universality for random regular graphs with weak disorder (family 219)
- Not evaluated : Directional zero–one laws and ballisticity in random environments (family 220)
- Not evaluated : The Mézard–Parisi formula for diluted spin glasses (family 221)
- Not evaluated : Perceptron free energies and microscopic jamming (family 222)
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