Not evaluated
Deterministic nonbipartite Ramanujan graphs in every fixed degree (family 178)
The gist
OpenAI claims, in a manuscript announced on October 6, 2026, deterministic nonbipartite Ramanujan graphs in every fixed degree.
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-178-deterministic-nonbipartite-ramanujan-graphs-r1
@misc{discoveria-oai-fam-178-deterministic-nonbipartite-ramanujan-graphs-r1,
author = {{DiscoverIA}},
title = {Deterministic nonbipartite Ramanujan graphs in every fixed degree (family 178)},
howpublished = {DiscoverIA registry, entry oai-fam-178-deterministic-nonbipartite-ramanujan-graphs},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-178-deterministic-nonbipartite-ramanujan-graphs#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A graph is a set of points joined by links; its degree is the number of links at each point, the same everywhere. Ramanujan graphs are very well connected; “nonbipartite” means the points cannot be split into two groups with every link running between the groups. If the manuscript held, such graphs would be obtained without random draws, for each fixed degree.
What remains unclear
No Lean file (a language in which a computer checks every step of a proof) is supplied for this family. The sources read mention no third-party evaluation, so it is not known whether the manuscript holds.
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 · Deterministic…link only, reading not recorded
Method
A manuscript dated September 23, 2026: “Deterministic nonbipartite Ramanujan graphs in every fixed degree”. It is listed in CONTENTS.md and classified under the section “Combinatorics” of overview.tex. 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 (Combinatorics)
- In openai/math
- family 178, section “Combinatorics”, 1 manuscript dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 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 172 of 372, by family number
- Not evaluated : Talagrand's conjectures and graph decompositions at expectation thresholds (family 175)
- Not evaluated : The second Kahn–Kalai conjecture (family 176)
- Not evaluated : Bounded-degree coboundary expanders in every dimension (family 177)
- Not evaluated : Deterministic nonbipartite Ramanujan graphs in every fixed degree (family 178)
- Not evaluated : The circulant Hadamard conjecture (family 179)
- Not evaluated : Barnette's Hamiltonian-cycle conjecture (family 180)
- Not evaluated : The Erdős–Gallai cycle-decomposition conjecture (family 181)
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