Edges versus triangles (minimum triangle density): -0.71171 (previous -0.71249, AlphaEvolve)
Status
Not evaluated
Recorded on · arxiv.org
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
No DiscoverIA status yet; this does not mean nobody has checked it.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
The gist
For the minimum density of triangles at a given number of edges, Together AI and EinsteinArena agents report -0.71171 (larger is better), against -0.71249 for AlphaEvolve; no DiscoverIA status yet.
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-ea-edges-vs-triangles-r1
@misc{discoveria-ea-edges-vs-triangles-r1,
author = {{DiscoverIA}},
title = {Edges versus triangles (minimum triangle density): -0.71171 (previous -0.71249, AlphaEvolve)},
howpublished = {DiscoverIA registry, entry ea-edges-vs-triangles},
note = {Status « Not evaluated », snapshot 1, recorded on October 12, 2026. new result},
year = {2026},
url = {https://discoveria.ai/en/fiche/ea-edges-vs-triangles/#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
Text written by an AI (DiscoverIA pipeline), on Reviewed by: nobody yetReport an error
What has not been reviewed?
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.
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.
Key facts
- Claimed by
- Together AI et agents d'EinsteinArena (agent non nommé par la source pour la valeur du papier)
announced on Mar 2026 - Nature
- new result
- Field
- Mathematics (extremal combinatorics / graph theory, triangle density)
- Checked by
- the platform's public checker (a tool); no third party named
- Sources (domains)
- 6 : 2 read word for word, 4 links only
- This entry
- AI draft, not reviewed
To understand
Analogy
Imagine a group of people in which a certain share of the pairs are friends: what is the smallest share of trios of friends all linked to one another that can be obtained?
What it changes
If the value holds, it would improve the best known construction, AlphaEvolve's (version 2, November 2025), from -0.71249 to -0.71171. The platform's repository already gave -0.712256 in March 2026, so the paper's value is later.
What remains unclear
The verifier is a public program, not a third party, and the source names neither the agent behind the paper's value nor its date. The online ranking shows -0.7117091757692579 (an agent, 27 June 2026), equal to the paper's value once rounded. The verifier may have been revised after the record.
6 sources.
For experts
Sources(domains)
- primairearxiv.orgpage read word for word · consulted on Oct 12, 2026 ·
we additionally report the previous best known result and the current best result
- articletogether.aipage read word for word · consulted on Oct 12, 2026 ·
we currently have the best known results for the following problems
- depotgithub.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
Method
Status “not evaluated” recorded on 12 October 2026 from arxiv.org (page read, quotation checked word for word).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. DiscoverIA has recorded no independent evaluation as of this date.
Imagine a group of people in which a certain share of the pairs are friends: what is the smallest share of trios of friends all linked to one another that can be obtained?
In the same set
EinsteinArena: a platform where AI agents tackle open problems with public verifiers · 16 entries
- Not evaluated : Prime number theorem (lower bound on the score functional): 0.99490 (previous 0.92129, AlphaEvolve)
- Not evaluated : Circles in a rectangle, 21 of them: sum of radii 2.365832255 (previous 2.365832133, AlphaEvolve)
- Not evaluated : Tammes problem (50 points on the sphere): 0.5134721 (previous 0.5134719, AlphaEvolve)
- Not evaluated : Edges versus triangles (minimum triangle density): -0.71171 (previous -0.71249, AlphaEvolve)
- Not evaluated : 12 unit hexagons in a hexagon: side 3.9416523 (previous 3.9419123, AlphaEvolve v2)
- Not evaluated : Heilbronn problem for convex regions (14 points): 0.0278355805 (previous 0.0278355715, AlphaEvolve v2)
- Not evaluated : Kakeya needle problem, discretised (n=128): area 0.10675394 (platform's cited state of the art: 0.107067)
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
not evaluated: only the platform's public checker, no third party named
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
Related frontiers
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