Not evaluated
Edges versus triangles (minimum triangle density): -0.71171
Previous -0.71249, AlphaEvolve
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.
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-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/entry/ea-edges-vs-triangles#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 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, June 27, 2026), equal to the paper's value once rounded. The verifier may have been revised after the record.
Read the paper
Harnessing the Collective Intelligence of AI Agents in the Wild for New Discoveries
What it establishes : The authors present EinsteinArena and report that by May 2026 its agents had set 11 new records across 15 open problems, including the kissing number in dimension 11, raised from 593 to 604.
Where to start : The abstract, then Table 1 (Section 2.2): the 15 problems, with the previous and new records. Section 3 and Appendix B cover dimension 11 in detail, Appendix A each problem. The arXiv abstract page announces 12 records, the paper itself 11.
Written by an AI · reviewed by a human
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org
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 sourcearxiv.orgpage read word for word · consulted on Oct 12, 2026 ·
we additionally report the previous best known result and the current best result
- Papertogether.aipage read word for word · consulted on Oct 12, 2026 ·
we currently have the best known results for the following problems
- Repositorygithub.comlink only, reading not recorded
- Repositoryeinsteinarena.com · api/problems/edges-vs-triangleslink only, reading not recorded
- Repositoryeinsteinarena.com · bestlink only, reading not recorded
- Repositoryeinsteinarena.com · problems/edges-vs-triangleslink only, reading not recorded
Method
DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from arxiv.org (page read, quotation checked word for word: “we additionally report the previous best known result and the current best result”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- Together AI and EinsteinArena agents (agent not named by the source for the paper's value)
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
- 6 : 2 read word for word, 4 links only
- This entry
- AI draft, not reviewed
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.
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)
Related frontiers
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