Not evaluated
Circles in a rectangle, 21 of them: sum of radii 2.365832255
Previous 2.365832133, AlphaEvolve
The gist
For packing 21 circles in a rectangle so that the sum of their radii is as large as possible, the EinsteinArena paper reports 2.365832255, against 2.365832133 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-circles-in-rectangle-n21-r1
@misc{discoveria-ea-circles-in-rectangle-n21-r1,
author = {{DiscoverIA}},
title = {Circles in a rectangle, 21 of them: sum of radii 2.365832255 (previous 2.365832133, AlphaEvolve)},
howpublished = {DiscoverIA registry, entry ea-circles-in-rectangle-n21},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/ea-circles-in-rectangle-n21#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 2.365832133 to 2.365832255. The gap only concerns the last decimals.
What remains unclear
The verifier is a public program of the platform, not a third party: no outside reviewer is named. Three values circulate for the best score: 2.365832255 in the paper, 2.3658323759 in the repository and on the online ranking, whose origin is unexplained. The verifier may have been revised since 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/circles-rectanglelink only, reading not recorded
- Repositoryeinsteinarena.com · bestlink only, reading not recorded
- Repositoryeinsteinarena.com · problems/circles-rectanglelink 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
- an agent (submission of 2026-04-07 at 2.365832254667658, equal to the paper's value) (Name replaced by a role)
announced on Apr 7, 2026 - Nature
- new result
- Field
- Mathematics (circle packing / geometric optimisation, n=21)
- 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 : Flat polynomials of degree 69: 1.28093 (previous 1.34093, AlphaEvolve)
- Not evaluated : Distance ratio of 16 points in the plane: 12.889230 (previous 12.889266, AlphaEvolve)
- 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)
Related frontiers
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