Circles in a rectangle, 21 of them: sum of radii 2.365832255 (previous 2.365832133, 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 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.
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/en/fiche/ea-circles-in-rectangle-n21/#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
- un agent (agent ; soumission du 2026-04-07 à 2,365832254667658, égale à la valeur du papier) (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 (domains)
- 6 : 2 read word for word, 4 links only
- This entry
- AI draft, not reviewed
To understand
Analogy
Imagine washers of different sizes to be fitted into a rectangular box without overlapping, aiming for the largest possible sum of their radii.
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.
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 washers of different sizes to be fitted into a rectangular box without overlapping, aiming for the largest possible sum of their radii.
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)
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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