12 unit hexagons in a hexagon: side 3.9416523 (previous 3.9419123, AlphaEvolve v2)
Status
Not evaluated
Recorded on · raw.githubusercontent.com
- 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
To fit 12 unit hexagons inside one hexagon, Together AI claims a side of 3.9416523 (platform repository, April 2026), against 3.9419123 for AlphaEvolve; smaller is better; 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-hexagon-packing-n12-r1
@misc{discoveria-ea-hexagon-packing-n12-r1,
author = {{DiscoverIA}},
title = {12 unit hexagons in a hexagon: side 3.9416523 (previous 3.9419123, AlphaEvolve v2)},
howpublished = {DiscoverIA registry, entry ea-hexagon-packing-n12},
note = {Status « Not evaluated », snapshot 1, recorded on October 12, 2026. new result},
year = {2026},
url = {https://discoveria.ai/en/fiche/ea-hexagon-packing-n12/#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 (dépôt new-SOTA « Ours », avril 2026) ; agent non nommé
announced on Apr 2026 - Nature
- new result
- Field
- Mathematics (hexagon packing / geometric optimisation, n=12)
- Checked by
- the platform's public checker (a tool); no third party named
- Sources (domains)
- 4 : 2 read word for word, 2 links only
- This entry
- AI draft, not reviewed
To understand
Analogy
Imagine looking for the smallest hexagonal box that can hold a set of identical hexagonal tiles without overlap.
What it changes
If the value holds, the smallest known hexagon containing these 12 hexagons would be slightly smaller than AlphaEvolve's (3.9419123, version 2, November 2025), by 0.0002600. The blog post of 13 April 2026 lists it.
What remains unclear
The verifier is a public program, not a third party, and the agent is not named. This value appears in the repository README and in the blog, but not in the arXiv paper. On 12 October 2026 the problem is no longer listed by the online API, so no current ranking allows a comparison.
4 sources.
For experts
Sources(domains)
- primaireraw.githubusercontent.compage read word for word · consulted on Oct 12, 2026 ·
Improvement over the AlphaEvolve baseline
- 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
- depotgithub.comlink only, reading not recorded
Method
Status “not evaluated” recorded on 12 October 2026 from github.com (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 looking for the smallest hexagonal box that can hold a set of identical hexagonal tiles without overlap.
In the same set
EinsteinArena: a platform where AI agents tackle open problems with public verifiers · 16 entries
- 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)
- Not evaluated : Two-deletion correcting code of length 16: at least 219 codewords (public record cited: 215, Weindel and Heckel 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: raw.githubusercontent.comread word for word
An observation is added; none is ever erased.
Related frontiers
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