Apr 11, 2026 Not evaluated

Kissing number in dimension 11: at least 604 spheres

Previous bound 593, AlphaEvolve

Replayed by DiscoverIA only · level N1

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Author's artefacts

Published solution raw.githubusercontent.com
Repository or problem page github.com

DiscoverIA replayed it on Oct 12, 2026: reproduced. See the receipt

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The gist

In April 2026, AI agents on the EinsteinArena platform reported fitting 604 spheres around a central sphere in dimension 11, up from 593 before.

DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.

Status detailsDetails

Text written by an AI, reviewed by Antoine Olivier, Oct 13, 2026

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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

DiscoverIA. (2026, October 12). Kissing number in dimension 11: at least 604 spheres (previous bound 593, AlphaEvolve) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/ea-kissing-number-d11#releve-1

BibTeX @misc, key discoveria-ea-kissing-number-d11-r1

@misc{discoveria-ea-kissing-number-d11-r1,
  author       = {{DiscoverIA}},
  title        = {Kissing number in dimension 11: at least 604 spheres (previous bound 593, AlphaEvolve)},
  howpublished = {DiscoverIA registry, entry ea-kissing-number-d11},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/ea-kissing-number-d11#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/ea-kissing-number-d11#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

If the configuration is valid, the kissing number in dimension 11 is at least 604, instead of at least 593. This is a lower bound: it does not prove that 604 is the maximum.

What remains unclear

No named third party has checked the configuration in the sources read: the platform's verifier is a program, and the exact check comes from the team claiming the record. DiscoverIA's reproduction of October 12, 2026 finds the same result, which does not change this.

In the glossary : Kissing number

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

Version read: v2 of Aug 26, 2026.Open access, according to OpenAlex, checked on Oct 23, 2026.

For experts

Sources, method, key facts, status history, reproduction receipt, report an error

Status

Not evaluated

Recorded on Oct 12, 2026 · arxiv.org

Step 1 of 4 on the scale: not evaluated. Next step: under review.

Apr 11, 2026Announced
Oct 12, 2026Recordednot 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.

Full history

Proofs: vérificateur public exécutable (Python), solution publique téléchargeable

Sources

Main sourcearxiv.orgpage read word for word · consulted on Oct 12, 2026 · improved the best known lower bound from 593 to 604
Main sourcearxiv.orgpage read word for word · consulted on Oct 12, 2026 · a collaborative effort among AI agents improved this lower bound to
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
Repositoryraw.githubusercontent.comlink only, reading not recorded
Status sourceeinsteinarena.compage read word for word · consulted on Oct 12, 2026 · A valid 604-point non-overlapping configuration was certified on EinsteinArena.
Repositoryeinsteinarena.com · api/problems/kissing-number-d11link only, reading not recorded
Repositoryeinsteinarena.com · bestlink only, reading not recorded
Repositoryeinsteinarena.com · problems/kissing-number-d11link only, reading not recorded

Method

The new-SOTA repository publishes 604 vectors with coordinates in Z[√2]^11 (of the form a + b√2 with integers a and b); the documented check requires ||xi-xj||² >= 36 in exact integer arithmetic, with no tolerance, and the check of contact with the central sphere is not detailed. A first configuration of 594 spheres came from an agent (LSQR followed by integer rounding); the paper credits the extension to 604 to "the agent" without naming it. As of October 12, 2026, the platform listed no valid configuration with 605 spheres. 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: “improved the best known lower bound from 593 to 604”). Reproduction by DiscoverIA on October 12, 2026: reproduced; it does not count towards the status.

Limits

No named third party: the recorded checks come from the claimant or from a platform tool.

Key facts

Claimed by: EinsteinArena agents: one agent (initial basin), one agent (LSQR + integer rounding); the extension to 604 is credited to an unnamed “agent” by the paper (Name replaced by a role)
announced on Apr 11, 2026
Nature: new result
Field: Mathematics (discrete geometry / kissing number, dimension 11)
Checked by: the platform's public checker (a tool); no third party named
Sources: 9 : 4 read word for word, 5 links only
Part of: EinsteinArena: a platform where AI agents tackle open problems with public verifiers
This entry: Reviewed by Antoine Olivier, Oct 13, 2026

Status history

Only one observation so far.

01Oct 12, 2026
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.

Published reproductions

Reproduction receipt repro-ea-kissing-d11-2026-10-12

ReproducedReproduced on Oct 12, 2026DiscoverIA status of the entry: Not evaluated

Statement replayed

Il existe 604 sphères unité non chevauchantes tangentes à une sphère unité centrale en dimension 11, c'est-à-dire 604 vecteurs de même norme dont les angles deux à deux sont au moins 60 degrés (borne inférieure du nombre de contact en dimension 11 : 604, contre 593 pour AlphaEvolve). La configuration publiée est un fichier de 604 vecteurs à coordonnées dans Z[sqrt 2], mis à l'échelle de sorte que la norme au carré vaut 36.

Evidence, item by item

Reproduction evidence, item by item
Item	Value	Evidence, fingerprint	Checkable by
Result
Claimed value	604		reading the source
Value obtained	604		anyone with the command and environment given
Equality	yes	arithmetic in exact integers	anyone with the command and environment given
Fingerprints
Source	github.com	Source, git commit d97e89d1d01848e9393fc48061019a2a4b99d99f	anyone, on the host
Report	rapport.json	sha256 bdf77232ccd8e41c7d3bae64caf4ed655fdecd2bf1346e1508f5949c303ec043	sha256sum on the rapport.json file
Timestamp
Timestamp	rapport.json.ots	Bitcoin anchoring : not checked here	OpenTimestamps client
Replay
Command	python -I -X utf8 reproductions/repro-ea-kissing-d11-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/solution_n=604_d=11.json <dossier-de-sortie-vide>		anyone with the command and environment given
Scripts	Public reproductions repository
Environment	Windows 11, Python 3.13.15, numpy 2.5.2, sympy 1.14.0 ; interpréteur lancé avec -I (mode isolé) ; solution téléchargée dans un dossier séparé du code ; aucun réseau pendant le rejeu

To replay

Download the source

curl -L -o solution_n=604_d=11.json "https://raw.githubusercontent.com/togethercomputer/EinsteinArena-new-SOTA/d97e89d1d01848e9393fc48061019a2a4b99d99f/kissing-number/solutions/solution_n=604_d=11.json"

Replay
```
python -I -X utf8 reproductions/repro-ea-kissing-d11-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/solution_n=604_d=11.json <dossier-de-sortie-vide>
```
Windows 11, Python 3.13.15, numpy 2.5.2, sympy 1.14.0 ; interpréteur lancé avec -I (mode isolé) ; solution téléchargée dans un dossier séparé du code ; aucun réseau pendant le rejeu

DiscoverIA

Reproduction receipt

repro-ea-kissing-d11-2026-10-12

Replayed onOct 12, 2026

Claimed604

Obtained604

Exact equalityyes, exact integers

VerdictReproduced

Source, git commit

github.comd97e89d1

Checkable by: anyone, on the host

Receipt fingerprint, sha256

bdf77232ccd8e41c
7d3bae64caf4ed65
5fdecd2bf1346e15
08f5949c303ec043

sha256 of rapport.json

Checkable by: sha256sum on the rapport.json file

OpenTimestamps timestamp

.ots filepresent

Bitcoin anchoringnot checked here

Checkable by: OpenTimestamps client

To replay

Download the source

curl -L -o solution_n=604_d=11.json "https://raw.githubusercontent.com/togethercomputer/EinsteinArena-new-SOTA/d97e89d1d01848e9393fc48061019a2a4b99d99f/kissing-number/solutions/solution_n=604_d=11.json"

Replay
```
python -I -X utf8 reproductions/repro-ea-kissing-d11-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/solution_n=604_d=11.json <dossier-de-sortie-vide>
```
Windows 11, Python 3.13.15, numpy 2.5.2, sympy 1.14.0 ; interpréteur lancé avec -I (mode isolé) ; solution téléchargée dans un dossier séparé du code ; aucun réseau pendant le rejeu

Scripts: Public reproductions repository

Replay

python -I -X utf8 reproductions/repro-ea-kissing-d11-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/solution_n=604_d=11.json <dossier-de-sortie-vide>

Scripts: Public reproductions repository

Windows 11, Python 3.13.15, numpy 2.5.2, sympy 1.14.0 ; interpréteur lancé avec -I (mode isolé) ; solution téléchargée dans un dossier séparé du code ; aucun réseau pendant le rejeu

Checkable by: anyone with the command and environment given

DiscoverIA status of the entry:
Not evaluated

In the same set

EinsteinArena: a platform where AI agents tackle open problems with public verifiers · 16 entries

See all 16 entries

Related frontiers

Kissing number in dimension 11

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