Kissing number in dimension 11: at least 604 spheres (previous bound 593, 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
In April 2026, AI agents on the EinsteinArena platform reported fitting 604 spheres around a central sphere in dimension 11, up from 593 before.
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-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/en/fiche/ea-kissing-number-d11/#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
Text written by an AI (DiscoverIA pipeline), on Reviewed by: Antoine Olivier, Oct 13, 2026Report an error
What has not been reviewed?
The status and its sources come from the registry; the explanatory text has been reviewed by a human.
The status and its sources come from the registry; the explanatory text has been reviewed by a human.
Key facts
- Claimed by
- agents d'EinsteinArena : un agent (bassin initial), un agent (LSQR + arrondi entier) ; l'extension à 604 est attribuée à « l'agent » sans nom par le papier (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 (domains)
- 9 : 4 read word for word, 5 links only
- This entry
- Reviewed by Antoine Olivier, Oct 13, 2026
To understand
Analogy
Picture a marble at the centre, surrounded by identical marbles that all touch it without overlapping: how many can fit, in a space with far more than three dimensions, impossible to picture?
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.
9 sources.
For experts
Sources(domains)
- primairearxiv.orgpage read word for word · consulted on Oct 12, 2026 ·
improved the best known lower bound from 593 to 604
- primairearxiv.orgpage read word for word · consulted on Oct 12, 2026 ·
a collaborative effort among AI agents improved this lower bound to
- 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
- depotraw.githubusercontent.comlink only, reading not recorded
- source-statuteinsteinarena.compage read word for word · consulted on Oct 12, 2026 ·
A valid 604-point non-overlapping configuration was certified on EinsteinArena.
- depoteinsteinarena.comlink only, reading not recorded
- depoteinsteinarena.comlink only, reading not recorded
- depoteinsteinarena.comlink 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 12 October 2026, the platform listed no valid configuration with 605 spheres. Status “not evaluated” recorded on 12 October 2026 from arxiv.org (page read, quotation checked word for word). it does not count towards the status.
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.
Picture a marble at the centre, surrounded by identical marbles that all touch it without overlapping: how many can fit, in a space with far more than three dimensions, impossible to picture?
In the same set
EinsteinArena: a platform where AI agents tackle open problems with public verifiers · 16 entries
- Not evaluated : Kissing number in dimension 11: at least 604 spheres (previous bound 593, AlphaEvolve)
- Not evaluated : Erdős minimum overlap problem: upper bound 0.380871 (previous 0.380876, TTT-Discover)
- Not evaluated : First autocorrelation inequality: upper bound 1.5028609 (previous 1.5028629, TTT-Discover)
- Not evaluated : Second autocorrelation inequality: lower bound 0.9626 (previous 0.9610, AlphaEvolve)
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.
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