Oct 6, 2026 Not evaluated

Kakeya needle problem, discretised (n=128): area 0.10675394

Platform's cited state of the art: 0.107067

Replayed by DiscoverIA only · level N1

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Author's artefacts

Published solution einsteinarena.com
Repository or problem page einsteinarena.com

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

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In your message: the link to your report (discoveria-rapport-reproduction/1 format), whether you used the author's artefacts, and the name to publish if you agree to it being published.

DiscoverIA reviews each report before publishing it. A replay confirms the computation, not the framework: it does not change the status on its own.

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The gist

For the discretised Kakeya needle problem (n=128), an agent submitted an area of 0.10675394 on October 6, 2026, against 0.107067 cited by the platform (the Station); smaller is better; no DiscoverIA status yet.

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

Status detailsDetails

AI draft, not reviewedWhat has not been reviewed?

Text written by an AI (DiscoverIA pipeline), on Oct 13, 2026. 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.

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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). Kakeya needle problem, discretised (n=128): area 0.10675394 (platform's cited state of the art: 0.107067) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/ea-kakeya-needle-128#releve-1

BibTeX @misc, key discoveria-ea-kakeya-needle-128-r1

@misc{discoveria-ea-kakeya-needle-128-r1,
  author       = {{DiscoverIA}},
  title        = {Kakeya needle problem, discretised (n=128): area 0.10675394 (platform's cited state of the art: 0.107067)},
  howpublished = {DiscoverIA registry, entry ea-kakeya-needle-128},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/ea-kakeya-needle-128#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/ea-kakeya-needle-128#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

If the value holds, the best known swept area would drop from 0.107067 to 0.10675394 on this discretised version of the problem. A reproduction made by DiscoverIA on October 12, 2026 gives the verdict reproduced.

What remains unclear

The platform itself marks the statement and the verifier « Under active review »: this must be confirmed against the literature before calling it a record. No primary source (paper, blog) mentions this result, which is later than the May 2026 paper. The verifier is a public program, not a third party.

For experts

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

Status

Not evaluated

Recorded on Oct 12, 2026 · einsteinarena.com · leaderboard

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

Oct 6, 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, exact), solution publique téléchargeable (API)

Sources

Main sourceeinsteinarena.com · api/problems/kakeya-needle-128link only, reading not recorded
Repositoryeinsteinarena.com · leaderboardpage read word for word · consulted on Oct 12, 2026 · "agentName":"[an agent]","bestScore":0.10675394011230244
Repositoryeinsteinarena.com · bestlink only, reading not recorded
Repositoryeinsteinarena.com · problems/kakeya-needle-128link only, reading not recorded
Reference listeinsteinarena.comlink 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 einsteinarena.com (page read, quotation checked word for word: “"agentName":"[an agent]","bestScore":0.10675394011230244”). 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: an agent, submission of 2026-10-06 (Name replaced by a role)
announced on Oct 6, 2026
Nature: new result
Field: Mathematics (geometry / discretised Kakeya needle problem, 128 triangles)
Checked by: the platform's public checker (a tool); no third party named
Sources: 5 : 1 read word for word, 4 links only
Part of: EinsteinArena: a platform where AI agents tackle open problems with public verifiers
This entry: AI draft, not reviewed

Status history

Only one observation so far.

01Oct 12, 2026
First observation:Not evaluatedCurrent status
not evaluated; the platform marks the statement and the checker “Under active review”
Source: einsteinarena.comread word for word

An observation is added; none is ever erased.

Published reproductions

Reproduction receipt repro-ea-kakeya-needle-128-2026-10-12

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

Statement replayed

Pour n = 128, les 128 décalages publiés (chaînes décimales à 25 décimales au plus) donnent, pour les triangles T_j = enveloppe convexe de (x_j, 0), (x_j + 1/128, 0), (x_j + j/128, 1), j = 1..128, une réunion d'aire 0,10675394011230244 (double renvoyé par le vérificateur public de la plateforme) : C_T(128) <= 0,10675394011230244, contre 0,107067 pour l'état de l'art cité par l'énoncé (la Station, août 2026). La valeur revendiquée est un double : on la note comme le rationnel dyadique exact de ce double.

Evidence, item by item

Reproduction evidence, item by item
Item	Value	Evidence, fingerprint	Checkable by
Result
Claimed value	961554009820195/9007199254740992		reading the source
Value obtained	961554009820195/9007199254740992		anyone with the command and environment given
Equality	yes	arithmetic in exact rationals	anyone with the command and environment given
Fingerprints
Source	einsteinarena.com	Source, content sha256 8a9e475f2c54b96d21b6bb385b04d55d559029a9ad96b83e92eddb9173609c29	anyone, on the host
Report	rapport.json	sha256 2cc7170720e74958f4e9e0732636802381ada0ca0ed22a28f8d79cffe7871f4e	sha256sum on the rapport.json file
Timestamp
Timestamp	rapport.json.ots	Bitcoin anchoring : not checked here	OpenTimestamps client
Replay
Command	python -B -I -X utf8 reproductions/repro-ea-kakeya-needle-128-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/best.json <dossier-téléchargement>/problem.json <dossier-de-sortie-vide>		anyone with the command and environment given
Scripts	Public reproductions repository
Environment	Windows 11, Python 3.13.15 (bibliothèque standard seule pour les moteurs A et B ; shapely 2.1.2 pour le témoin flottant) ; interpréteur lancé avec -B -I ; solution extraite dans un dossier temporaire supprimé à la fin ; aucun réseau pendant le rejeu

To replay

Download the source

curl -L -o best "https://einsteinarena.com/api/solutions/best?problem_id=26&limit=1"

Replay
```
python -B -I -X utf8 reproductions/repro-ea-kakeya-needle-128-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/best.json <dossier-téléchargement>/problem.json <dossier-de-sortie-vide>
```
Windows 11, Python 3.13.15 (bibliothèque standard seule pour les moteurs A et B ; shapely 2.1.2 pour le témoin flottant) ; interpréteur lancé avec -B -I ; solution extraite dans un dossier temporaire supprimé à la fin ; aucun réseau pendant le rejeu

DiscoverIA

Reproduction receipt

repro-ea-kakeya-needle-128-2026-10-12

Replayed onOct 12, 2026

Claimed961554009820195/9007199254740992

Obtained961554009820195/9007199254740992

Exact equalityyes, exact rationals

VerdictReproduced

Source, content sha256

einsteinarena.com8a9e475f2c54b96d…

Checkable by: anyone, on the host

Receipt fingerprint, sha256

2cc7170720e74958
f4e9e07326368023
81ada0ca0ed22a28
f8d79cffe7871f4e

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 best "https://einsteinarena.com/api/solutions/best?problem_id=26&limit=1"

Replay
```
python -B -I -X utf8 reproductions/repro-ea-kakeya-needle-128-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/best.json <dossier-téléchargement>/problem.json <dossier-de-sortie-vide>
```
Windows 11, Python 3.13.15 (bibliothèque standard seule pour les moteurs A et B ; shapely 2.1.2 pour le témoin flottant) ; interpréteur lancé avec -B -I ; solution extraite dans un dossier temporaire supprimé à la fin ; aucun réseau pendant le rejeu

Scripts: Public reproductions repository

Replay

python -B -I -X utf8 reproductions/repro-ea-kakeya-needle-128-2026-10-12/scripts/rejouer.py <dossier-téléchargement>/best.json <dossier-téléchargement>/problem.json <dossier-de-sortie-vide>

Scripts: Public reproductions repository

Windows 11, Python 3.13.15 (bibliothèque standard seule pour les moteurs A et B ; shapely 2.1.2 pour le témoin flottant) ; interpréteur lancé avec -B -I ; solution extraite dans un dossier temporaire supprimé à la fin ; 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

Discretised Kakeya needle (n=128): upper bound on the minimal area

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