# Largest known cap set in dimension 8

A record target in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: capset:dimension-8
- Collection: Extremal combinatorics
- Page: https://qed.bot/t/capset-dimension-8
- Record: 512 points, held by FunSearch, since 14 Dec 2023
- Machine-checked: yes, by qed.bot
- Source: https://github.com/google-deepmind/funsearch/tree/main/cap_set

## Record history

- 2004: 496 points, Yves Edel; moved the record. https://doi.org/10.1023/a:1027365901231
- 14 Dec 2023: 512 points, FunSearch, with AI; moved the record. https://deepmind.google/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/

## AI claims

### FunSearch, 14 Dec 2023

An explicit cap set of 512 points in dimension 8.

- Outcome: record
- Autonomy A2: Directed. The system produced the result while building on literature or framing supplied to it.
- Evidence V3: Machine-checked. The artifact was rebuilt at a pinned commit by someone other than its authors — qed.bot, or a registry that publishes the check — and it holds: a proof that elaborates on the standard axioms alone, or an object that meets the problem's own constraints. Checked by qed.bot.
- Source: DeepMind, FunSearch, https://deepmind.google/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/

## Checks

- verified, by qed.bot: 512 points in dimension 8, no three collinear (https://github.com/google-deepmind/funsearch/blob/main/cap_set/n8_size512.txt)

Cite as: qed.bot, "Largest known cap set in dimension 8", https://qed.bot/t/capset-dimension-8, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/