# Smallest dimension in which Borsuk's conjecture is known to fail

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: borsuk:dimension
- Collection: Discrete geometry
- Page: https://qed.bot/t/borsuk-dimension
- Record: 63, held by Max Grinsztajn, with GPT-5.5 Pro, since 26 May 2026
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://github.com/maaxgrin/borsuk-63-counterexample

## Record history

- 1993: 1325, Jeff Kahn and Gil Kalai; moved the record. https://doi.org/10.1090/s0273-0979-1993-00398-7
- 2003: 298, Aicke Hinrichs and Christian Richter; moved the record. https://doi.org/10.1016/s0012-365x(02)00833-6
- May 2013: 65, Andriy Bondarenko; moved the record. https://arxiv.org/abs/1305.2584
- Aug 2013: 64, Thomas Jenrich; moved the record. https://arxiv.org/abs/1308.0206
- 26 May 2026: 63, Max Grinsztajn, with GPT-5.5 Pro, with AI; moved the record. https://github.com/maaxgrin/borsuk-63-counterexample
- 12 Aug 2026: 63, Yibo Ji, with GPT 5.6 Sol, with AI; did not move the record. https://arxiv.org/abs/2608.12561

## AI claims

### GPT-5.5 Pro, 26 May 2026

A 321-point set in dimension 63 that cannot be split into 64 parts of smaller diameter, improving 64.

- Outcome: record
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V2: Artifact reported. A proof or a constructed object is published, but nobody independent of its authors has rebuilt it.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: Max Grinsztajn
- Source: Grinsztajn, A 63-dimensional counterexample to Borsuk's conjecture, https://github.com/maaxgrin/borsuk-63-counterexample

### GPT-5.6 Sol, 12 Aug 2026

The same dimension, 63, from a construction the author said was generated entirely by ChatGPT; withdrawn on 14 August when he found the earlier posting.

- Outcome: matched
- Autonomy A3: Autonomous. The system produced the result without significant human mathematical involvement.
- Evidence V2: Artifact reported. A proof or a constructed object is published, but nobody independent of its authors has rebuilt it.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: Yibo Ji
- Source: Ji, An AI generated counterexample to Borsuk problem in dimension 63 (withdrawn), https://arxiv.org/abs/2608.12561

Cite as: qed.bot, "Smallest dimension in which Borsuk's conjecture is known to fail", https://qed.bot/t/borsuk-dimension, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/