# Erdős Problem 623

A statement 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: erdos:623
- Collection: Erdős
- Page: https://qed.bot/s/erdos-623
- Formal record: open; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://www.erdosproblems.com/623

## AI claims

### GPT-5.5 Pro, 4 Jun 2026

Candidate full solution

- Outcome: candidate
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V0: Claimed. No public artifact, or the claim is marked unverified at source.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: Sungchul Lee
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

## Claimed on erdosproblems.com

Proof claims posted on erdosproblems.com, which says that listing a claim is no guarantee of proof correctness. Nobody has examined them, and none counts in the register's totals.

- Casey Crawford, using Claude Sonnet 5 High, ChatGPT 5.6 Luna (Thinking): a partial proof claimed, 21 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/623/proof-claims#proof-claim-216

## Formal statements

- FormalConjectures/ErdosProblems/623.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/623.lean

Cite as: qed.bot, "Erdős Problem 623", https://qed.bot/s/erdos-623, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/