# Erdős Problem 501

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:501
- Collection: Erdős
- Page: https://qed.bot/s/erdos-501
- Formal record: mixed; at its source: not disprovable
- Machine-checked: no independent check has verified it
- Fidelity F2: The correspondence is declared through a Comparator challenge, an alignment table and written divergences.
- Source: https://www.erdosproblems.com/501

## AI claims

### GPT-5.5 Pro, 1 Jun 2026

Candidate conditional partial result (conditional solution to first part)

- 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 F2: Declared. The authors record how the formal statement corresponds to the claim — a comparator challenge, an alignment table or written divergences — or a statement corpus cites the proof against its own statement.
- 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.

- Elliot Glazer, using GPT5.6 Sol, Fable 5, Opus 4.8: a full proof claimed, 17 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/501/proof-claims#proof-claim-207

## Formal statements

- FormalConjectures/ErdosProblems/501.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/501.lean

Cite as: qed.bot, "Erdős Problem 501", https://qed.bot/s/erdos-501, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/