# Erdős Problem 521

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:521
- Collection: Erdős
- Page: https://qed.bot/s/erdos-521
- Formal record: solved; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F2: The statement corpus cites this proof against its own statement.
- Source: https://www.erdosproblems.com/521

## AI claims

### GPT-5.5 Pro, 25 Apr 2026

Solution to variant problem

- Outcome: partial
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V1: Informal. A public write-up exists and has had community scrutiny.
- 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: Vjekoslav Kovač
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### GPT-5.5 Pro, 30 Apr 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 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: Vjekoslav Kovač
- 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.

- XianJun An, Vincent Lin, using GPT 5.5 Pro: a full proof claimed, 1 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/521/proof-claims#proof-claim-178
- Rob Sneiderman, using GPT 5.6 Sol: a full proof claimed, 21 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/521/proof-claims#proof-claim-98

## Formal statements

- FormalConjectures/ErdosProblems/521.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/521.lean

Cite as: qed.bot, "Erdős Problem 521", https://qed.bot/s/erdos-521, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/