# Erdős Problem 619

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:619
- Collection: Erdős
- Page: https://qed.bot/s/erdos-619
- Formal record: solved; at its source: solved (Lean)
- 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/619

## AI claims

### Claude Fable 5, Codex, GPT-5.5, 9 Jun 2026

Full solution (Lean)

- Outcome: full
- 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 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.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

## Checks

- not self-contained, by qed.bot: imports project modules: FormalConjectures.Util.ProblemImports (https://github.com/google-deepmind/formal-conjectures/blob/b8c7a76f267c29eaa41d1212c211a920be8b05ea/FormalConjectures/ErdosProblems/619.lean#L6009)
- not self-contained, by qed.bot: imports project modules: Erdos (https://github.com/nick-kuhn/erdos-619/blob/7f65718b8c1019ecc24e6c9a6b04ec4c66a4e26f/Solution.lean#L5869)

## Formal statements

- FormalConjectures/ErdosProblems/619.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/619.lean

Cite as: qed.bot, "Erdős Problem 619", https://qed.bot/s/erdos-619, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/