# Erdős Problem 205

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:205
- Collection: Erdős
- Page: https://qed.bot/s/erdos-205
- Formal record: mixed; at its source: disproved (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/205

## AI claims

### Aristotle, GPT-5.2 Thinking, 10 Jan 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

## Formal statements

- FormalConjectures/ErdosProblems/205.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/205.lean

Cite as: qed.bot, "Erdős Problem 205", https://qed.bot/s/erdos-205, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/