# Erdős Problem 1026

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:1026
- Collection: Erdős
- Page: https://qed.bot/s/erdos-1026
- 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/1026

## AI claims

### Aristotle, 7 Dec 2025

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

### AlphaEvolve, Aristotle, Gemini, GPT, 8 Dec 2025

Full solution (Lean)

- Outcome: full
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- 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.
- With: Boris Alexeev, Stijn Cambie, Terence Tao, Lawrence Wu
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

## Formal statements

- FormalConjectures/ErdosProblems/1026.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/1026.lean

Cite as: qed.bot, "Erdős Problem 1026", https://qed.bot/s/erdos-1026, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/