# Erdős Problem 1054

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:1054
- Collection: Erdős
- Page: https://qed.bot/s/erdos-1054
- Formal record: open; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F2: The correspondence is declared through an alignment table and written divergences.
- Source: https://www.erdosproblems.com/1054

## AI claims

### Claude Opus 4.8, GPT-5.5 Pro, Principia Math, 23 Jun 2026

Partial result (Lean)

- Outcome: partial
- 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/1054.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/1054.lean

Cite as: qed.bot, "Erdős Problem 1054", https://qed.bot/s/erdos-1054, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/