# Erdős Problem 346

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:346
- Collection: Erdős
- Page: https://qed.bot/s/erdos-346
- Formal record: solved; at its source: solved
- Machine-checked: yes, by qed.bot
- Fidelity F1: A formal artifact exists, but nothing records that its statement says what the claim says.
- Source: https://www.erdosproblems.com/346

## AI claims

### Codex, GPT-5.5 Pro, 19 Jun 2026

Solution to variant problem (Lean)

- Outcome: partial
- Autonomy A3: Autonomous. The system produced the result without significant human mathematical involvement.
- Evidence V3: Machine-checked. The artifact was rebuilt at a pinned commit by someone other than its authors — qed.bot, or a registry that publishes the check — and it holds: a proof that elaborates on the standard axioms alone, or an object that meets the problem's own constraints. Checked by qed.bot.
- Fidelity F1: Unaudited. A formal artifact exists, but nothing records that its statement says what the claim says.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### Codex, GPT, 21 Jun 2026

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 V3: Machine-checked. The artifact was rebuilt at a pinned commit by someone other than its authors — qed.bot, or a registry that publishes the check — and it holds: a proof that elaborates on the standard axioms alone, or an object that meets the problem's own constraints. Checked by qed.bot.
- Fidelity F1: Unaudited. A formal artifact exists, but nothing records that its statement says what the claim says.
- With: Kenta Kitamura
- 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.

- Liam Price, using GPT Pro, GPT 5.5: a full proof claimed, 15 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/346/proof-claims#proof-claim-59

## Checks

- verified, by qed.bot: 346 theorems on the standard axioms only (https://github.com/kitaken1/erdos346-ratio-limit-lean/blob/main/346lean/LimitExistsVariant.lean)

## Formal statements

- FormalConjectures/ErdosProblems/346.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/346.lean

Cite as: qed.bot, "Erdős Problem 346", https://qed.bot/s/erdos-346, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/