# Erdős Problem 306

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:306
- Collection: Erdős
- Page: https://qed.bot/s/erdos-306
- Formal record: mixed; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://www.erdosproblems.com/306

## AI claims

### Claude, Claude Code, 17 Jun 2026

Partial result (Lean)

- Outcome: partial
- 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 F0: Absent. No formal statement is attached to the result.
- With: Shisheng Li
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### Unspecified, 19 Jun 2026

Candidate full solution (Lean)

- Outcome: candidate
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V0: Claimed. No public artifact, or the claim is marked unverified at source.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: Yuren Tang
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### GPT-5.2 Thinking, 25 Feb 2026

Partial results found

- Outcome: partial (a supporting task)
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V1: Informal. A public write-up exists and has had community scrutiny.
- Fidelity F0: Absent. No formal statement is attached to the result.
- 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.

- Shisheng Li, using GPT-5.6-sol, GPT-6-astra, Claude Opus 5.5: a full proof claimed, 29 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/306/proof-claims#proof-claim-371

## Formal statements

- FormalConjectures/ErdosProblems/306.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/306.lean

Cite as: qed.bot, "Erdős Problem 306", https://qed.bot/s/erdos-306, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/