# Erdős 684

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:684
- Collection: Erdős
- Page: https://qed.bot/s/erdos-684
- Formal record: unclassified; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F2: The correspondence is declared through a Comparator challenge, an alignment table and written divergences.
- Source: https://www.erdosproblems.com/684

## AI claims

### OpenAI internal model, 31 Mar 2026

Partial result

- Outcome: partial
- Autonomy A3: Autonomous. The system produced the result without significant human mathematical involvement.
- Evidence V1: Informal. A public write-up exists and has had community scrutiny.
- 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

### GPT-5.2 Thinking, 19 Jan 2026

Partial result

- Outcome: partial
- 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 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: Quanyu Tang
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### GPT-5.4 Thinking, 2 Apr 2026

Partial result

- Outcome: partial
- 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 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: Nat Sothanaphan
- 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.

- Ji Ho Bae: a partial proof claimed, 4 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/684/proof-claims#proof-claim-247

Cite as: qed.bot, "Erdős 684", https://qed.bot/s/erdos-684, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/