# Erdős 1039

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:1039
- Collection: Erdős
- Page: https://qed.bot/s/erdos-1039
- Formal record: unclassified; 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/1039

## AI claims

### GPT-5.5 Pro, 7 May 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 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

### Aristotle, Claude Opus 4.6, 8 Mar 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: Houi
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### Codex, GPT-5.5, 15 May 2026

GPT-5.5 Pro (2026)

- 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

### GPT-5.5 Thinking, 8 May 2026

GPT-5.5 Pro (2026)

- 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.

- Yujian Geng, Dong Qiu, using ChatGPT: a full proof claimed, 9 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/1039/proof-claims#proof-claim-288

Cite as: qed.bot, "Erdős 1039", https://qed.bot/s/erdos-1039, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/