# Erdős Problem 488

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:488
- Collection: Erdős
- Page: https://qed.bot/s/erdos-488
- Formal record: open; at its source: falsifiable
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://www.erdosproblems.com/488

## AI claims

### Aristotle, 27 Nov 2025

New solution to variant problem (Lean)

- Outcome: partial
- Autonomy A2: Directed. The system produced the result while building on literature or framing supplied to it.
- 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.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### Aristotle, GPT-5.4, 20 Mar 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 F0: Absent. No formal statement is attached to the result.
- With: Przemek Chojecki
- 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.

- shoal-rat (project curator), using GPT-6 Astra (OpenAI Codex): a partial proof claimed, 29 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/488/proof-claims#proof-claim-372
- Declan Gessel, using GPT-6 Astra (Codex): a full proof claimed, 5 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/488/proof-claims#proof-claim-266
- Lucas Ewing, using GPT 5.6: a partial proof claimed, 28 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/488/proof-claims#proof-claim-225

## Formal statements

- FormalConjectures/ErdosProblems/488.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/488.lean

Cite as: qed.bot, "Erdős Problem 488", https://qed.bot/s/erdos-488, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/