# Erdős Problem 848

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:848
- Collection: Erdős
- Page: https://qed.bot/s/erdos-848
- Formal record: solved; at its source: decidable
- Machine-checked: no independent check has verified it
- Fidelity F2: The statement corpus cites this proof against its own statement.
- Source: https://www.erdosproblems.com/848

## AI claims

### Gemini 3.1 Pro, GPT-5.2 Thinking, GPT-5.4 Thinking, 23 Mar 2026

Derived explicit bound; Partial result of variant problem

- Outcome: full
- Autonomy A2: Directed. The system produced the result while building on literature or framing supplied to it.
- 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

### Claude Opus 4.6, GPT-5.4, 15 Mar 2026

Incorrect proof found

- Outcome: incorrect
- 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: Malek Zribi
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### GPT-5, 20 Nov 2025

Full solution

- Outcome: full
- 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: Mehtaab Sawhney, Mark Sellke
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### Aristotle, Claude, GPT-5.2, 28 Jan 2026

Sawhney (2025)

- Outcome: full (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 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

## 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.

- Alex Chengyu Li, using OpenAI ChatGPT 5.5, OpenAI ChatGPT 5.6, a personally developed AI-assisted research, proof-engineering system: a full proof claimed, 16 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/848/proof-claims#proof-claim-204

## Formal statements

- FormalConjectures/ErdosProblems/848.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/848.lean

Cite as: qed.bot, "Erdős Problem 848", https://qed.bot/s/erdos-848, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/