# Erdős Problem 872

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:872
- Collection: Erdős
- Page: https://qed.bot/s/erdos-872
- Formal record: open; 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/872

## AI claims

### GPT-5.2 Pro, 16 Feb 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

### GPT-5.4 Pro, 16 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 F0: Absent. No formal statement is attached to the result.
- With: Om_Buddhdev_sensho
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### GPT-5.5 Pro, 29 Apr 2026

Candidate partial result

- 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: Jonas Silva
- 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.

- Om Buddhdev, using Fable 5, GPT 5.6 Pro, some others over ~400 prompts, 3mo (noted in writeup): a full proof claimed, 30 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/872/proof-claims#proof-claim-170

## Formal statements

- FormalConjectures/ErdosProblems/872.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/872.lean

Cite as: qed.bot, "Erdős Problem 872", https://qed.bot/s/erdos-872, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/