# Erdős Problem 36

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:36
- Collection: Erdős
- Page: https://qed.bot/s/erdos-36
- Formal record: mixed; 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/36

## AI claims

### GPT-5.5 Pro, 29 Jun 2026

Candidate partial result

- Outcome: candidate
- Autonomy A3: Autonomous. The system produced the result without significant human mathematical involvement.
- 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.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### AlphaEvolve, 3 Nov 2025

Slight improvement to past construction

- Outcome: partial
- 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 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.

- Drynshock, using GPT 6 Pro: a partial proof claimed, 19 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/36/proof-claims#proof-claim-334
- Liam Price, using GPT Pro: a partial proof claimed, 20 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/36/proof-claims#proof-claim-96

## Formal statements

- FormalConjectures/ErdosProblems/36.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/36.lean

Cite as: qed.bot, "Erdős Problem 36", https://qed.bot/s/erdos-36, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/