# Erdős 81

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:81
- Collection: Erdős
- Page: https://qed.bot/s/erdos-81
- 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/81

## AI claims

### Aristotle, GPT-5.5 Pro, 19 Jun 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: Wouter van Doorn
- 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.

- Juan Pablo Traverso Gianini, using models from OpenAI, Anthropic, Aristotle from Harmonic: a full proof claimed, 22 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/81/proof-claims#proof-claim-337
- Morluto, Yang Luo, Yinzhen Huang, Grace Lee, using GPT-5.6, GPT-6 Astra: a full proof claimed, 8 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/81/proof-claims#proof-claim-285
- Juan Pablo Traverso, using GPT, Claude, Gemini, Aristotles: a partial proof claimed, 29 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/81/proof-claims#proof-claim-235
- Ricky Cipollini: a partial proof claimed, 10 Aug 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/81/proof-claims#proof-claim-201

Cite as: qed.bot, "Erdős 81", https://qed.bot/s/erdos-81, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/