# Erdős Problem 12

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:12
- Collection: Erdős
- Page: https://qed.bot/s/erdos-12
- Formal record: mixed; at its source: open
- 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/12

## AI claims

### DeepMind prover agent, 7 Apr 2026

Partial result (Lean) (solutions to first part and second part)

- 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 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

### GPT-5.4 Thinking, 7 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 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: Nat Sothanaphan, Terence Tao
- 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.

- Philip Ndikum, Serge Ndikum, using Libertas Superintelligence © (open-weight models, white-box reasoning): a partial proof claimed, 30 Jul 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/12/proof-claims#proof-claim-172

## Checks

- not self-contained, by qed.bot: imports project modules: FormalConjectures.Util.ProblemImports (https://github.com/mo271/formal-conjectures/blob/118a6a60df73a9f47d6c89f3cdb3786eaa2e8d0a/FormalConjectures/ErdosProblems/12.lean#L740)
- not self-contained, by qed.bot: imports project modules: FormalConjectures.Util.ProblemImports (https://github.com/mo271/formal-conjectures/blob/2663234a28260853790aa5752d8d4550ff0ab1ca/FormalConjectures/ErdosProblems/12.lean#L39)
- not self-contained, by qed.bot: imports project modules: FormalConjectures.Util.ProblemImports (https://github.com/mo271/formal-conjectures/blob/8d872b465955e46e2d28bc165d186ea41fd0da9e/FormalConjectures/ErdosProblems/12.lean#L810)

## Formal statements

- FormalConjectures/ErdosProblems/12.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/12.lean

Cite as: qed.bot, "Erdős Problem 12", https://qed.bot/s/erdos-12, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/