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Erdős·erdos:12

Erdős Problem 12

conjecture formal record: mixed source: open F2 declared

Checked, not verified. 3 independent checks recorded, with verdict not self-contained. The checks are set out below.

Fidelity F2: The statement corpus cites this proof against its own statement.

number theory·Source

AI activity

How grades work
DeepMind prover agent

7 Apr 2026

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

partial A2 V2 F2
Reasoning and sources

Autonomy

AI building on literature supplied to it

Details

literature: 🟡 Erdős and Sárközy (1970)

GPT-5.4 Thinking

7 Apr 2026·with Nat Sothanaphan, Terence Tao

Partial result

partial A1 V1 F2
Reasoning and sources

Autonomy

AI collaborating with humans

Claimed on erdosproblems.com

1

Proof claims posted on erdosproblems.com, which says that listing a claim “is no guarantee of proof correctness”. The register records who claims what, with which systems, and links to each claim there. Nobody has examined them, and none counts in the register's totals.

Philip Ndikum, Serge Ndikum

a partial proof claimed·30 Jul 2026·using Libertas Superintelligence © (open-weight models, white-box reasoning)·2 comments there

Formalisation at commit 7cd9c8a08fc7

candidateA? V0

Fidelity

How fidelity is graded

F2 declared. The statement corpus cites this proof against its own statement.

Checks

3
  • not self-contained·qed.bot

    imports project modules: FormalConjectures.Util.ProblemImports

    proof rebuilt and axioms inspected·2026-08-21

  • not self-contained·qed.bot

    imports project modules: FormalConjectures.Util.ProblemImports

    proof rebuilt and axioms inspected·2026-08-21

  • not self-contained·qed.bot

    imports project modules: FormalConjectures.Util.ProblemImports

    proof rebuilt and axioms inspected·2026-08-21

Follow and discuss

All discussion

Discussion and bounties for this problem load here.

Something wrong or missing here? Request a correction or add a claim, with its sources.

Formal material

Formal statements · 1
Cited proofs · 3

Recorded elsewhere

Compare the registries
  • vibemathed — Erdős Problem #12

    checked·machine-led·their labels: lean-verified, ai-discovered

Also known as · 3
  • https://www.erdosproblems.com/12
  • https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/12.lean
  • FormalConjectures/ErdosProblems/12.lean

Cite this record

qed.bot, “Erdős Problem 12”, https://qed.bot/s/erdos-12, as of 30 Sep 2026.

This record as plain text, with each claim, its grades and its sources.