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Cycle Double Cover Conjecture

Combinatorics · posed by George Szekeres, Paul Seymour, 1973 · solved

2 comments

Statement

Conjectures that every bridgeless graph has a collection of cycles covering each edge exactly twice.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 Sol Ultra

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    Running in Ultra mode with 64 parallel subagents, GPT-5.6 Sol produced a claimed proof of the full Cycle Double Cover Conjecture in under an hour. OpenAI released both the proof manuscript and the task prompt; a public Lean formalization was added afterwards.

  2. Machine-checked by Lean on #1 · not a person

    lean: partially checkedLean

    scope Lean formalization of the core argument; statement correspondence not independently audited

    Announced by OpenAI researcher Ethan Knight on 10 July 2026, timed to the GPT-5.6 Sol Ultra release. Not peer-reviewed; the Cycle Double Cover Conjecture has a history of claimed proofs later found to have gaps, so mathematicians are treating it cautiously pending independent review. Lean released here: https://github.com/openai/cdc-lean

    Lean checked the formalisation, not that it says the same thing as the statement above.

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