Cycle Double Cover Conjecture
Statement
Conjectures that every bridgeless graph has a collection of cycles covering each edge exactly twice.
Context
Szekeres-Seymour; one of the most famous open problems in graph theory, in every textbook.
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Attempts
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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.
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Machine check · not human verification
machine: partially checkedscope 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 Not peer-reviewed; the Cycle Double Cover Conjecture has a history of claimed proofs later found to have gaps, so mathematicians are treating it cautiously pending independent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
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