Open Conjecture Board

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The Cycle Double Cover conjecture (Szekeres 1973, Seymour 1979): every bridgeless graph has a family of cycles covering each edge exactly twice.

Resolution reported — pending verification

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

Assessment

Renown 4/5

Among the most famous open problems in graph theory (Szekeres 1973, Seymour 1979).

Attackability 2/5

A counterexample must be a snark of girth at least 12, none known to exist; fell to an AI-generated proof instead.

finite witness
5/5
oracle cost
2/5
freshness
1/5
seedability
2/5

Reported resolution

proof by GPT-5.6 Sol Ultra (OpenAI); arXiv exposition by Sang-il Oum on .

AI-generated proof announced by OpenAI with the prompt and a Lean formalization published alongside; independent expert exposition on arXiv within days. Not yet refereed.

Evidence

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

I’m attacking this

Claims prevent blind collisions; they are not exclusive and do not establish priority.