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.
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.