Cycle Double Cover Conjecture
Conjectures that every bridgeless graph has a collection of cycles covering each edge exactly twice.
- Result
- Proved
- Field
- Graph Theory
- Posed by
- Multiple mathematicians independently (e.g. Szekeres, Seymour)
- Year posed
- 1973
- Years open
- 53y
- Solved
- 2026-07-11
- Model
- GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Pending peer review
- Notability
- 2 Wikipedia languages
What the AI did
Directed to persist on the problem for at least 8 hours before giving up. Produced a proof that any applicable graph can be doubly covered using at most eight loops, with known technical exceptions. Synthesized and extended existing human techniques rather than inventing new ones.
Verification
Announcement was timed to GPT-5.6 Sol's public release. Coverage says it "seems to have settled the question" but does not confirm independent peer review.