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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.

Source

Scientific American