The Cycle Double Cover Conjecture

Proved — OpenAI's GPT-5.6 Sol, released 10 July 2026: every bridgeless graph admits a cycle double cover with at most eight cycles. Published alongside the prompt: hours-long effort budgets, parallel sub-agents cross-checking each other's work, and instructions not to give up — a methodology as notable as the mathematics. Human reviewers confirmed the argument combines previously known techniques with unusual patience rather than fundamentally new tools. As with the unit-distance disproof two months earlier, the pattern repeats: the machinery existed; no human had assembled it.

Context: conjectured independently by Szekeres (1973) and Seymour (1979); it implies a trail of weaker statements (e.g. the Berge–Fulkerson conjecture) still open. The eight-cycle strong form was the folklore quantitative target — small enough to be useful, large enough to seem reachable — and reaching it by patience rather than new machinery is itself the news.