AI 中文总结
介绍 OpenAI 对圈双覆盖猜想的证明，该猜想称无桥图有特定圈列表使每条边恰在两个圈中，阐述对证明做了微调以便更易理解。
AI 中文摘要
圈双覆盖猜想指出，每个无桥图都有一个圈列表，使得每条边恰好位于其中两个圈中。2026年7月，OpenAI宣布了一个证明。本阐述给出了该证明，并做了一些微调使其更易懂。
英文摘要
The cycle double cover conjecture states that every bridgeless graph has a list of cycles such that every edge is in exactly two of them. In July 2026, OpenAI announced a proof. This exposition presents the proof with slight modifications intended to make it more accessible.
Comments10 pages; Adding subsections on small cycle double cover conjecture (suggested by Adrian Bondy) and implications to matroids, due to Jamshy and Tarsi
