An OpenAI model may have solved the Cycle Double Cover Conjecture, a decades-old problem in graph theory, according to a three-page paper hosted on OpenAI’s official content-delivery network. The paper claims the proof was produced entirely by GPT-5.6 Sol Ultra, with Codex and GPT-5.6 Sol helping turn the work into a written paper. The conjecture asks whether every connected network without a critical single point of failure can be covered by a collection of loops so that every connection appears exactly twice. The paper’s argument first reduces the problem to a simpler category of networks where every point has exactly three connections, then uses an established mathematical tool known as a “flow” to assign labels, reorganizing them so connections naturally form loops, with the remaining mismatch resolved using linear algebra. If independent mathematicians confirm the proof, it would be evidence that advanced AI systems may be able to generate original mathematics strong enough to solve problems humans have struggled with for years. For now, the result remains a claimed proof rather than an accepted breakthrough.