OpenAI's GPT-5.6 Sol Ultra Claims Proof of 50‑Year‑Old Cycle Double Cover Conjecture

OpenAI announced that its latest artificial‑intelligence model, GPT‑5.6 Sol Ultra, produced a proof of the Cycle Double Cover Conjecture, a graph‑theory problem that has remained unsolved for about 50 years. The claim was posted on X by OpenAI researcher Ethan Knight on July 12, with a PDF of the paper and the prompting details. According to the announcement, the model ran up to 64 parallel sub‑agents, avoided internet searches, and completed the proof in roughly one hour, using a reduction to cubic graphs, the 8‑flow theorem, GF(3) edge labeling and linear‑algebraic construction. The resulting document is a three‑page paper that has not undergone peer review or formal verification, prompting cautious scrutiny from mathematicians. University of Manchester mathematician Thomas Bloom described the work as "a very impressive proof," while also noting missing citations and the lack of formal checks. The mathematics community plans to examine the logical steps over the coming days and weeks before judging its validity.

The announcement has drawn attention across the AI and mathematics fields, highlighting both the potential of large‑scale models to tackle deep theoretical problems and the need for rigorous validation of AI‑generated proofs.