OpenAI says its GPT-5.6 Sol Ultra model proved the 50-year-old Cycle Double Cover Conjecture

OpenAI published a document on July 10 claiming a proof of the Cycle Double Cover Conjecture, a roughly 50-year-old graph-theory problem, and attributed the argument to its GPT-5.6 Sol Ultra model. The claim has not been peer reviewed or confirmed by mathematicians.

The conjecture, posed independently by mathematicians George Szekeres and Paul Seymour in the 1970s, holds that every bridgeless graph contains a set of cycles covering each edge exactly twice. It is considered one of the major open problems in graph theory, which is what makes a machine-generated proof a notable claim, if it holds up.

GPT-5.6 Sol Ultra is the top tier of the GPT-5.6 model family, which OpenAI made generally available on July 9. In an accompanying post, OpenAI staff said the model produced the proof using 64 subagents in just under an hour, and OpenAI published the prompt alongside the argument.

The caveats are substantial. The proof has not been checked by independent mathematicians, and OpenAI did not disclose the internal structure of the argument, the compute it consumed, how much human editing shaped the released text, or which experts, if any, reviewed the draft before publication. AI systems have produced confident-looking mathematical arguments that later proved flawed, so a self-published document is a starting point for review, not a settled result.

Verification now rests with graph theorists, whose scrutiny of the released proof will decide whether the claim survives contact with the field.