OpenAI claims its model proved a graph theory conjecture open since 1973

OpenAI says its model proved a conjecture that stood open for half a century.

The Cycle Double Cover Conjecture, posed in 1973, asks whether every bridgeless graph contains a set of cycles that covers each edge exactly twice. It is one of graph theory’s stubborn classics: generations of graph theorists chipped away at it without closing it.

How the proof was produced

On July 10, 2026, OpenAI reported that GPT-5.6 Sol Ultra produced a proof in just under one hour. The method is as notable as the result: the system ran 64 subagents that pursued competing approaches, audited each other, and rejected partial arguments along the way.

That structure looks less like a single model having an insight and more like a self-contained research group: parallel attempts, adversarial review, and dead ends discarded internally before anything was published.

One more detail stands out. Authorship of the published proof PDF is credited to the model itself, according to OpenAI.

The honest caveat

The proof has not passed peer review yet, and that caveat deserves full weight here, because this particular conjecture has broken several human “proofs” before. A 50-year-old problem accumulates failed attempts, and some of them looked convincing until reviewers found the gap.

Working mathematicians are reading the proof right now. Until they finish, the accurate status is “claimed,” not “closed.”

What it means if it holds

If the proof survives review, this becomes one of the first major named conjectures closed by an AI system. That would be a milestone of a different kind than benchmark wins: not performing well on problems with known answers, but settling a question no human had settled.

It would also force an interesting question about the 64-subagent approach. If competing, mutually auditing AI agents can compress decades of stalled progress into an hour, the bottleneck in mathematics starts to look different. And there is the deeper question the authorship credit raises: would you trust a proof no human wrote? Peer review is about to give its first real answer.