GPT-5.6 Claims to Solve a 50-Year-Old Math Problem. Nobody Can Confirm It.

OpenAI just published a 3-page proof of the Cycle Double Cover Conjecture. The conjecture has been open for 50 years. The proof was generated entirely by GPT-5.6 Sol Ultra using 64 cooperating agents. There is one problem. Nobody has verified that the proof is correct. The Cycle Double Cover Conjecture is one of those problems that sounds simple enough for an undergraduate to understand but has resisted some of the best graph theorists alive. Every bridgeless graph (a graph you cannot disconnect by removing a single edge) should have a collection of cycles that covers each edge exactly twice. That is it. Paul Seymour, Paul Tutte, and others posed versions of it going back to the 1970s. Nobody proved it. Until maybe now. What OpenAI Published On July 10, 2026, OpenAI released two documents. The first is a 3-page proof. The second is the prompt they used to get the model to produce it. Both are available on their CDN. The proof itself is compact. It reduces the problem to cubic graphs (graphs where every vertex has degree 3), uses the 8-flow theorem to label edges with elements of a finite field, and then converts that labeling into a cycle double cover through a linear algebra argument. The key step is Lemma 2.2, which claims that a certain system of equations always has a solution. The proof PDF states: "The proof in this note is entirely due to GPT 5.6 Sol Ultra and the writeup with Codex (with GPT 5.6 Sol)." That is a remarkable claim. No human mathematician is credited with the proof itself. You can read it yourself here: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf The Prompt Is the Real Story The prompt OpenAI used is just as interesting as the proof. It is not a simple "prove this" instruction. It is a detailed engineering document for a multi-agent search system. The prompt tells the model to use "multiagent v2" with up to 64 concurrent agents. It specifies how agents should explore different mathematical approaches independen