GPT-5.6 Sol Ultra claims proof of Cycle Double Cover Conjecture
Original: GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture [pdf]
Why This Matters
If verified, this would mark a historic milestone for AI solving a decades-old open problem in mathematics.
OpenAI's GPT-5.6 Sol Ultra model has reportedly produced a mathematical proof of the Cycle Double Cover Conjecture, a longstanding open problem in graph theory. The proof document was published as a PDF on OpenAI's CDN, suggesting an official release.
A PDF hosted on OpenAI's official content delivery network indicates that GPT-5.6 Sol Ultra — an advanced reasoning model from OpenAI — has generated a purported proof of the Cycle Double Cover Conjecture (CDC Conjecture). The CDC Conjecture is a well-known unsolved problem in graph theory, first proposed in the 1970s, which states that every bridgeless graph has a collection of cycles that together cover every edge exactly twice. No general proof has been accepted by the mathematical community to date. The document appears to be a formal mathematical paper produced by the model, representing a significant claim if verified by independent mathematicians. OpenAI has not yet issued a public press statement, but the hosting of the PDF on its CDN suggests the company is presenting this as a notable output of its latest model. Independent verification by the mathematics community will be essential before the proof can be considered valid.