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OpenAI PDF Asserts Proof of the Cycle Double Cover Conjecture

A document hosted on OpenAI's servers claims an AI cracked a famous graph theory problem, but the model cited isn't a known public release.

A PDF hosted on OpenAI's servers claims that an AI produced a complete proof of the Cycle Double Cover Conjecture, one of the most durable open problems in graph theory.

The paper appeared online linked to a file on OpenAI's content delivery network. It credits the proof to a model called "GPT-5.6 Sol Ultra" — an identifier that matches no publicly announced OpenAI product. The Cycle Double Cover Conjecture asks whether every bridgeless graph can be decomposed into cycles that cover each edge exactly twice; the problem has sat unsolved for roughly five decades. OpenAI has not issued any statement, and no peer review has been announced.

If the proof holds, this would be a different kind of milestone than any AI math result so far — not a benchmark win or a verified existing proof, but original structural reasoning on a hard open problem. That distinction matters: it would shift AI from math assistant to math author.

The more immediate question is whether "GPT-5.6 Sol Ultra" is a typo, an internal codename, or a signal of an unannounced release — and mathematicians will need weeks, not hours, to answer the other one.

TR

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