OpenAI researcher Ethan Knight said on X on July 12 that GPT-5.6 Sol Ultra generated a proof paper and prompting setup for the cycle double cover conjecture, a well-known unsolved problem in graph theory. According to Knight, the model completed the result in about one hour, using up to 64 parallel sub-agents and without internet search.
OpenAI’s public paper is three pages long. It first reduces the problem to cubic regular graphs, then uses the 8-flow theorem and GF(3) labels, and applies linear algebra to build a structure in which each edge is contained in exactly two cycles. The claim has not been published in an academic journal, has not gone through peer review, and has not been checked by formal verification systems such as Lean or Coq.
Thomas Bloom, a mathematician at the University of Manchester in the UK, called the proof “very impressive” while also saying the references were not sufficient. The report was cited by ZDNet Korea Semiconductor and carried by Odaily.
OpenAI researcher Ethan Knight said on X on July 12 that GPT-5.6 Sol Ultra generated a proof paper and prompt set for the cycle double cover conjecture, a representative unsolved problem in graph theory. He said the model produced the result in about one hour, with up to 64 parallel sub-agents and without using internet search.
A three-page paper outlines the approach
The paper released by OpenAI is three pages long. It reduces the problem to cubic regular graphs, then uses the 8-flow theorem and GF(3) labels, before applying linear algebra to construct a structure in which each edge appears in exactly two cycles.
No journal publication or formal verification yet
The result has not been published in an academic journal and has not undergone peer review. It also has not been verified through formal systems such as Lean or Coq.
Early reaction from a mathematician
Thomas Bloom, a mathematician at the University of Manchester in the UK, described the proof as “very impressive,” while adding that its references were insufficient.
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