OpenAI researcher Ethan Knight said on the 12th on social platform X that GPT-5.6 Sol Ultra generated a proof paper and prompts related to the graph theory open problem known as the cycle double cover conjecture. According to Odaily, the model produced the result in about one hour without using internet search, using a configuration of up to 64 parallel sub-agents.
The publicly shared paper is three pages long. It first reduces the problem to cubic regular graphs, then applies the 8-flow theorem and GF(3) labeling, and uses linear algebra to construct a structure in which each edge is contained in exactly two cycles.
The result has not been published in an academic journal, has not undergone peer review, and has not been verified using formal proof systems such as Lean or Coq. University of Manchester mathematician Thomas Bloom described the proof as “very impressive,” while noting that its references were insufficient.
AI TRENDS | OpenAI Researcher Says GPT-5.6 Sol Ultra Generated Paper Claiming Proof of Cycle Double Cover Conjecture
2026-07-12 08:14:37
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