OpenAI: GPT-5.6 Sol Ultra Solves a 50-Year-Old Graph Theory Conjecture in 1 Hour

Odaily reports that OpenAI researcher Ethan Knight stated on social platform X on the 12th that GPT-5.6 Sol Ultra has generated a proof paper and prompt regarding the unsolved problem in graph theory, the "Cycle Double Cover Conjecture." Under the configuration of up to 64 parallel sub-agents, without using internet search, the model completed the result generation in about 1 hour.

The paper publicly released by OpenAI is 3 pages long. It first reduces the problem to cubic graphs, then uses the 8-flow theorem and GF(3) labels, and constructs a structure where each edge is contained in exactly two cycles using linear algebraic methods. This result has not yet been published in an academic journal, undergone peer review, nor passed formal verification systems such as Lean or Coq. Thomas Bloom, a mathematician at the University of Manchester, UK, evaluated the proof as "excellent," but noted its lack of sufficient references in the bibliography. (Source: ZDNet Korea Semiconductor).