OpenAI states its internal model generated the natural language proof for Yang-Mills existence on Sept 9 and the quantum chromodynamics proof on Sept 18, completing the Lean verification for Yang-Mills by Oct 16. The Yang-Mills result addresses the existence component of the $1 million Clay Millennium Prize problem, which Jaffe co-formulated with Edward Witten, though it does not resolve the full mass gap requirement.

Separately, the computer scientists organizing the independent review of OpenAI’s 67 page pre-print refuting the Exponential Time Hypothesis cautioned in an open letter that their participation “should not be taken as certification” of the result. Original 1999 hypothesis proposers Russell Impagliazzo and Ramamohan Paturi, writing with MIT’s Ryan Williams, noted that “if the claim is correct, it will change an important part of theoretical computer science” by showing 3-SAT problems on n variables can be solved in subexponential time, though OpenAI confirmed the algorithm does not compromise existing cryptosystems or settle P versus NP.