Claude completes a nine-loop calculation in planar N=4 super-Yang-Mills

Anthropic reports that Claude has taken a scattering-amplitude calculation in planar N=4 super-Yang-Mills to nine loops. Eight loops was the previous record in this simplified model, set by SLAC’s Lance Dixon and collaborators. Researchers use successive “loops” as finer corrections; most calculations stop at two or three because each added loop requires exponentially more computation.

Anthropic says physicist and science writer 4gravitons issued a challenge last month to push past eight loops with only a compute budget an academic could reasonably access. Given a single prompt, Claude ran largely unsupervised for days in Claude Science and solved the problem using methods developed by Dixon and his colleagues, at a total cost of a few thousand dollars. Dixon independently verified the result, and von Hippel wrote about the work for Anthropic’s Science Blog, Yes, Claude can do Nine Loops.