Anthropic announces Claude computed nine-loop N=4 super-Yang-Mills amplitude

On September 26 Beijing time, Anthropic formally announced that its large model Claude completed a nine-loop six-particle scattering amplitude in planar N=4 super-Yang-Mills theory on the Claude Science platform, running with minimal human supervision over several days. The result breaks the eight-loop record set in 2023 by Lance Dixon and collaborators at the SLAC National Accelerator Laboratory, and marks the first time a large language model has pushed the world record in this long-standing frontier of theoretical physics.

During the run, two Anthropic physicists described the task to Claude and then checked progress every four to six hours, requiring almost no continuous intervention. Claude used two independent routes — a direct route with Python and SymPy that ran for one week on 96 CPUs with pure compute cost of about $100, and a second independent route for cross-validation. Including Claude’s long-horizon inference cost, a single complete route came in at roughly $1,000 to $2,000. Dixon independently verified the final expression and confirmed it satisfies regression checks against all known physical limits.

The nine-loop six-particle amplitude is not a description of real-world particle physics but an idealized laboratory for stress-testing new computational methods. Each additional loop makes the perturbative expansion grow in factorial-like complexity, and the public record has been stuck at eight loops for years. Anthropic stresses that Claude did not invent new physical methods — it completed the reduction chain a research team would normally execute — but the combination of long-horizon unsupervised symbolic reasoning, physical-limit unit tests, and external independent verification is being treated as a new operating pattern for agents on hard-science problems. On the same cycle, Song He’s group at the Chinese Academy of Sciences separately announced it had used GPT-6 to reach nine loops on a partially overlapping target.