The Pulse
Claude Computes a Nine-Loop Particle-Physics Amplitude
Anthropic says Claude computed a nine-loop, six-particle scattering amplitude in planar N=4 super Yang-Mills. Physicist Lance Dixon checked the result, which Claude reached using two established calculation methods.
AI.info Team ·
“I thought it would be too hard to do the amplitude directly.”
Lance Dixon, professor of particle physics and astrophysics at SLAC and Stanford
Dixon was describing a calculation that Claude had completed: a nine-loop, six-particle scattering amplitude in planar N=4 super Yang-Mills, a mathematical model physicists use to test calculation methods. Anthropic published the account on September 25, 2026, in a guest post by physicist and science writer Matt von Hippel, with an addendum from Dixon, who checked the result.
A challenge from amplitude physics
Von Hippel had challenged AI companies to tackle a difficult scattering-amplitude problem using computing resources within reach of an academic researcher. Anthropic researchers Liam Fitzpatrick and Siddharth Mishra-Sharma chose the nine-loop calculation in N=4 super Yang-Mills. In these calculations, “loops” mark successive layers of interaction complexity; higher loop counts generally demand more computation.
The target is a six-particle, or hexagon, amplitude. N=4 super Yang-Mills is not a description of the physical world, but a simplified theory that researchers use to develop and test techniques. The achievement is a calculation in that model, not a new prediction about particles observed in nature.
Two routes to the same result
According to von Hippel, Claude completed the calculation using two approaches: a direct bootstrap and a route through a related quantity called a form factor. A bootstrap starts with a set of possible answers and applies known constraints to narrow them down. Dixon says he checked Claude’s amplitude result largely by translating it back into the form-factor calculation.
The work ran through Fable 5.1 in Claude Science, using Python and the SymPy package for the bootstrap calculation. Von Hippel estimates that either approach would cost an end user roughly $1,000 to $2,000, largely because of the extended model use. He separately puts the bootstrap’s computing expense at about $100, corresponding to 96 CPUs running for a week.
Dixon checked the calculation
Dixon says the result stood out not simply because of the computing load, but because the calculation depended on a fragile workflow with many details that can cause a run to fail. Claude wrote the code for the calculation from scratch, according to his account. Dixon independently checked the result, using the form-factor relationship that he and collaborators had developed in earlier work.
A second effort came from a group led by Song He. Dixon’s addendum says the group computed the symbol portion of the nine-loop amplitude with help from GPT-6 on some constraints, but did not use AI to build the overall framework. The two efforts show that Claude’s result arrived alongside human-led work on the same problem, rather than revealing a wholly inaccessible calculation.
A hard calculation, not new physics
Von Hippel’s assessment is more measured than the headline achievement might suggest. He writes that Claude used established methods and more computing than researchers had previously tried, rather than producing a new physical principle. He also argues that the work suggests some technically daunting problems may be more tractable with programming and computing resources than specialists expect.
The result demonstrates that Claude completed a demanding, well-defined calculation with limited scientific direction, and that a domain expert checked the output. It does not establish that the system can formulate new theories or transfer the same performance to less structured problems. The concrete result is a nine-loop amplitude in a mathematical model, checked by Dixon.