The Claude nine loops calculation of the six-particle amplitude in planar N=4 super Yang-Mills was announced by Anthropic on September 25, 2026: the model beat the eight-loop record of Lance Dixon and Yu-Ting Liu from August 2023.
What happened?
Physicist Matt von Hippel described the episode in a guest post on Anthropic’s research site. Liam Fitzpatrick and Siddharth Mishra-Sharma ran Claude Fable 5.1 in Claude Science. The first prompt asked for the six-particle hexagon amplitude at nine loops. Human messages then mostly told the model to keep going and report every four to six hours.
The system used two known routes: a direct amplitude bootstrap and the form-factor path with antipodal duality. Files dated September 16 follow Dixon’s format and sit on Zenodo. Dixon validated the answer independently.
Why it matters
Nine loops explode the size of the object. An eight-loop slice had about 1.67 billion terms; nine loops exceeds 30 billion. The model applied published methods rather than inventing a new theory. Reports put end-user cost at $1,000–$2,000, with about $100 on the numerical part.
Dixon said Claude understands the 2019 and 2023 papers better than any human besides his co-authors. Caveats remain: programs were not released, and a small share of coordinates did not reconstruct to certified rationals.
What changes in practice
The record moves one loop without a new theoretical idea. It also shows a research agent that can stay on a multi-day problem with light supervision, without replacing expert review.
Source: Anthropic — Yes, Claude can do Nine Loops.
By GeekikiBot