Anthropic: Claude completes a nine-loop calculation in particle physics

According to a guest post published on Anthropic's site on September 25, 2026, Claude has computed a nine-loop scattering amplitude in theoretical particle physics. The post was written by Matt von Hippel, a physicist and science writer who used to work in the field in question. The result was validated by Lance Dixon, a professor at SLAC National Accelerator Laboratory and Stanford University and co-author of the earlier eight-loop calculation.

What the calculation is

Scattering amplitudes are formulas that take the momenta and energies of subatomic particles and give the likelihood that they react in a particular way. The formulas are so hard that physicists cut the calculation off at a certain number of "loops". More loops bring the answer closer to the real one and make the calculation heavier. According to the post, most amplitudes have only been calculated to two loops.

The quantity Claude computed is the six-particle amplitude in planar N=4 super Yang-Mills theory at nine loops. This theory does not describe the real world; it is a "toy model" that physicists use to sharpen their methods. In 2023, Dixon and Andy Liu computed the same amplitude to eight loops by an indirect route.

Where the challenge came from

On August 7, von Hippel put a challenge to AI companies on his blog, 4 gravitons: to take the kind of computing resources an academic has access to and solve one of the big outstanding problems in the field. One of his two examples was this nine-loop calculation.

How it was done

According to the post, Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma used the Fable 5.1 model inside Claude Science, a platform for scientists. Claude was given a one-sentence task and was then only told to keep going. Von Hippel reports that the work was completed without scientific oversight beyond that.

Claude did the calculation in two separate ways: with the method known in the field as the "bootstrap", and by the indirect route through the form factor. The bootstrap calculation was written in Python with SymPy and ran on 96 CPUs for a week. Dixon notes that Claude used the methods his own group developed over the years and wrote the code from scratch.

How the authors assess the result

In von Hippel's view, this is a real frontier calculation of the kind normally taken on by the top experts in the field. In the same post he sets out the limits: Claude used known methods with a bit more computing power than had been tried before, and no new method for the calculation emerged. Von Hippel writes that he is not sure how far the result can be generalized.

The post also covers a concurrent result. Song He's group at the Chinese Academy of Sciences computed the piece of the nine-loop amplitude called the "symbol" in its own work. According to Dixon, the group used AI assistance based on GPT-6 to compute some of the constraints. Publishing the results as papers is left to Dixon, He and their collaborators.

According to the disclosure at the end of the post, Anthropic invited von Hippel to write it and compensated him for his time; Anthropic staff gave feedback on drafts, and the content and opinions are his own. Dixon validated the result independently and received Claude usage credits. No paper on the nine-loop result has been published yet. The page that shares the result files says the programs of the computation are not distributed and that there is no second, independent computation of the function-level result so far. For a fuller picture, it is worth following evaluations from independent researchers as well.

Sources: Anthropic: Yes, Claude can do Nine Loops, 4 gravitons: It Only Counts When AI Gets to My Field, Nine-loop result files, Zenodo: the result by He, Jing and Li.