The nine-loop experiment: particle physics between automated calculation and assumptions still to be checked

On 25 September 2026, Anthropic's science blog published a guest piece by science writer Matt von Hippel describing how a challenge he had posted on 7 August on his personal blog, "4 gravitons", had been met. The result concerns the six-gluon scattering amplitude at nine loops in planar N=4 super Yang-Mills theory, a simplified model used as a testing ground for studying how particles interact. The previous record, from 2023, belonged to physicist Lance Dixon of SLAC National Accelerator Laboratory and his collaborators, who had reached eight loops. The other goal in the challenge, N=8 supergravity at seven loops, remains open.

The work was done with Fable 5.1 inside Claude Science, a paid setup that von Hippel himself describes as a "harness": a program that surrounds the language model with structured rules and instructions. The calculation followed two routes already developed by Dixon and his collaborators: the bootstrap method (run in Python with the SymPy library) and the form factor approach. According to the post, the bootstrap took about a hundred dollars of the budget, and the computation needed 96 CPUs for a week. On his own blog, von Hippel adds that 90% or more of the computing spend, around a thousand dollars, went to the language model rather than to the calculation itself. The overall estimate for an end user stays between one and two thousand dollars per method.

The data, published on 16 September 2026 under the name "Claude" on smsharma.io, come with clear methodological limits. The files state that the nine-loop function was computed only once, with no second independent run, and that it rests on the theoretical assumption that every relation valid at the level of the symbol also holds at the level of the function. The whole process has not yet been peer reviewed. Before publication the result was checked with Lance Dixon, mainly through the nine-loop form factor. The account of how it was run and what it cost, however, comes from Anthropic and its guest. Almost at the same time, on 17 September 2026, the group led by physicist Song He at the Chinese Academy of Sciences deposited an independent dataset on Zenodo with the symbols from two to nine loops. Anthropic's post credits them with using GPT-6, but von Hippel himself points out that the Chinese researchers obtained most of the result with far less help from AI. The comparison with the Chinese dataset, which concerns the symbols, is not publicly documented.

There is no new physics here. What the result shows is that a model with a scientific harness can carry out a known, lengthy procedure on its own, at a cost within reach of a single researcher.

— Olya