Claude completes a nine-loop amplitude calculation in a scientific harness

Anthropic describes Claude completing a nine-loop N=4 super-Yang-Mills amplitude calculation in Claude Science, with physicist Lance Dixon checking the result and the article stressing the limits of the claim.

Anthropic published a September 25, 2026 article by physicist and science writer Matt von Hippel describing how Claude tackled a frontier calculation in theoretical particle physics. The target was a six-particle nine-loop MHV scattering amplitude in planar N=4 super-Yang-Mills; in this work, a higher loop count represents a more complex set of interactions to calculate.

The problem is not a direct model of real-world particles. It is a toy model used in amplitudeology to stress-test calculation methods. Researchers can use a bootstrap to enumerate possibilities that satisfy known rules and then eliminate candidates with additional constraints. Anthropic’s article presents it as a task with a known general method but enough computation and engineering detail to make a naive attempt fragile.

Two Anthropic physicists used Fable 5.1 inside Claude Science. They first asked the model which problem it was most likely to complete and then allowed it to continue for long periods. The article says Claude completed the calculation through both the original bootstrap route and an indirect form-factor route. It estimates one or two thousand dollars of end-user cost for either approach, with one bootstrap run using about 96 CPUs for a week. Those cost and workflow details are reported by the article, not an independent audit.

Lance Dixon, a physicist at SLAC and Stanford, checked the result, mainly through the related form factor. The article also says a Chinese Academy of Sciences group had obtained much of the result around the same time with some GPT-6 assistance. That context matters: the event is not evidence that AI independently discovered a new physical law. It is evidence that a model can combine established methods, code, compute resources, and long-running task management to complete a calculation that researchers had considered too expensive or tedious to attempt directly.

The article’s own interpretation is cautious. Claude used known methods, more compute than people had previously tried, and possibly better software engineering practices; it did not produce a new physical principle in this task. The nine-loop result still needs human researchers to publish, explain, and analyze it. N=4 super-Yang-Mills is a method-testing model, so it cannot be treated as a general proof that AI can solve arbitrary real-world physics problems.

For scientific agent workflows, the important artifact is the harness. The task required problem selection, code generation and revision, compute management, state across hours or days, and independent expert checking. Without reproducibility, cost records, fixed versions, and an independent validation path, a polished long-running agent result is difficult to treat as reliable research.

The practical reading is therefore that AI is beginning to handle a class of frontier calculations with a clear structure and verification route, not that AI has replaced scientists. The next test is whether other researchers can reproduce the result, identify its limits, and transfer the workflow safely to scientific questions closer to the real world.

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