Claude Computes a Nine-Loop Physics Amplitude — One Loop Beyond the Human Record
Claude, running inside Anthropic's Claude Science harness, computed the nine-loop six-particle amplitude in planar N=4 super Yang-Mills — one loop beyond the previous human record — and the result was independently validated by SLAC's Lance Dixon.
The calculation was prompted by a public challenge from physicist and science writer Matt von Hippel, who asked AI companies to tackle frontier scattering-amplitude problems on an academic-scale compute budget. Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma took up the N=4 super Yang-Mills nine-loop target, using Fable 5.1 within Claude Science, a structured harness built on the Claude LLM. After asking Claude which problem it was most likely to solve, they gave it a minimal prompt specifying the six-particle hexagon amplitude at nine loops, then repeatedly told it to keep working. Claude completed the calculation two ways: the direct bootstrap method and the indirect form-factor approach.
The cost was modest. Either approach would have run an end-user roughly one to two thousand dollars, mostly from long-running Claude usage. The bootstrap calculation itself, done in Python with SymPy, consumed about $100 of that budget, corresponding to 96 CPUs for a week. Notably, Claude executed the full recipe without external scientific oversight beyond instructions to continue, despite the fragility of the setup — a single mistake in the computational recipe collapses the whole construction.
Lance Dixon, professor at SLAC and Stanford and co-author of the prior eight-loop result, validated the nine-loop amplitude, largely by converting it to the related form factor. He had considered the direct amplitude calculation too hard and had expected to reach nine loops only indirectly. Days after Anthropic's result, Song He's group at the Chinese Academy of Sciences reported they had computed the majority of the result — the symbol — using GPT-6 for some constraints but not for the overall framework. Dixon notes Claude used the methods his collaborators developed and presented the solution in their established format.
Von Hippel's assessment is measured: this was not a superintelligent leap but evidence of more low-hanging fruit than experts expected. Claude used known methods with somewhat more compute than people had tried, and better software engineering practices. The result moves the frontier by one loop in a toy-model theory, not a real-world amplitude, and the humans involved will publish the analysis.