Claude Science Computes a Nine-Loop Amplitude, Verified by Dixon

Particle physicists predict how particles interact by computing formulas called scattering amplitudes. Exact answers are out of reach, so they build approximations in layers called loops. Each loop allows more complicated interactions, which brings the answer closer to reality but makes the calculation much harder. Most real-world amplitudes have only been computed to two loops. To test new techniques, specialists use toy theories that are easier to compute with. One of these is planar N=4 super Yang-Mills, which describes no real-world physics. In that theory, Anthropic says, Claude has now computed the six-particle amplitude at nine loops, one beyond the eight-loop result that SLAC's Lance Dixon and a collaborator reached in 2023. The method behind these results is called a bootstrap. Instead of tracing every particle interaction, it writes down every form the answer could take and then eliminates candidates with known constraints until only one survives. Von Hippel compares it to Sudoku.

According to the guest post by physicist and science writer Matt von Hippel, the work answered a challenge he had issued: solve a frontier amplitudes problem using the kind of computing resources an academic has. Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, gave Fable 5.1 a one-line description of the problem inside Claude Science, a harness that wraps Claude in structured rules and prompts for scientific work. After that, they mostly just told it to keep going. Claude did the calculation two ways: the direct bootstrap and Dixon's indirect route through a related, easier object called a form factor. Each approach would have cost an end user about one or two thousand dollars, mostly to keep Claude running. Within that, the bootstrap computation itself, run in Python with SymPy, used about 100 dollars, or 96 CPUs for a week. Dixon validated the result, mainly by converting it back into the nine-loop form factor his own team had been working toward. He had thought the direct calculation was too hard, and says what impressed him was less its size than its fragility: one mistake in the recipe makes the whole thing collapse, and many details had never been fully written up, so Claude had to write that code from scratch.

Von Hippel draws a deliberately limited conclusion. A few days after Anthropic contacted him, Song He's group at the Chinese Academy of Sciences reported that they already had most of the result. They had used GPT-6 for some constraints, but not to run the overall framework. In von Hippel's account, Claude used known methods with somewhat more compute than people had tried before. The lessons are that the field had more low-hanging fruit than experts assumed, and that a harness can now carry a messy frontier calculation to the end with no oversight beyond telling it to continue. That is a step up from Vibe Physics in March, where Harvard physicist Matthew Schwartz found he had to check Claude's work closely. Von Hippel had hoped to see new and unexpectedly powerful methods for the calculation itself, and says he did not. Anthropic invited and paid von Hippel to write the post and gave feedback on drafts, and Dixon received Claude usage credits. Anthropic posted the full result, but this review could not open that file.