Claude’s Nine-Loop Physics Result: What Anthropic Reported and What It Proves

Anthropic reported that physicists using Claude Fable 5.1 calculated a six-particle scattering amplitude in planar N=4 super-Yang–Mills theory through nine loops. That is one perturbative order beyond the earlier eight-loop result, and reporting says physicist Lance Dixon independently checked the new calculation. The achievement concerns a demanding but deliberately simplified model—not particle scattering in general.182032

Why nine loops matters

A scattering amplitude is a mathematical ingredient used to predict how particles interact. Physicists calculate amplitudes in successive orders of approximation, called loops; adding an order generally makes the calculation harder. Anthropic describes two or three loops as a common stopping point and identifies eight loops as the previous record for this simplified setting.32 That comparison illustrates the difficulty, but nine loops here should not be read as a nine-loop result for every physical theory.

The earlier eight-loop calculation is attributed to Dixon and Liu in 2023. Available secondary accounts disagree on Liu’s given name: one says Andy Liu, while another says Yu-Ting Liu. Both describe a route involving a related quantity called a form factor and a relationship known as antipodal duality.3839 Anthropic’s reported nine-loop result therefore extends an existing line of work rather than starting from a blank slate.

How Claude was used

Matt von Hippel had challenged AI companies to tackle a frontier problem on an academic budget; Anthropic’s September 25, 2026, account presented the nine-loop calculation as an answer to that challenge.2539 Reporting identifies Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma as directing Fable 5.1 within Claude Science. One account says they gave it a short task prompt, instructed it to continue working overnight, and requested periodic updates.8

The reported work took two routes: a direct bootstrap of the amplitude and an indirect calculation through a form factor.838 Using distinct routes is significant because agreement can provide a check on a difficult computation. The excerpts available here, however, do not fully document each implementation or establish how independent the routes were.

Cost figures need similar care. One account attributes to von Hippel an estimate of roughly $1,000–$2,000 for either route, largely for running Claude over an extended period.8 Another describes $1,000–$2,000 total.9 Without a consistent accounting of model usage, other computing costs, and researcher time, neither figure should be treated as a verified all-in price for reproducing the result.

What was checked—and what remains open

Reporting says Dixon independently checked the result. It also acknowledges a separate human-led team working toward much of the same calculation.1820 The material available here does not establish Dixon’s exact validation timeline or confirm claims that Claude wrote every line of code from scratch. Nor does it provide enough evidence to assess the reported scope, deposit date, or AI assistance associated with Song He’s group. Credit and priority for parallel work require a more detailed record than these excerpts supply.

The strongest supported interpretation is that Claude, under expert direction, helped extend established computational methods to a new loop order in a useful testing ground. That could be an important example of AI assisting frontier research. It does not, on its own, show that the model found a new physical principle or that the same workflow will transfer unchanged to less symmetric, more realistic theories.1831