Anthropic says Claude has taken a simplified particle-scattering calculation from the published eight-loop result to nine loops, one additional level in the formula physicists use to estimate how likely six gluons are to interact. Physicist Lance Dixon says he checked the answer; it does not predict a new outcome for real-world particle collisions.
A scattering amplitude is a formula physicists use to calculate how likely particles are to interact. Its loop order marks successive levels in a perturbation calculation; each higher level adds more mathematical structure. The target was planar N=4 super-Yang-Mills, a highly symmetric theory researchers use to test calculation methods because it is more tractable than models of known particles. “Six-gluon” identifies the particles in the calculation; it is not a report of six particles colliding in an experiment.
Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma ran Claude’s Fable 5.1 model through Claude Science. In physicist and science writer Matt von Hippel’s account, they gave Claude a one-sentence task and asked it to continue working with periodic updates. It tackled the result by two routes: a direct amplitude bootstrap, which narrows possible formulas by applying known constraints, and an indirect route through a related three-point form factor, a simpler quantity linked to the amplitude by antipodal duality.
The linked result archive provides machine-readable coefficients and validation records. It says the direct bootstrap and form-factor routes agree on every coefficient compared, including 107,053 nonzero coefficients in one comparison. The archive also says the programs used for the calculation are not distributed and that the full function-level result was computed once. The public files make the result inspectable, but do not yet allow another group to rerun the entire calculation from released code.
Dixon, a particle physicist at SLAC and Stanford, says he independently checked the result, mainly by comparing it with the related form factor. He described the calculation as technically fragile: a small mistake in the recipe can invalidate the output. The eight-loop comparison is Dixon and Yu-Ting Liu’s published 2023 calculation for the same amplitude.
This is a long, computer-assisted calculation using established physics methods in an idealized theory. It is not a new physical principle or evidence that the same workflow can solve arbitrary research problems. Von Hippel says the researchers plan to publish a fuller account; that write-up should make the calculation and its checks easier to assess.
Sources
- Anthropic’s report, including von Hippel’s account and Dixon’s validation addendum
- Nine-loop result files and validation records
- Dixon and Liu’s 2023 eight-loop amplitude paper
Image: “Feynman diagram general properties” by Maschen, Wikimedia Commons, CC0 1.0. The diagram is conceptual and does not depict the reported nine-loop calculation.