Anthropic reported on September 25 that Claude completed the calculation of a six-particle amplitude at nine loops in planar N=4 super-Yang–Mills theory, a frontier problem in the mathematical study of particle interactions. The result is not limited to a textual answer: the team released numerical and symbolic representations, method documentation, validation files, and checksums so that specialists can examine them.

The work responded to a challenge posed by physicist Matt von Hippel: to test whether an AI could push past a computational limit that remained unresolved for that amplitude using resources accessible to an academic group. According to his account, Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma used Fable 5.1 within Claude Science, an environment that organizes prolonged model runs with rules and tools for research. Von Hippel was invited and compensated by Anthropic to write the explanation, a relationship that the publication explicitly discloses.

Two calculation routes and verifiable artifacts

Claude approached the problem through two routes: a direct bootstrap of the amplitude and an indirect route based on a form factor. The Cosmic9 technical page states that the two representations agree on every coefficient compared. It also documents which assumptions were used, which tests were run, and which aspects have not yet been checked.

The release includes the amplitude in several representations, coefficient matrices, mathematical bases, files exceeding one gigabyte, and a SHA-256 manifest. This level of detail distinguishes the announcement from a simple staged demonstration: other researchers can download the objects produced, verify their integrity, and reproduce specific comparisons. The publication does not, however, amount to a complete peer review or demonstrate that the system can solve any theoretical-physics problem.

Anthropic says the main calculation cost the user between $1,000 and $2,000 in model usage. One computational component run with Python, SymPy, and 96 CPUs over a week accounted for approximately $100 of that budget. This is a figure reported by the company, not an independent audit of total cost.

Validation and a concurrent human result

Amplitudes physicist Lance Dixon independently validated the result, according to the article; he received Claude usage credits. In addition, Song He, Jirong Jing, and Xiang Li deposited on Zenodo a concurrent calculation of six-gluon amplitude symbols up to nine loops. That human work, which also used AI assistance for part of the process according to the account, provides an external reference for comparing the result, although it does not by itself validate every decision in Claude's autonomous workflow.

The complete files for Claude's result are available on Cosmic9, while the concurrent calculation can be consulted on Zenodo. The explanation and conditions of the experiment appear in Anthropic's publication.

The advance is concrete because it combines a frontier scientific task, two calculation approaches, and inspectable artifacts. Its scope remains specific: N=4 super-Yang–Mills is a highly structured theory, and the bootstrap method is especially compatible with algebraic constraints. The relevant signal is not that AI has “solved physics,” but that a tool-assisted system was able to sustain a lengthy investigation, produce a verifiable mathematical object, and reach a result comparable to concurrent expert work.