Anthropic Physicists Use Fable 5.1 in Claude Science to Compute 9-Loop Amplitude

Anthropic staff physicists Liam Fitzpatrick and Siddharth Mishra-Sharma utilized the Fable 5.1 model within the Claude Science platform to calculate the 9-loop MHV six-particle amplitude in planar N=4 super Yang-Mills theory. The calculation, which Lance Dixon of SLAC/Stanford had considered too difficult to perform directly using standard bootstrap methods, was verified independently by Dixon. Dixon noted that the model correctly applied methodologies from his team's 2019 and 2023 papers, effectively validating their previous work. The bootstrap approach cost Anthropic approximately $100 in compute resources (running 96 CPUs for one week), though the text notes that either approach would have cost an end-user around one to two thousand dollars. Concurrently, Song He's group at the Chinese Academy of Sciences computed the symbol of the same amplitude using GPT-6 for constraint generation.