Anthropic / Lance Dixon verification
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AnthropicClaudeSciencePhysicsClaude computes nine-loop particle physics amplitude, beating 2023 record
September 25, 20262 min read
Anthropic physicists used Claude Fable 5.1 inside Claude Science to compute the six-particle scattering amplitude in planar N=4 super Yang-Mills at nine loops — one loop past Lance Dixon’s 2023 eight-loop record. The run cost roughly $1,000–2,000 and was largely unsupervised; Dixon independently checked the result.
Why it matters
A concrete, independently verified advance on a frontier theoretical-physics calculation done mostly by an AI system at academic-scale cost. It sits alongside the ART enzyme result as evidence that agentic models are already useful for research that previously required specialist human effort over years.
Anthropic reported that Claude Fable 5.1, running inside its Claude Science research harness, computed the six-particle (hexagon) scattering amplitude in planar N=4 super Yang-Mills theory at nine loops. That extends the previous record of eight loops set in 2023 by SLAC/Stanford physicist Lance Dixon and collaborators.
Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, gave the model a short problem statement and then largely let it continue working over several days, with periodic prompts to keep going. Claude pursued the calculation via two independent routes — a direct bootstrap and an indirect path through a related form factor using antipodal duality — and the results agreed. Estimated cost was on the order of $1,000–2,000. Dixon independently verified the nine-loop result. The output files were released in the same format used for earlier loop orders.
The work answers a public challenge from physicist and science writer Matt von Hippel asking whether AI systems could push past eight loops on this class of amplitude calculation with a compute budget accessible to an academic researcher.