Anthropic researchers used the Claude Science harness (built on Fable 5.1) to have the Claude LLM compute the nine‑loop MHV six‑particle (hexagon) amplitude in planar N=4 super‑Yang‑Mills theory. They prompted Claude with a clear statement of the problem and then let it run autonomously, requesting updates every 4–6 hours. Claude pursued two independent routes: the original bootstrap method and an indirect form‑factor approach. The bootstrap implementation was written in Python with the SymPy library, consuming roughly $100 of compute—equivalent to running 96 CPUs for one week—while the total effort for either method was estimated at one to two thousand dollars, mainly from Claude usage. The result was validated independently by Lance Dixon, who confirmed the nine‑loop amplitude, and by Song He’s group, which had previously obtained much of the same outcome using GPT‑6 for constraint generation. The computation relied on established amplitude‑bootstrap techniques rather than discovering new physical principles, demonstrating that a large language model can execute a complex, multi‑step symbolic calculation on a modest budget and with minimal human oversight.