---
id: "lib-2026-09-25-claude-nine-loop-yang-mills"
type: "library"
title: "Claude nine-loop Yang-Mills"
lang: "EN"
org: "Anthropic"
source_type: "Article"
date: "2026-09-25"
week: "2026-W39"
url: "https://nosov.ai/library/lib-2026-09-25-claude-nine-loop-yang-mills/"
original_url: "https://www.anthropic.com/research/yes-claude-can-do-nine-loops"
tier: "A"
tier_name: "Strong evidence"
tier_reason: "A concrete frontier physics result with stated cost and compute, independently validated by the SLAC physicist who led the earlier loop orders, though published on the vendor's site by a compensated guest author."
summary_basis: "full-text"
original_minutes: "15"
tags: ["capability", "scientific r&d"]
---

# Claude nine-loop Yang-Mills

Tier A (Strong evidence): A concrete frontier physics result with stated cost and compute, independently validated by the SLAC physicist who led the earlier loop orders, though published on the vendor's site by a compensated guest author.

Summary based on the full text.

## In short

A September 2026 guest post on Anthropic's site by Matt von Hippel, a former theoretical physicist turned science writer, with an addendum by Lance Dixon (SLAC and Stanford). Von Hippel had challenged AI companies to compute a nine-loop amplitude in N=4 super Yang-Mills on an academic budget. Two Anthropic physicists ran Claude inside the Claude Science harness and got the result about a month later; Dixon validated it. Von Hippel's conclusion: the model used known methods with more compute, and the barrier was lower than experts assumed.

## Key numbers

- 9 loops: six-particle amplitude in planar N=4 super Yang-Mills, one loop beyond the previous record of eight
- US$1,000-2,000: estimated end-user cost per approach, mostly model usage
- 96 CPUs x 1 week: compute for the bootstrap calculation, about US$100 of the budget

## What it reports

- Most scattering amplitudes are computed to two loops, a few to three; Dixon reached eight loops in this toy theory via a form-factor route with Andy Liu in 2023.
- Prompt given: compute the six-particle amplitude in planar N=4 SYM at nine loops; afterwards mostly "keep going" instructions with updates every 4-6 hours.
- Claude solved it two ways, the direct bootstrap and the indirect form-factor approach.
- Each approach would cost an end user about US$1,000-2,000; the bootstrap in Python/SymPy used about US$100 of compute, 96 CPUs for a week.
- Anthropic contacted Dixon on 1 September 2026; he spent two weeks validating the result.
- A human group led by Song He (Chinese Academy of Sciences) independently computed most of the result (the symbol) with some GPT-6 assistance.
- Dixon notes Claude wrote all the fragile pipeline code from scratch and used his group's published methods and format.

## How they got it

A single worked case. Model: Fable 5.1 in the Claude Science harness, run by Anthropic staff Liam Fitzpatrick and Siddharth Mishra-Sharma. Validation by Dixon, mainly by deriving the form factor from the amplitude and checking it against his group's constraints.

## Limits

- Vendor-hosted and commissioned: Anthropic paid von Hippel and gave draft feedback; Dixon received usage credits.
- One problem in a toy theory chosen partly because Claude rated it tractable; internal error rates are unknown.
- No new physical method was found; a human team reached most of the same answer in parallel.

## Why it matters for companies

The relevant lesson is cost and autonomy: a well-defined, hard computation ran for days with minimal supervision for a few thousand dollars. Von Hippel's takeaway applies outside physics: many problems experts consider out of reach are blocked by engineering effort, not ideas. The case also shows the precondition that made it safe, an expert with a ready way to verify the answer. Companies looking at long-running agent work should secure that verification step first.

Original: https://www.anthropic.com/research/yes-claude-can-do-nine-loops