Claude nine-loop Yang-Mills
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·Original: about 15 minutes to read
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 loopssix-particle amplitude in planar N=4 super Yang-Mills, one loop beyond the previous record of eight
- US$1,000-2,000estimated end-user cost per approach, mostly model usage
- 96 CPUs x 1 weekcompute for the bootstrap calculation, about US$100 of the budget
As reported by the source.
English·Web page·opens anthropic.com
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.
Summary based on the full text. Read the original for the full argument and data.Read the original on anthropic.com
- Tags
- AI capability