What "nine loops" means
When two protons collide at the LHC, physicists compute how the debris flies using scattering amplitudes. These are calculated as a series of terms: the first term is a tree diagram; each subsequent term adds a closed loop. Most textbook amplitudes stop at two loops; a few reach three. The most precise particle-physics prediction ever made — the electron's anomalous magnetic moment — uses five loops.
On September 25, 2026, Anthropic published a guest post titled "Yes, Claude can do Nine Loops," reporting that an AI model computed the six-particle amplitude in planar N=4 super Yang-Mills (N=4 SYM) to nine loops. The previous record of eight loops was set in 2023 by Lance Dixon (SLAC National Accelerator Laboratory) and collaborators.
The public challenge
On August 7, 2026, former theoretical physicist and science blogger Matt von Hippel posted on his blog 4gravitons an article titled "It Only Counts When AI Gets To My Field." He issued two challenges: compute N=8 supergravity to seven loops, or compute the six-particle N=4 SYM amplitude to nine loops — with the condition that the compute budget be one an academic researcher could afford.
His reasoning: both problems are hard because of scale, not ideas. Amplitude specialists could solve them with known methods and enough compute; what he wanted proven was the combination of compute power and execution, not inspiration.
One prompt, then just "continue"
Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, took up the challenge. According to von Hippel's guest post and Simon Carter's coverage, they used the Fable 5.1 model on the research-oriented Claude Science platform.
The workflow was strikingly short: they first asked the model which of the two problems was most tractable, then gave a single prompt — the problem is to compute the nine-loop six-particle (hexagon) amplitude in planar N=4 SYM. After that, the researchers' instructions were essentially just one word: continue. They let it work overnight, reporting progress every four to six hours.
The model wrote Python and SymPy code, ran it, inspected outputs, fixed its own errors, and iterated autonomously for days.
Two independent routes, one answer
The model used two independent methods:
- Hexagon bootstrap: list all possible answers on a dedicated symbol alphabet, then apply known physical constraints until only one solution remains, with leftover constraints for cross-checks.
- Indirect route: first compute the nine-loop form factor, then map it to the amplitude via antipodal duality — the same path Dixon's team used for eight loops in 2023.
- Whether independent teams reuse the publicly available nine-loop symbol to test conjectured structures;
- The other half of von Hippel's challenge — the seven-loop N=8 supergravity divergence — remains unclaimed;
- Whether the "academic-level compute" constraint holds elsewhere; if so, every "good idea, insufficient compute" research problem is affected;
- Whether naive loop-scaling with known methods can reach ten or eleven loops, or hits a complexity wall.
Both routes agreed on all 107,053 non-zero coefficients of the nine-loop symbol.
The bill: $100 and $2,000
According to von Hippel, the bootstrap computation itself cost roughly $100 — equivalent to about 96 CPUs running for a week. The entire project, including the indirect cross-validation, cost roughly $1,000–2,000 end-to-end, most of it going to the model's extended run rather than numerical computation.
From the August 7 challenge to Anthropic's confirmation took about 25 days. The result files were posted to Zenodo on September 16, 2026 — 8 files totaling over 100 MB, in a format fully compatible with the earlier six-, seven-, and eight-loop results.
Verification by the record holder himself
The verifier was Lance Dixon of SLAC and Stanford — creator of the eight-loop record. He independently checked the result.
Dixon called it "quite an impressive victory," noting the model executed every step of a complicated recipe and organized the compute. He added that, aside from his collaborators, Claude understood their team's 2019 and 2023 papers better than anyone. Notably, Dixon had previously considered a direct nine-loop amplitude computation too hard, and his team had been preparing for it for years.
What the model did *not* do
Von Hippel himself set the boundaries: Claude used known methods, just with more compute than anyone had been willing to spend.
The model introduced no new mathematical tools and no new physical insight; the bootstrap is established machinery in the amplitude community. The change was at the execution level — writing code, debugging, running numbers, backing out of failed paths, repeatedly, unattended for days. What was replaced is not physics creativity but the cost of "long-duration, low-error-rate completion of defined drudgery."
Three caveats
1. It's a toy theory. N=4 SYM is a highly symmetric, physically unrealistic simplification of Yang-Mills, used as a proving ground for new methods. Nine loops pushes the depth of the testbed, not reality. 2. Zenodo is not peer review. The results are published as machine-readable, reusable files with high reproducibility, but as of the announcement they have not undergone journal peer review. Von Hippel's validation and Dixon's independent check are the main endorsements. 3. Disclosure. The guest post was commissioned and paid for by Anthropic; Anthropic employees commented on a draft, but content and opinions belong to von Hippel.
A parallel note: according to Simon Carter, a Beijing team using GPT-6 obtained partial results. Multiple groups are on this track; Anthropic delivered the first complete result.
What to watch next
Sources
1. Matt von Hippel, guest post "Yes, Claude can do Nine Loops," Anthropic Research, 2026-09-25 (with Anthropic-commissioned payment disclosure) 2. Matt von Hippel, 4gravitons, "It Only Counts When AI Gets To My Field," 2026-08-07 3. Unite.AI, "Anthropic Says Claude Computed a Nine-Loop Particle Physics Amplitude," 2026-09-25 4. Simon Carter, "Claude computed a nine-loop particle physics amplitude for around $2,000," 2026-09-25 5. Fitzpatrick & Mishra-Sharma, machine-readable nine-loop results, Zenodo, 2026-09-16 (8 files, >100 MB) 6. Dixon et al., eight-loop six-particle amplitude (via nine-loop form factor and antipodal duality), 2023