Claude computed a nine-loop scattering amplitude, and the recipe was not new
Anthropic says its model computed a nine-loop scattering amplitude in planar N=4 super Yang-Mills. We check the file set, the caveats, and who verified it.
Vlad Makarovreviewed and published
On September 25, Anthropic published a guest post titled "Yes, Claude can do Nine Loops" on its research site. It reports that two of the company's physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, used Fable 5.1 inside Claude Science — a paid harness that wraps the model in structured rules and prompts — to compute a scattering amplitude in planar N=4 super Yang-Mills theory to nine loops, one order past the previous record. The post was written by Matt von Hippel, a physicist and science writer who set the problem as a public challenge in August, and it is candid about what the result does and does not establish.
What a loop buys you
An amplitude is the quantity that tells you how likely a given scattering outcome is, and in this theory it is computed as a series in a coupling constant. Each successive term is one loop, and each loop multiplies the bookkeeping rather than improving a measured accuracy. Von Hippel's own framing is that costs grow exponentially or factorially per loop, which is why the frontier moves one step at a time. Planar N=4 super Yang-Mills is a deliberately simplified model: it describes no particles that exist in nature, and physicists work with it because its symmetries make hard questions tractable. A nine-loop amplitude is therefore not a better account of the physical world. It is a stress test of how far a method can be pushed.
The challenge it answers
On August 7, von Hippel posted an essay titled "It only counts when AI gets to my field" and set a public test. His terms were specific: "Give us N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops." The design was the point. He did not ask for a new idea or a solved conjecture; he asked for the computationally expensive part of a problem the field already knows how to attack, done on resources an academic group could plausibly afford and in a form a human could check. That is a deliberately narrow target of the kind a hype cycle usually skips over.
How the run actually went
The prompt that started it was almost nothing. Fitzpatrick and Mishra-Sharma first asked Claude which problem it thought it was most likely able to tackle, then handed it a single sentence naming the task: "The problem is to compute the Six-particle (hexagon) amplitude in planar N=4 SYM at nine loops." From there the instructions were mostly instructions to continue. "I'm going to sleep and won't be available for another several hours. Keep working on this until I tell you to stop. Give me updates every 4-6 hours."
Two routes produced the answer — the established bootstrap method and the indirect form-factor route, the same approach that yielded the eight-loop result. The estimated end-user cost was roughly $1,000 to $2,000 per approach, mostly for running Claude. The bootstrap leg, written in Python with SymPy, accounted for about $100 of that, the equivalent of 96 CPUs running for a week.
What the released files claim
Two days before the Anthropic post, the pair published the result on their own page, dated September 16, with computer-readable files in the same format as the six-, seven- and eight-loop amplitudes and eight files over 100 MB on Zenodo. The caveats on that page are the most useful part of the release, and they read as a ledger of what has and has not been checked:
| Check | Published figure | What it says |
|---|---|---|
| Coefficients compared across the two representations | 107,053 | they agree on every one |
| Coordinates reconstructing to certified rationals | 1,014,476 of 1,018,297 | 99.62%; 3,821 do not |
| Independent computations of the amplitude as a function | one | no second computation exists |
| Files over 100 MB on Zenodo | eight | DOI 10.5281/zenodo.22949278 |
| Extra assumptions added at function level | one | symbol-level relations assumed to hold |
The two representations agree everywhere they were compared, and nearly every coordinate reconstructs to a certified rational. What is missing matters more. The amplitude as a function has been computed once, with no second independent computation; the programs themselves are not distributed; the function rests on one extra assumption; and some final ambiguities depend on flux-tube inputs for which no independent check is sensitive. That is a more honest document than the headline attached to it.
A human group got there the same week
Worth stating plainly, because it changes what the result means. A group led by Song He at the Chinese Academy of Sciences, with Jirong Jing and Xiang Li, published "The Symbols of Six-Gluon MHV Amplitudes through Nine Loops" on Zenodo on September 17, covering two through nine loops. Von Hippel writes that they had already obtained the majority of the result and used GPT-6-based assistance for some constraints, with humans handling the overall framework. So the nine-loop frontier fell twice in two days. The interesting variable is not whether a model can produce the answer; it is how much human framing the answer needed.
Who checked it, and who paid
Lance Dixon of SLAC and Stanford, a co-author of the eight-loop paper, says the Anthropic pair told him on September 1 and asked him to validate. He spent about two weeks on it, mostly through the nine-loop form factor, and his conclusion is narrow: Claude executed the recipe, developed all of the code from scratch, and presented the solution in the established format. That is a strong statement about sustained execution and a weak one about new physics, and his phrasing keeps the two apart.
The disclosures matter as much. Anthropic invited von Hippel to write the post and compensated him, company staff gave feedback on drafts, and Dixon received Claude usage credits. Superpower Daily and Kingy AI both revisited the release; the Kingy explainer verified file hashes against the published manifest and re-checked the coefficient records modulo the two stated primes, which is internal consistency, not a recomputation. The independent verification here is real but narrower than "confirmed."
What it does not mean
Von Hippel's own summary is the last place to look for cheerleading. Claude accomplished the calculation in one shot, he writes, without scientific oversight more sophisticated than repeated instructions to keep working, and his biggest takeaway is that there is more low-hanging fruit in the field than experts expect. He also notes what did not happen: the model used known methods with somewhat more compute than researchers had tried, and it did not deliver the glimpse of unexpected new technique he had hoped for. That distinguishes it from the AI physics work he describes from March 2026, which ran at a student level with substantial hand-holding.
For a reader deciding what to make of it, the honest frame is a workflow milestone. The model sustained a demanding research process built on methods other people invented. The FrontierMath results and the earlier physics arguments around AI in research sit on the same spectrum of impressive execution with familiar ideas. Nine loops is one more term in a series. It is not a new principle.
