Yes, Claude can do Nine Loops (von Hippel, with a Dixon addendum)

A guest post on Anthropic's research blog, dated 25 September 2026. Written by Matt von Hippel, a former theoretical physicist turned science writer who blogs at 4gravitons.com — Anthropic invited and paid him to write it; the post states Anthropic staff commented on drafts but "the content and opinions are his own." It carries a signed addendum by Lance Dixon (SLAC/Stanford), the physicist who validated the result and who received Claude usage credits for doing so. Both facts stay attached to the tier: this is Anthropic's own capability claim, told through a paid outside writer and checked by an outside expert who was compensated in the vendor's own currency.

What happened

Two Anthropic physicists, Liam Fitzpatrick and Siddharth Mishra-Sharma, ran Fable 5.1 inside Claude Science — Anthropic's paid research harness (already named without a page on anthropic-scientist-access-expansion; see Cross-spoke context below) — on one prompt: "compute the six-particle (hexagon) amplitude in planar N=4 super-Yang-Mills at nine loops." Steering after that was minimal — mostly "keep working on this until I tell you to stop."

Claude solved it two independent ways, writing all the code itself in Python with SymPy:

• Direct bootstrap — treat the amplitude like a Sudoku: start from every candidate answer, then eliminate candidates with known physical constraints.
• Indirect form-factor route — the path through what Dixon calls "antipodal duality," the same route he used to reach eight loops in 2023.

Prior frontier: eight loops, Dixon and Andy Liu, 2023 (arXiv 2308.08199), via the form-factor route only. Nine loops is one step past the best published human result, by the same route plus a second, independent one Claude found on its own.

Cost: each approach would run an end user roughly $1,000–$2,000, almost all of it Claude usage. The bootstrap alone, in Python/SymPy, ran ~$100 of that — 96 CPUs for about a week.

Validation: Anthropic contacted Dixon on 1 September and asked him to check the result independently. He did it mainly by converting Claude's answer back into the nine-loop form factor, a check that took about two weeks. He calls the setup fragile — any error "crashes down like a failed soufflé" — and says Claude "understands our 2019 and 2023 papers better than any human" apart from his own co-authors.

Caveats the source states itself

• No new method: von Hippel is explicit that "Claude used known methods, with a bit more compute than people had tried to use before." The result is a compute/persistence story, not a new technique.
• Matched independently, at the same time, by a different model: Song He's group at the Chinese Academy of Sciences (with Jirong Jing and Xiang Li) reached most of the same result around the same time, with "some AI assistance, based on GPT-6" — a competing lab, a competing vendor's model, and a human-led process, converging on the same answer.
• Unclear how far it generalizes: von Hippel wanted something stranger and concludes he "was too naïve about where the limit was"; he flags that this specific problem may be unusually suited to an AI-driven brute-force search, not representative of amplitude calculations generally, let alone physics research broadly.
• The humans keep the result: publication and analysis of the actual physics is left to the human researchers, not Claude.

Why this matters for the model page, and why it's thin evidence

claude-fable-5-1 had one flagged gap: nothing in this spoke covered Fable 5.1's agentic or long-horizon behaviour — the thing the Fable tier is actually sold for, as opposed to single-turn benchmark scores. This is the first source here that does: hours-to-days of largely unsupervised tool use (writing and running its own Python/SymPy code across two independent solution paths) on a problem with a checkable, non-fuzzy answer.

It is also, by this spoke's own tier rule, exactly the shape of evidence to read cautiously: Anthropic picked the problem, ran the harness, invited and paid the writer, and paid-in-credits the one outside person positioned to say the number is right. Dixon's validation is real domain expertise applied independently — he is not an Anthropic employee and used his own two-week re-derivation, not Claude's work, to check it — which is more than a self-report carries on its own. It is not the same as a disinterested third party running the harness with no vendor relationship at all, and the corpus should keep both facts in view rather than average them into a clean "verified" or a clean "vendor talk."

Cross-spoke context

Two facets of this source belong to sibling spokes and are noted here rather than paged there:

• ../agentic-tooling-wiki — the load-bearing mechanism is Claude Science, a long-autonomous-run agent harness (minimal steering, multi-day tool use, self-written code across two solution paths). That is agentic-tooling-wiki's subject; this spoke keeps only what it says about the model's capability. If Claude Science earns its own page, agentic-tooling-wiki is where it belongs — this page and anthropic-scientist-access-expansion both name it without one.
• ../mathematics-wiki — the actual object computed, the nine-loop MHV six-particle amplitude in planar N=4 super-Yang-Mills, is theoretical-physics/mathematical-physics subject matter with no physics spoke in this hub to hold it. Noted here as the runner-up match rather than parked or forced into a spoke that doesn't fit.

Related

claude-fable-5-1 · anthropic · anthropic-scientist-access-expansion · matt-von-hippel · lance-dixon · synthesis