Claude (Fable 5.1 in Claude Science) computes the nine-loop six-gluon amplitude in planar N=4 super-Yang-Mills, answering a physicist's public challenge
On Sept 25, 2026 Anthropic published a guest post by physicist-turned-writer Matt von Hippel. In August he had challenged AI companies to compute "N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops". Anthropic physicists Liam Fitzpatrick and Siddharth Mishra-Sharma had Claude Fable 5.1, running in the Claude Science harness, compute the six-particle (hexagon) amplitude in planar N=4 SYM at nine loops, one loop past the previous record. Their prompting was little more than "keep going". Claude did it two independent ways (form-factor/antipodal-duality route and direct hexagon bootstrap), for about $1–2K of usage. SLAC's Lance Dixon verified the result. A Beijing group led by Song He had independently obtained most of it with GPT-6-based assistance.
Key facts
- Challenge: von Hippel's 4gravitons post of Aug 7, 2026 ('It only counts when AI gets to my field') asked for N=8 supergravity at seven loops or N=4 SYM at nine loops on academic-scale compute; Anthropic reached out at the end of August
- Setup: Claude Fable 5.1 in Claude Science; initial prompt 'The problem is to compute the Six-particle (hexagon) amplitude in planar N=4 SYM at nine loops', then instructions like 'Keep working on this until I tell you to stop. Give me updates every 4-6 hours'
- Two routes: (1) bootstrap the nine-loop three-point form factor and map it to the amplitude via antipodal duality (the method Dixon used for eight loops, arXiv 2308.08199); (2) a direct bootstrap of the symbol in the space of hexagon functions. The two agree on every coefficient compared
- Cost: about $1,000–2,000 end-user price per approach, mostly Claude usage; the SymPy bootstrap cost ~$100 of compute (96 CPUs for about a week)
- Verification: checked with Lance Dixon (SLAC), who holds the six-, seven- and eight-loop results; the form factor is certified over the rationals at three 31-bit primes, the amplitude computed modulo two primes (99.62% of nonzero symbol coordinates reconstruct to certified rationals)
- Data released on Mishra-Sharma's 'Cosmic9' page and Zenodo (symbol as 424 quintuple coproducts over a 5,431-dimensional weight-13 hexagon symbol space); the programs are not distributed
- Priority: Song He's group (Chinese Academy of Sciences, Beijing) had independently obtained 'the majority of the result' using GPT-6-based AI assistance; the human groups will publish the physics analysis
- Von Hippel's verdict: Claude 'used known methods, with a bit more compute than people had tried to use before', not new methods; but 'this is a real frontier calculation' done essentially autonomously, and 'there is more low-hanging fruit out there than you'd expect'
Science result
- Field
- physics / theoretical particle physics (scattering amplitudes)
- Problem
- Six-gluon MHV amplitude in planar N=4 super-Yang-Mills at nine loops (previous record: eight loops, Dixon et al.)
- Result
- Nine-loop symbol of the six-particle amplitude computed by two independent routes and released as computer-readable files
- AI system
- Claude Fable 5.1, Claude Science
- Human role
- Anthropic physicists chose the problem (after asking Claude which it was most likely to solve) and prompted 'keep going'; Lance Dixon verified; human groups to publish analysis
- Verification
- Expert-checked (Lance Dixon); two independent computational routes agree; finite-field certification
- Status
- confirmed
- Why surprising
- The challenger expected nine loops to need new methods or far more compute; an almost unsupervised agent did it on an academic budget in weeks.
What happened
Scattering amplitudes are usually computed to two or three loops. The planar N=4 super-Yang-Mills "toy model" has been pushed furthest with the amplitude bootstrap. Dixon and collaborators reached eight loops indirectly through a form factor. Anthropic's physicists asked Claude which of von Hippel's two challenges it was most likely to solve, then let the Claude Science harness run for days with minimal oversight. Von Hippel says either route would have cost an end user about one or two thousand dollars.
Why it matters
It is a frontier-level computation in theoretical physics done almost autonomously by an AI agent on a modest budget. As the challenger notes, it used known methods rather than new ones, and humans (Song He's group, with GPT-6 help) were close behind. It suggests that much "compute-limited" science is really limited by labour and engineering.
Changelog
- 2026-09-30: created (found in the lab-blog check; not previously covered)
Related events
- Anthropic launches Claude Science, an AI workbench for researchers (beta) ★★★
- Anthropic releases Claude Fable 5.1 and Claude Mythos 5.1 ★★★★★
- Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue) ★★★★
Sources (4)
- officialAnthropic (guest post by Matt von Hippel): Yes, Claude can do nine loops
- codeCosmic9: nine-loop six-point amplitudes computed by Claude (data page)
- discussion4gravitons: It only counts when AI gets to my field (the challenge, Aug 7, 2026)
- paperarXiv 2308.08199: eight-loop amplitude via form factor and antipodal duality (Dixon et al.)
id: 2026-09-25-claude-nine-loop-amplitude-n4-sym · updated 2026-09-30 · open in the interactive timeline