What was already known
Dixon and collaborators had reached eight loops. Song He’s group produced a concurrent nine-loop symbol with GPT-6 assistance; precise overlap and priority between the two outputs remain unresolved.
AI involvement
Fitzpatrick and Mishra-Sharma set the target and continuation prompts. Claude Fable 5.1 carried out the form-factor and direct-bootstrap calculations using established human-developed methods.
Within the supplied physics task, Claude executed the central nine-loop computation by two routes with only continuation prompts and no scientific steering reported.
Importance
Extends a frontier theoretical calculation from eight to nine loops and releases data for further checks.
Limitations
This is a calculation in a theoretical model, not a prediction for observed particles. The programs are not distributed, and released checks do not provide a complete exact certificate for every coefficient and constraint.
Technical verification
The site documents exact modular cross-checks and sample comparisons, and Dixon reports an independent human validation mostly through the form factor. Published checks do not constitute a complete exact certificate of every coefficient and all physical constraints; some rational coordinates remain unreconstructed.
Independent checking
Independent validation chiefly by deriving/checking the form factor relation and comparing with his group’s expected format. Nine-loop form factor and resulting amplitude
- Checker
- Lance Dixon
- Scope
- Claude computed the nine-loop six-particle MHV amplitude in planar N=4 super Yang–Mills using established bootstrap methods. The released symbol uses quintuple coproducts modulo two 31-bit primes; most, but not all, nonzero coordinates are reconstructed as certified rationals. A separate direct bootstrap agrees on compared coefficients, and a nine-loop function is reported.
- Basis
- Reported by the linked checker
Formal checking
Exact finite-field coefficient comparisons, rank/structure checks and 1,000-word eight-loop comparison. Nine-loop symbol representations and eight-loop control
- Checker
- Claude computation team and released validation scripts
- Scope
- Claude computed the nine-loop six-particle MHV amplitude in planar N=4 super Yang–Mills using established bootstrap methods. The released symbol uses quintuple coproducts modulo two 31-bit primes; most, but not all, nonzero coordinates are reconstructed as certified rationals. A separate direct bootstrap agrees on compared coefficients, and a nine-loop function is reported.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Dixon identifies the established bootstrap and antipodal-duality recipe and explains how Claude applied it; the result uses known human methods rather than an unexplained new mechanism.
Correction and publication history
The nine-loop computation is assessed within the released modular and rational-reconstruction scope.
Read this published revision