Direct discovery · Physics · Mathematics

BootLoops reports fifteen new Feynman-integral results with standalone numerical checks

Thirty multi-loop integral results with evaluation code: fifteen literature reproductions and fifteen claimed new results on explicitly stated kinematic domains.

Summary

A released manuscript presents thirty Feynman integrals spanning polylogarithmic, elliptic and Calabi–Yau cases. Fifteen reproduce known results and fifteen are claimed new, including restricted-domain nonplanar W-pair and light-by-light calculations. Each has an analytic form or differential equation with boundary data and standalone evaluation code. The author reports agreement with separate numerical calculations to at least thirty digits at points excluded from fitting.

AI role

Claude selected and operated deterministic symbolic and numerical tools in a human-directed hybrid bootstrap workflow.

Narrative role

Adds inspectable AI-assisted physics outputs beyond benchmark questions, while distinguishing new calculations from reproductions and retaining their exact domain restrictions.

Caveat

Author-reported results, with no independent execution or peer review verified in this run. Several new answers cover only slices, paths or fixed mass ratios; they are not complete physical scattering amplitudes. Schwartz was visiting Anthropic during the work.

Event

Date: 2026-10-01
Timeline role: Notable
Progress relevance: Scientific output
Validation: Internally reported

Evidence

Paper · Frontier lab announcement

Observed metrics

Integral outputs: 30 total; 15 claimed new; The other fifteen reproduce literature results; novelty is the author’s assessment.
Reported numerical acceptance: relative error below 1e-30; Separate numerical evaluations at held-out kinematic points, repeated at two working precisions.

Source: Matthew D. Schwartz / BootLoops ↗