  The four-loop Sudakov form factor in maximal super Yang-Mills theory is
analysed in detail. It is shown explicitly how to construct a basis of
integrals that have a uniformly transcendental expansion in the dimensional
regularisation parameter, further elucidating the number-theoretic properties
of Feynman integrals. The physical form factor is expressed in this basis for
arbitrary colour factor. In the nonplanar sector the required integrals are
integrated numerically using a mix of sector-decomposition and Mellin-Barnes
representation methods. Both the cusp as well as the collinear anomalous
dimension are computed. The results show explicitly the violation of quadratic
Casimir scaling at the four-loop order. A thorough analysis concerning the
reliability of reported numerical uncertainties is carried out.
