We construct the complete (planar and non-planar) integrand for the
six-loop four-point amplitude in maximal $D\le10$ super-Yang-Mills.
This construction employs new advances that combat the
proliferation of loops and state-sums when evaluating
multi-loop $D$-dimensional unitarity cuts. Concretely, we introduce
two graph-based approaches, applicable in a range of theories, to
evaluating generalized unitarity cuts in $D$ dimensions: 1)
recursively from lower-loop cuts, or 2) directly from known
higher-loop planar cuts. Neither method relies on explicit state
sums or any sewing of tree-level amplitudes. The first method
meshes particularly well with the Method of Maximal Cuts to allow
direct construction of the complete six-loop integrand.