  We extend the applications of prescriptive unitarity beyond the planar limit
to provide local, polylogarithmic, integrand-level representations of
six-particle MHV scattering amplitudes in both maximally supersymmetric
Yang-Mills theory and gravity. The integrand basis we construct is diagonalized
on a spanning set of non-vanishing leading singularities that ensures the
manifest matching of all soft-collinear singularities in both theories. As a
consequence, this integrand basis naturally splits into infrared-finite and
infrared-divergent parts, with hints toward an integrand-level exponentiation
of infrared divergences. Importantly, we use the same basis of integrands for
both theories, so that the presence or absence of residues at infinite loop
momentum becomes a feature detectable by inspecting the cuts of the theory.
Complete details of our results are provided as ancillary files.
  This work has been updated to take into account the results of
[arXiv:1911.09106], which leads to a simpler and more uniform representation of
these amplitudes.
