  We introduce a prescriptive approach to generalized unitarity, resulting in a
strictly-diagonal basis of loop integrands with coefficients given by
specifically-tailored residues in field theory. We illustrate the power of this
strategy in the case of planar, maximally supersymmetric Yang-Mills theory,
where we construct closed-form representations of all ($n$-point N$^k$MHV)
scattering amplitudes through three loops. The prescriptive approach contrasts
with the ordinary description of unitarity-based methods by avoiding any need
for linear algebra to determine integrand coefficients. We describe this
approach in general terms as it should have applications to many quantum field
theories, including those without planarity, supersymmetry, or massless spectra
defined in any number of dimensions.
