  Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic
physical and mathematical constraints, including physical constraints on their
branch cut structure and various empirically discovered connections to the
mathematics of cluster algebras. The power of the bootstrap program for
amplitudes is inversely proportional to the size of the intersection between
these physical and mathematical constraints: ideally we would like a list of
constraints which determine scattering amplitudes uniquely. We explore this
intersection quantitatively for two-loop six- and seven-point amplitudes by
providing a complete taxonomy of the Gr(4,6) and Gr(4,7) cluster polylogarithm
functions of arXiv:1401.6446 at weight 4.
