Dynamics and symmetries for pure phase mass matrices

We explore Higgs field interactions that can produce fermion mass matrices in the highly textured symmetric pure phase form, a form consistent with phenomenology. The potentials that can be made consistent with the symmetric pure phase form imply a simple set of discrete symmetries in the structure of the Lagrangian, symmetries closely connected to the hierarchical structure of fermion masses and the Cabibbo-Kobayashi-Maskawa matrix.