An ambitious goal for this class of models is to unify all the forces and particles in nature using a single scalar field and a simple rule for describing the evolution of that field.
All energy is electromagnetic.
This requires some way to construct neutral matter from an electromagnetic field. The Klein Gordon equation for a particle with rest mass presents an additional problem. This is the classical wave equation with a new term involving the rest mass of the particle. This may be possible if there is a high carrier frequency near the highest frequencies that can exist in the discrete model. It would be the equation for a wave that modulates the high frequency carrier.