Unfaithful embedding of causal sets

In the causal set approach, spacetime is a continuous approximation of a faithful embedded causal set. But the faithful embedded causal set describes the empty spacetime and cannot describe matter. Only faithful embedding of coarse grained causal set is necessary for the emergence of spacetime. The initial causal set can be unfaithfully embedded. The following properties of the universe can be the consequences of the unfaithful embedding: antiparticles, fields of interactions, the inhomogeneous distribution of the matter.