In discrete models of spacetime, what are some implications of the Einstein equation

We have several models of discrete spacetime. Sorkin has a causal growth dynamics, there's spin foams, Panangaden showed a correspondence between interval domains and spacetimes. I am looking for anything that looks like the Einstein equation. Specifically, what are some required properties of a morphism of a spacetime (however it is modelled)?

• A non-trivial model of "something" has to be able to predict some non-trivial properties of "something". What, exactly, can these things predict? – CuriousOne Jul 2 '15 at 23:08