Hi, I'm trying to understand how relativity follows from the fundamentals of the model. In the paper by Jonathan I read:

"One of the foundational features of conventional special relativity is that two events are causally related if and only if they are timelike-separated. From our definition of the discrete Minkowski norm and the properties of layered graph embedding, we can see that a pair of updating events are causally related (i.e.connected by a directed edge in the causal graph) if and only if the corresponding vertices are timelike separated in the embedding of the causal graph into the discrete Minkowski lattice Z(1,n), as required."

Would it be possible to elaborate a bit more on the "if and only if the corresponding vertices..." ? For me this is not clear.

Thanks!