Is this thread a duplicate of https://community.wolfram.com/groups/-/m/t/1950038 ?
Anyway, as I explained in your other thread regarding this topic, layered digraph embedding for acyclic graphs is a well-defined optimization problem, and hence the embedding of both causal graphs and multiway evolution graphs into integer lattices is well-defined (so the resultant norm is, as well). Please do let me know if you think I missed something important here, but I believe this is explained in my two papers :)