@paraw @cminz @paulbalduf

For the partial order, there exists both a convention where it is a strict causal precedence, as well as one where it is precedes or equal to. As mentioned, we can (though it is uncommon) get unrelated elements (sometimes called non-Hegelian) which have the exact same causal relations to every other element and are therefore indistinguishable based on their set of relations.

@paraw @cminz @paulbalduf

Some of the challenges mentioned above are more serious for dynamically producing causal sets. Kinematically, things are easier, and we mainly need to worry about computational challenges of working with large matrices. Poisson sprinklings are the main way we (practically) produce such causal sets for kinematic and phenomenological studies. These sprinklings are a random sampling of a manifold using a Poisson process.

@paraw @cminz @paulbalduf

There is definitely a lot to be explored, graph theoretically, about the structure of causal sets. It is something that hasn't received enough attention in the past, but is very natural and fruitful to do.