I skim through it rapidly, but the paper seems interested in building a framework for finding out if and when a microstate participates in the outcome of the ma

I skim through it rapidly, but the paper seems interested in building a framework for finding out if and when a microstate participates in the outcome of the macrostate, or if the macrostate dynamics can be evaluated without looking at the microstate. That is, given a time series Z observed as a function of another time series X (what is called in the paper coarse-graining function), past values of Z are enough to establish causal connections with future values, without knowing X. This is what I understood, at least.