That’s all nice,… but what does it tell you?
One of the most pressing question from my point of view is finding a proper physical interpretation for the framework. Most objects on the abstract side of the CFS have a nice correspondence to the classical objects in the continuum limit. The only thing that is really the odd one out is the central piece there of, namely the causal action (and constraints). Sure there is the straight forward interpretation that the action minimizes the amount of timelike separation in a spacetime. But somehow I do not find this a sufficient answer.
One direction that might be interesting that in the correspondence, the map F is given by the local correlation operator. This might lead way to an entropic interpretation of the causal action principle. As in, that it tries to minimize the correlation of the sea states in your spacetime which at first glance can also be thought of as maximizing chaos, which would lead towards an entropic interpretation.
Note one interesting interpretation that comes immediately from the formalism (if taken seriously) is that the Hilbert space and hence the Dirac sea is the stage on which the physical world plays.
So are the bosonic fields given by collective deformations of the sea states. I like to compare that to a walk on the beach. If I want to know the shape of your foot, I can either look at your foot, or I can look at the collective behavior of the grains of sand where you just stepped. The information obtained is equivalent.