IIRC based on my reading of this a while back: the non-local glue is some sort of mega-deterministic theory where everything about the universe is encoded in some function meaning non-local stuff happens because in the end everything is in the universe.
There is some state function that takes the universe… which was my understanding of the theory and ultimately very unsatisfying.
You only need the topology to carry quantum numbers, as I understand it. Anyons are experimentally confirmed to carry non-local quantum state (ie, a single quantum value shared across the constituent electrons).
I was thinking about Bohm's theory which is the usual example of "hidden-variables" theory. Where the (not so) "hidden" part are the actual particles and their evolution is guided by the (non-local) wave function (defined in a 3N-dimensional configuration space).
There is some state function that takes the universe… which was my understanding of the theory and ultimately very unsatisfying.