It so happens that the standard formalism of quantum theory provides a rather simple mathematical description of these correlations. And it is certainly far from obvious how this might emerge from detailed mechanisms associated with threads in a network. But the fact that this and other results seem simple in the standard formalism of quantum theory should not be taken to imply that they are in any sense particularly fundamental. And indeed my guess is that most of them will actually in the end turn out to depend on all sorts of limits and idealizations in quantum theory—and will emerge just as simple approximations to much more complex underlying behavior.
In its development since the early 1900s quantum theory has produced all sorts of elaborate results. And to try to derive them all from the kinds of models I have outlined here will certainly take an immense amount of work. But I consider it very encouraging that some of the most basic quantum phenomena seem to be connected to properties like causal invariance and the network structure of space that already arose in our discussion of quite different fundamental issues in physics.
And all of this supports my strong belief that in the end it will turn out that every detail of our universe does indeed follow rules that can be represented by a very simple program—and that everything we see will ultimately emerge just from running this program.