I think perhaps the first question should be, how are material particles
realized in this network? The impression I had was that the lqg spin networks were effectively "a theory of gravity without matter"-- that the spin networks described the dynamics of spacetime, but no one was sure where you "fit" the matter into that spacetime. The only work I'd heard of related to adding matter to LQG was the program Marcus mentions occasionally where, as I understood things, particles are considered to be persistent, propagating "braids" in spacetime.
Is any of this incorrect? Is there more to the present understanding of LQG than spacetime?