Without having a first clue about the mathematical details, I can tell you it's most related to the work out of Sean Carrol et al trying to derive GR from QM, with spacetime being an emergent property of networks of quantum entanglement. Wolfram's idea is even more stripped down to hypergraphs of nodes with nothing but identity, and some number of neighbour nodes. Then they're exploring the space of possible various update rules for these graphs(he calls this rulial space). He claims that it should be possible to derive "all of physics" from this model, including the Schrodinger equation. He says the resulting emergent QM is most similar to Many Worlds, but interestingly in their model it seems like branches in fact merge together again(eventually, though it might take the entire lifespan of the universe). Carrol seems to think that starting with the Schrödinger equation is cleaner and more austere(of course he's rather biased), and I tend to agree.
My gut reaction to his mention of a rulial space is to be reminded of the Calabi-Yao manifold situation in string theory. If the space is even close to similar in size to that parameter space, that would be a theoretical nightmare.
My gut reaction to his mention of a rulial space is to be reminded of the Calabi-Yao manifold situation in string theory. If the space is even close to similar in size to that parameter space, that would be a theoretical nightmare.