What is the difference between physical space and branchial space?

In Wolfram's model both spaces emerge from the same underlying rewriting, but by two different limits. Physical space is the large-scale shape of the spatial hypergraph — where things are — so distance there measures how relations inside one state connect. Branchial space is the large-scale shape of the branchial graph, where two states are close when they share a recent common ancestor in the multiway system; distance there measures shared history, not spatial proximity. The claim that branchial space is the arena for quantum mechanics is a proposal, not established physics.