Computational Locality

Computational Locality is the principle that the substrate evolves by strictly local recursive rules: each point interacts only with the points inside a finite interaction radius, so influence spreads at a finite speed bounded by computational constraints. The book builds it from two pieces. A neighborhood definition fixes which points can couple at all, the local coupling structure that sets the substrate's connectivity, which the book calls a cosmic social network. An interaction weight then says how strongly they couple: the weight falls off exponentially with separation over an interaction decay length W(x,y) = w_0 × exp(−||x−y||²/σ_0²), where w_0 is the coupling strength [∅] and σ_0 the Interaction Decay Length [𝕃], so the weight is [∅]. The book compares this to physics-like models of computation in which update rules are limited to nearest neighbors. The neighborhood is N(x) = {y ∈ D | ||x − y|| ≤ r_0}, where N(x) is the neighborhood around position x [𝕃³], y a position in the domain [𝕃], D the spatial domain [𝕃³], ||x − y|| the Euclidean distance between positions [𝕃], and r_0 the interaction radius that establishes computational locality [𝕃]. Computational Locality connects to Zero Substrate, Local Neighborhood Configuration Matrix, Spatial Coupling Kernel, Recursive State Evolution and Causal Propagation.