Volume III reconstructs regionality, locality, causal organization, physical time, propagation, topology, geometry, field structure, states, spectra, correlations, effective expansions, and renormalization without assuming spacetime or quantum field theory as primitives. Applying a mandatory five-regime master-constraint tribunal—requiring light-like propagation, induced time, localized matter, gravitational coupling, and cosmological drift—the volume reduces fourteen inherited candidate-world families to two inequivalent surviving operator architectures: a normal quasilocal family and a singular, domain-sensitive unbounded family.