Building on Paper A (canonical emergence of the density operator) and Paper B (relative modular dynamics and CPTP completion), we introduce phase structure and the emergence of locality in a conservative, information-theoretic manner. A phase is specified by an access structure encoded by an optimal partition P , the corresponding accessible algebra AF , and a pointer/center structure ZF . The reference state σF within a macro-constraint class is defined canonically via a maximum-entropy (MaxEnt) construction under macroscopic constraints extracted from AF . We emphasize the equivalence between MaxEnt references and relative-entropy projections, which provides a canonical and minimal notion of phase stability. We introduce a canonical information-geometric metric (BKM/Fishertype) on the state manifold and connect these constructions to modular spectral diagnostics used in numerical protocols, such as spectral quantiles kq = −log λq and commutator-based probes.