Structural Determination Theory III: Structural Determination of Evolution

Structural Determination Theory (SDT) develops a unified framework in which higher-order organization is progressively determined from primitive foundations through internally determined development. This work establishes admissible evolution and realization as induced structures determined from scalar preservation and relational consistency. Building upon primitive differentiation and admissible scalar structure established previously, admissible evolution is determined as the semigroup of scalar-preserving transformations, with the corresponding generator induced as the minimal internal mapping associated with infinitesimal transformation organization. Admissible evolution further induces relational ordering and coexistence through admissible reachability and compatibility. Reconstruction limitation consequently forces realization as the minimal distinction-preserving structure compatible with admissible reconstruction. The resulting framework preserves scalar, algebraic, relational, and dynamical consistency without introducing independent dynamical primitives.