Three Laws of Selective Realization: A Process-Theoretic Reformulation of Classical and Relativistic Dynamics

This work presents a process-theoretic reformulation of physical dynamics based on three laws of selective realization. Instead of treating forces, energy transfer, or variational principles as fundamental causes of motion, the framework introduces realizability as the primary structural condition governing admissible worldlines in spacetime. A non-negative functional of structural incompatibility, ΦΣ, defines whether a worldline is realizable within a given realization system Σ, encompassing spacetime geometry, boundary and contact constraints, internal degrees of freedom, and environmental context. Structurally incompatible configurations (ΦΣ > 0) cannot persist and undergo a normalization process in a distinct process time τ, governed by a covariant gradient flow. Physical motion emerges as the stable fixed point of this normalization under system invariants, with the classical action principle and geodesic motion arising as limiting cases rather than fundamental postulates. The framework replaces instantaneous dynamical causation with covariant processual selection and provides a unified structural account of elastic and inelastic collisions, gravitational free fall, metastability, and degeneracy of realizations. Classical mechanics and general relativity are recovered as effective descriptions of structurally rigid regimes in which admissible realizations are unique. This work is intended as a foundational formulation. Explicit construction of system-specific incompatibility functionals, empirical reconstruction, and extensions to quantum regimes are left for future studies.