Phase–Flow Coherence (PFC v4): The Inevitability of Quantum Dynamics and Probability

This record contains Part I and Part II of Phase–Flow Coherence (PFC v4), uploaded as a single unified work. PFC v4 establishes, by eliminative (Type-A) reasoning, the inevitability of Schrödinger-type dynamics and Born-rule probability as the only internally coherent representation compatible with: • finite resolution,• irreversible internal projection,• non-privileged phase representation. Part I fixes the dynamical form by eliminating all non-linear, dissipative, or representation-dependent alternatives, leaving Schrödinger-type bookkeeping as the unique stable vessel. Part II fixes the minimal fluctuation statistics required for finite-resolution stability, preparing the ground for Alpha Locking without introducing optimization, fitting, or probabilistic postulates. This version is a structural and conceptual completion of PFC v3.No new assumptions are added; all results follow by exclusion.