Coherence-Constrained Path Resolution: The Structural Inevitability of Finite Processing Rate

This paper establishes a single structural result: any universe that maintains coherent realization must exhibit a finite local rate of physical evolution. The argument is purely logical and proceeds without invoking dynamics, optimization, energy, or physical assumptions of any kind; the paper makes no empirical claims. Starting from the requirement that realization remain globally coherent, the paper shows that evolution must proceed by selective resolution of mutually incompatible continuations; that such selection cannot occur simultaneously across all incompatible candidates; and that the resulting ordered resolution necessarily implies a finite density of realized transitions — an effective local processing rate. This rate is not a primitive input but an unavoidable structural consequence of coherence preservation. Two features of the ordering carry the downstream weight. First, it is a partial order generated by dependency: precedence relations arise only where the admissibility of one resolution depends on the prior resolution of another, so only dependency-related events are ordered — mutually independent resolutions are not — which is the structure a relativistic causal order requires, derived here rather than postulated. Second, coherence-preserving evolution must defer unresolvable incompatibilities rather than settle them; the deferred ("dependent") states persist, and their persistence is what the rate measures — the seed of the directional substrate developed in the companion papers. The directional asymmetry of physical time — its arrow — follows from the same argument: coherent realization proceeds by ordered, irreversible exclusion of incompatible continuations. Once a possibility is excluded, coherence prevents its reinstatement. The arrow is logical, not statistical. The identification of the throughput with physical proper time is operational, not metaphorical: clocks are matter, subject to the same coherence constraints as everything else, so no clock can register transitions faster than the local resolution throughput. Since proper time is operationally what clocks measure, the identification is forced by the universality of the constraints across all matter, measurement devices included. The framework connects two levels of description. The Realization Structure Theory (RST) establishes single-history primacy — the commitment from which CCPR's conclusions follow, and which the paper states as its explicit conditionality. Processing-Rate Theory (PRT) derives the dynamics and physical predictions of the resulting rate field. The present work bridges these levels by showing why a rate description becomes structurally necessary, independently of its physical implementation: CCPR gives the necessity — the ordering, the arrow, and the finiteness of the rate; PRT gives its dynamics. A constructive simulation study (DOI: 10.5281/zenodo.18057662) provides a numerical existence proof that CCPR-style incompatibility resolution, instantiated on a minimal discrete substrate without energy or stochastic dynamics, generically produces bottlenecks, metastability, and irreversible ordering — confirming the structural claims constructively. No new physical fields, forces, or ontological entities are introduced. The analysis is minimal by design: it establishes what must hold in any coherent realization, and leaves every physical instantiation to the downstream frameworks. Companion to: The Realization Structure Theory (DOI: 10.5281/zenodo.17885662), The Resolution Substrate (DOI: 10.5281/zenodo.19441705), Processing-Rate Theory (DOI: 10.5281/zenodo.18331952), Einstein Field Equations from Shell Geometry and Horizon Thermodynamics of a Universally Coupled Scalar Field (DOI: 10.5281/zenodo.19417275), The Radiative and Tangential Gravitational Sectors (DOI: 10.5281/zenodo.20499618)