Dynamics of Coherence Capacity: Constitutive Transport, Balance Laws, and First Exit

Coherence capacity is a sourced diagnostic of the remaining validity of an effective description. A diagnostic does not move merely because it has been named. To discuss transport one must additionally choose a base space, an ordering variable, a fixed normalized capacity representative, a velocity or flux, source and repair terms, boundary conditions, and a solution concept. This paper supplies that missing model-level framework. We distinguish three inequivalent equations: material transport of a scalar reserve, a balance law for an additive density, and advection–diffusion–reaction of a field. We derive the corresponding integral balance, show exactly how nonlinear reparameterization changes a continuity equation, and extend the rowwise capacity budget to continuous trajectories. The bottleneck is the minimum of the reserve rows and is generally nonsmooth when the active row changes. Under a unique active row and a regular-value hypothesis, its first-exit set is a moving codimension-one hypersurface with an explicit normal-velocity formula. Two no-go results correct the former transport picture. Source-free passive transport preserves a positive reserve along characteristics. Source-free continuity transport preserves a positive density for every finite interval on which the flow has finite integrated divergence. Compression increases such a density; it does not by itself exhaust a reserve. A focusing inequality, finite-time zero, conservation law, or capacity bottleneck therefore requires additional dynamics or a declared constitutive relation. We give one explicit conditional model in which a compressing carrier lowers a reserve through a fixed decreasing constitutive map. No gravity, horizon, entropy, probability, collapse, irreversibility, or arrow of time is derived from transport alone.