Prospective Health Across Contexts

This paper develops the contextual and relational transport theory of prospective health introduced in Paper I. The fixed-query health architecture is retained unchanged: health at state (x), scenario (d), horizon (t), and requirement (r) is determined by constitutive realization together with adequacy of the prospective capacity generated from viable histories. Paper II introduces context-dependent whole-query licensing and the associated health-visible quotient of capacity. For each context, licensed requirements determine an observational equivalence relation on raw capacities, yielding a quotient that retains exactly the distinctions visible to the governed health language. The paper then studies how raw and health-visible information behave under relations between source and target states. A general relation-attained factorization theorem characterizes when a state relation and source/target capacity functions determine a unique transport map on attained capacity values. The same construction is applied to health-visible quotient observations, producing deterministic transport criteria, exact obstruction witnesses, and an explicit relation-valued transport that remains defined under branching. A finite developmental model separates stage-dependent health semantics from horizon-dependent prospective capacity. Its complete capacity census determines a unique global now-to-long capacity map at the declared capacity-representation level, and the resulting map is identified with an explicit recovery operation. Further finite controls exhibit stage-induced quotient refinement, branching and coalescence, raw-capacity indeterminacy with health-visible determinacy, and combined stage–horizon transport. An open-system support model provides corresponding raw and quotient-level factorization obstructions. A withdrawal control isolates the additional conditions required to transport full health truth: realization compatibility and licensed adequacy compatibility supplement health-visible transport. The paper distinguishes standard quotient and factorization mathematics from the health-specific organization of contextual licensing, observational equivalence, relation-generated capacity evolution, transport, obstruction, and full-health semantics. The principal definitions, proofs, finite witnesses, and obstruction calculations are displayed in the manuscript and independently machine checked in Lean.