Constitutive Continuation Capacity

This paper develops a machine-checked framework for prospective health as a property of present constitutive organization together with requirement-adequate continuation capacity. For a health specification ( S), requirement (r), scenario (d), horizon (t), and state (x), the foundational proposition is [Health{ S,r}(x;d,t){ S}(x){ S,r}!(Capacity{ S}(x;d,t)).] The formal development separates lawful response, constitutive continuation, observation, capacity representation, and adequacy. Viable continuations are identified exactly with the lawful histories satisfying the declared constitutive-continuation predicate. A domain capacity representation is then derived from this complete viable-continuation family through explicit observation and collection maps. For a fixed formal requirement language, the paper constructs a requirement-visible health-capacity quotient that identifies exactly those capacity differences invisible to every declared health requirement. A universal property characterizes this quotient as the coarsest requirement-sufficient partition of the capacity carrier. Finite machine-checked models establish requirement, scenario, and horizon relativity, strict quotient behavior, and qualified presentation invariance. Two boundary results delimit the foundational semantics: positive prospective capacity is insufficient in general to determine failure-sensitive robustness, and present-realization observation can be insufficient to determine prospective health. These results establish a formal measurand for prospective health while separating the system-level proposition from its observational and empirical identification. This is Paper I in a series on the formal and measurement foundations of health. Subsequent work develops query governance, richer future-response structure, and measurement and validation theory while retaining the foundational prospective-health normal form.