Constitutive Continuation Capacity

This paper formalizes prospective health as a property of a presently realized organization together with its capacity to continue adequately under specified future conditions. For a health specification S, formal requirement r, scenario d, horizon t, and present state x, the foundational form is Health_S,r(x; d, t) if and only if the system presently realizes the specified organization and its prospective capacity is adequate for the declared requirement.

The response semantics begin with the complete family of lawful histories and identify the viable continuations exactly as the constitutively continuing lawful subfamily. Capacity is then a downstream representation obtained by observing and collecting that viable family; it may therefore compress distinctions among viable responses. A two-sided constitutive response representation conservatively extends the positive capacity representation, while an explicit finite obstruction shows that positive persistence information alone need not determine failure-sensitive robustness.

A formal requirement language induces an equivalence relation on capacity: two capacity values are identified exactly when every declared adequacy predicate gives the same answer on both. Every adequacy predicate and prospective-health query descends to the resulting requirement-visible quotient, and every requirement-sufficient encoding uniquely determines that quotient on its attained range. Finite witnesses establish strict collapse of requirement-invisible variation while preserving requirement-visible differences.

The finite dynamic fixture also proves requirement, scenario, and horizon relativity for a single present state, while presentation invariance is obtained under explicit transport of realization, capacity, and adequacy. The framework ends with two information boundaries: positive prospective capacity does not in general imply robust persistence, and observing present realization alone need not suffice to determine prospective health. Scientific licensing, richer risk and control semantics, physiological measurement sufficiency, and empirical identification are retained as downstream layers.