Constitutive Observability and the Measurement of Prospective Health

A prospective Health measurement requires evidence of a system's present organization and of its capacity for lawful continuation. This paper makes the state-identification problem exact in a fully specified two-site exchange model. Two presently qualified states yield the same baseline exchange flux and constitutive cost, yet their future viability differs under the same prescribed forcing. The complete initial observation fiber can be characterized algebraically.

An informative experiment can reveal the hidden difference while also changing the very prospective property under investigation. The study proves two model-relative methods that both maintain the specified constitution and preserve the respective future Health classifications: a heterogeneous-response experiment distinguished by subsequent flux, and a fixed-drive alternative distinguished by repeated constitutive-cost observation. Each comes with explicit mathematical conditions and local uncertainty guarantees for its stated observation channel.

Continuous-time counterexamples establish further measurement limits: sampled maintenance does not automatically establish all-time maintenance under a different work specification, and apparently qualified endpoints can conceal an intermediate failure of survival. The paper establishes mathematical observability and preservation results within its declared exchange model. It does not claim physical calibration of an imaging instrument or validated physiological Health measurement.