Prospective Health under Declared Specifications

Description The formal definition of prospective Health requires an empirically grounded account of organizational realization, lawful continuation, and the adequacy of prospective capacity. This fifth paper in the Health, Formally Defined series investigates the measurement conditions under which those quantities can be reconstructed, computed, and evaluated from incomplete observations. Using longitudinal observations from the 35-hectare Harvard Forest ForestGEO plot, we construct an auditable empirical-synthetic measurement system comprising identity-sensitive observation processing, stochastic state reconstruction, demographic parameter estimation, prospective history generation, and query-relative Health evaluation. The framework preserves unconditional candidate-history weights, distinguishes viable from failed continuations, and evaluates continuation and reserve-qualified adequacy under declared specifications. The investigation addresses three scientific questions: identification and calibration of the required measurements and dynamical models; reliability of prospective adequacy decisions under reconstruction error, model discrepancy, and numerical uncertainty; and sufficiency of representations for the declared Health queries. Real-data reconstruction reveals substantial individual-diameter interval undercoverage and establishes nonidentification of biological threshold entry from available stem records. Controlled synthetic experiments demonstrate strong broad-range discrimination alongside markedly weaker near-boundary decision reliability. Four-way oracle experiments expose interacting contributions from state reconstruction and demographic parameter inference. An exact representation counterexample establishes the insufficiency of cohort RMS diameter for juvenile-sensitive queries. Independent adult-mortality observations provide a substantive predictive-model test. Among 7,557 matched hemlock stems, 685 deaths were observed against approximately 280 predicted. The observed count lies beyond the fitted shared-hazard model's central 95% predictive interval of 220–347 deaths. A separate path-level audit localizes a pronounced reconstruction-sensitive continuation difference entirely to terminal juvenile-support failure. These findings establish a computationally inspectable methodology for evaluating the evidential foundations of prospective Health measurement, identifying model inadequacy, and localizing consequential information loss. The resulting Health calculations remain conditional on their declared ecological specifications, observational support, and predictive laws. The study provides explicit requirements for subsequent biological identification, calibration, and prospective validation.