Representation Sufficiency in Prospective Health

Prospective health is evaluated through present realization and requirement-adequate continuation capacity. Papers I and II establish the viable-continuation family, query-visible quotient, and exact contextual transport. Paper III develops their common representation theory.

For a declared query family, the sufficient representations are exactly those that refine its canonical query-visible quotient. This principal criterion identifies the information needed to answer the full query language. The quotient is also the coarsest sufficient target for exact deterministic transport, while a state-level health observation is sufficient precisely when it preserves the distinctions of the full health-family quotient.

Explicit examples involving control, viable cost, route structure, finite probability, and failure-aware robustness connect these information boundaries to domain response semantics. Scalar success probability and attained minimum-cost codes provide concrete realizations of complete query-language quotients under their declared hypotheses.

The underlying definition of health remains unchanged. The machine-checked results characterize representation sufficiency, transport, health-observation requirements, and their limits; empirical observation design, calibration, uncertainty, and validation remain separate scientific obligations.