Research Series · Foundations of Health
This series develops a mathematical and measurement foundation for health as a prospective property of organized systems: what is presently realized, what can continue under specified conditions, which future capacities are adequate for a declared requirement, and what an observation must preserve to determine that judgment.
Program
Paper I begins from a present state and a declared health specification. It separates present constitution from future adequacy and defines prospective health through the normal form present realization + requirement-adequate continuation capacity. Scenario, horizon, and formal requirement remain explicit indices rather than being absorbed into one undifferentiated label.
The response semantics are built upstream of capacity. Lawful histories are restricted by the constitution to the complete viable-continuation family, and capacity is then formed as a downstream observation and collection of that family. This distinction permits the framework to state exactly where information can be compressed and where stronger response semantics are required.
Paper I also constructs the requirement-visible capacity quotient: two capacity values are equivalent exactly when every declared health requirement gives the same adequacy answer on both. The quotient therefore retains precisely the information visible to the declared health language. A universal property shows that every requirement-sufficient representation determines this quotient on its attained range.
The foundational paper ends with explicit boundaries rather than extending its authority beyond the proved layer. Positive prospective capacity does not in general determine failure-sensitive robustness, and observation of present realization alone need not determine prospective health. These stopping points define the work handed forward to later papers.
What information must be preserved for health to be a well-defined prospective property, and what additional structure is required before that property can be measured, licensed, or used empirically?
The series is intentionally open. Later papers can govern admissible requirement, scenario, and horizon families; enrich response structure with robustness, probability, risk, cost, and control; establish physiological measurement sufficiency; and develop the empirical identification and validation layers required to connect the formal health proposition to real biological and clinical observations.
Paper sequence
Paper I establishes the foundational prospective-health architecture and its first information boundaries. Subsequent papers extend the query, response, measurement, and empirical layers while retaining that foundational normal form.
Published preprint
A machine-checked framework for prospective health.
Prospective health is formalized as present realization together with requirement-adequate continuation capacity. The paper establishes exact lawful/viable response semantics, the requirement-visible capacity quotient and its universal property, query relativity, qualified presentation invariance, and explicit robustness and measurement-sufficiency boundaries.
Current horizon
The foundational proposition is now explicit enough to ask sharper downstream questions without changing what the word health means inside the program. The next stages concern which queries are scientifically admissible, what response information must be retained for stronger notions such as robustness or risk, and which measurements preserve enough health-relevant information to determine the formal proposition.
Empirical identification remains a separate layer. Biological correctness, physiological sufficiency, diagnostic authority, treatment authority, uncertainty, calibration, and comparison with competing health assessments require evidence beyond theorem proving. The series is designed to make those obligations explicit rather than silently importing them into the foundational definition.