KJ First Measurement Theory: Admissibility, Structural Non-Measurability, and Measurement Horizons

This paper introduces KJ First Measurement Theory, a foundational framework in which measurement is not treated as a primitive operation but as a derived, admissibility-constrained property of a system. Rather than assuming that all well-defined quantities are measurable in principle, the theory formalizes measurability as dependent on the existence of admissible measurement operations that preserve system identity and avoid structural collapse. Non-measurability is shown to be a structural property, not an epistemic limitation. The paper proves that unmeasurability admits finite certificates in the form of minimal infeasible constraint sets required by any attempted measurement. A partial order on measurable quantities is induced by inclusion of admissible measurement operations, yielding a measurability lattice in which logical conjunction and disjunction of measurements need not exist. The framework further introduces measurement horizons: maximal sets of jointly admissible quantities that define absolute limits on collective measurement. These horizons are shown to be invariant under admissible transformations, establishing global structural bounds on what can be measured simultaneously. The theory is developed axiomatically and independently of probabilistic, dynamical, or optimization-based assumptions, providing a pre-measurement foundation for scientific theory in which the limits of measurement arise from structural admissibility rather than noise, resolution, or incomplete knowledge.