Operational Principia of Knowability

This paper formulates a structural framework for the persistence and accumulation of functional structure in any substrate class admitting four primitive components: environment, functional structure, substrate, and observation function. The framework's claims are organised in two layers. The first is a scope claim about mechanism: in any system possessing the four primitives in which functional structure persists across times longer than the substrate persistence timescale, the operative mechanism is a cycle of variation, selection, retention, and (under conditions of substrate turnover) transmission. The second is a regime claim about dynamics: under postulates of multiplicative cycle action and open accumulation, the cycle generates cumulative functional structure along an exponential trajectory. Empirical evidence is presented for the conjunction in three independent substrate classes — biological evolution, scientific knowledge accumulation, and technological development — spanning eight orders of magnitude in iteration speed. A prospective predictive test is identified in the substrate class of large language model systems, with three classes of falsifying observation specified. The framework is positioned as a generalisation of the apparatus developed in Paper 0 of this series for the case of an internal cognitive observer in a simulated world; Paper 0 stands as the empirical anchor from which the present framework was extracted, not as a particular case of it.