Structural Axioms and Theorems of Coherence, Drift, and Directionality for Long-Horizon Adaptive Systems

This work presents a compact axiomatic and theorem-based foundation for long-horizon adaptive systems operating under structural coherence constraints. Information is treated not as stored data but as a persistent structural constraint on admissible future evolution. The framework formalizes coherent structural closure, residual-driven reactivation, inevitable drift, internal time as a viability horizon, and directionality as a primary ontological operator. The proposed axioms and theorems establish invariant principles governing coherence preservation, identity maintenance, and controlled adaptation under prolonged interaction with a changing environment. Drift is shown to be unavoidable, inertial propagation to be energetically dominant, residual structure to be the sole carrier of relevance, and internal time to bound validity independently of instantaneous error. These axioms and structural theorems constitute a minimal but non-trivial theoretical core underlying coherence-preserving architectures such as PETRONUS, in which spin, drift, residual, internal time, and directionality are realized as explicit operational variables.