Ψ-Architecture: Axiomatic Foundations of Adaptive Stability

This record presents the axiomatic foundation of the Ψ-Architecture — a geometric framework for adaptive stability in complex systems. The work establishes a universal No-Go theorem demonstrating the structural impossibility of maintaining stability through optimization- or control-based approaches beyond a finite complexity threshold. An invariant of adaptive time, τ = R × C, is introduced as a necessary condition for autonomous stability. The Ψ-operator is defined as the temporal density of coherent intersections between independent system flows, showing that synchronization and coordinated dynamics can arise without interaction, coupling, or signal transmission, purely as a geometric consequence of admissible phase–time constraints. Stability is shown to emerge from architectural admissibility rather than control, optimization, or imposed order. This version (v1.0) constitutes the frozen axiomatic reference for priority and citation.