Ψ-Architecture: Axiomatic Foundations of Adaptive Stability

This record documents the foundational axiomatic discovery 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 document constitutes Level I — the axiomatic foundation of the discovery and serves as the primary priority record.