Ψ-Architecture: Axiomatic Foundations of Adaptive Stability

This record presents the formalized Level I axiomatic foundation of the Ψ-architecture — a non-domain-specific framework for adaptive stability in complex systems. The work introduces a flow-centered ontology, establishes a universal No-Go theorem for optimization-based control beyond a finite complexity threshold, defines the adaptive time invariant τ = R × C, and proves that synchronization can arise without interaction or signal transmission as a geometric consequence of admissible phase–time constraints. The Ψ-operator is introduced as a measure of coherence density, and a directional invariant is defined to account for trajectory selection. This document serves as the primary reference for priority and citation; all subsequent elaborations are secondary to this axiomatic core.