Ψ-Architecture: Axiomatic and Technical Foundations of Adaptive Stability Level I–II Interim Fixation

This release constitutes an interim architectural fixation of the Ψ-Architecture, comprising its first two completed structural layers: Level I – Axiomatic Foundations A flow-centered ontology and a geometric theory of adaptive stability, introducing: – the invariant of adaptive time τ = R × C, – the No-Go theorem for optimization-based control in complex adaptive systems, – and the Ψ-operator as the architectural condition for invariant-preserving coherence. Level II – Technical and Geometric Realization A formal and operational development of the axiomatic core, including: – architectural conductance and phase–time constraints, – toroidal topology and the Temporal Integration Node (TIN) as necessary structures for adaptive circulation, – algorithmic and empirical protocols for signal-level realization and independent reproducibility. The Ψ-Architecture establishes stability, coherence, and adaptivity not as properties imposed through control or optimization, but as consequences of geometric admissibility within a unified circulation architecture encompassing physical, biological, cognitive, and artificial systems. This interim fixation is intended to secure architectural priority and provide a stable reference point for subsequent theoretical refinement, empirical expansion, and applied realizations. It does not represent a final or closed formulation, but a structurally complete foundation upon which further layers of the Ψ-Architecture will be built. Author: Anna Taranova ORCID: 0009-0002-7993-3243