Architectural Limits of Optimization and the Geometry of Adaptive Stability

This work introduces an architectural framework specifying the conditions under which stable regimes become realizable in complex adaptive systems. The framework is positioned at a pre-physical level: it does not describe dynamics, interactions, or optimization processes, but defines admissibility constraints that any realizable configuration must satisfy. Four architectural invariants are identified: structural time (τ), coincidence density (ζ), circulation topology (Ω), and admissibility boundary (B). Physical laws are treated as projections of admissible architectural regimes rather than fundamental constraints. The framework establishes a universal limit on control- and optimization-based stability in high-dimensional systems and introduces architectural causality, where realization is determined by invariant-preserving admissibility rather than interaction or signal transmission. A new class of physical coupling—architectural coupling—is defined as correlation through shared admissible regimes without energy exchange, information transfer, or field mediation. Explicit falsifiability conditions and predicted experimental signatures are provided. The results apply across physics, biology, artificial systems, and cognitive architectures, offering a unified geometric account of adaptive stability and realizability.