AAIS Phase V — Beta Module: Dynamical Interface Construction and Gamma Handover Protocol

Title: AAIS Framework: Dynamical Interface Construction (Phase V — Beta Module) Description: This repository contains the mathematical monographs and structural framework of Phase V (Beta Module) of the AAIS project. The primary objective of this module is to construct a mathematically rigorous dynamical interface between the static operator-algebraic foundations established in Phase V — Alpha and the higher mathematical structures reserved for the subsequent Gamma phase. The Beta Module operates strictly within the abstract domain of functional analysis and operator theory, without introducing empirical claims, physical interpretations, experimental predictions, or runtime dynamical assertions. Repository Structure (Parts I–IV): • Part I: Semigroup Dynamics and Dissipative Generator Foundations • Part II: Modular Evolution and RG–Modular Coupling • Part III: Construction of the Asymptotic Intertwiner • Part IV & Appendix G-A: Interface Certification and Gamma Initialization Boundary Core Mathematical Framework: The documents establish strongly continuous semigroup dynamics, dissipative generator structures, modular coupling frameworks, asymptotic intertwining constructions, and Strong Operator Topology (SOT) convergence mechanisms. The formally specified Beta interface payload is: Λ(Beta → Gamma) = (Hα, Tt, W∞) where Hα denotes the inherited Hilbert-space foundation, Tt the Beta contraction semigroup, and W∞ the asymptotic intertwiner constructed under the declared mathematical hypotheses. This repository represents the conditionally closed structural framework of the Beta Module, prepared for external mathematical review and subsequent Gamma-phase development.