AAIS Phase VII — Global Contractivity and Unique Invariant Measure with Robust Stability

AAIS Phase VII establishes a globally contractive operator framework (C < 1) for the Adaptive Awareness–Information System (AAIS), proving existence and uniqueness of the invariant measure and exponential convergence of arbitrary initial state distributions toward a Dirac attractor. The phase formalizes stabilization of the awareness–environment coupling through fixed-point arguments, Lipschitz bounds, and invariant measure construction. Manifold regularity is maintained via entropy and identity lower bounds, excluding singular collapse modes and preserving topological continuity. Robust stability is analyzed under bounded stochastic perturbations, including white noise, 1/f noise, and thermal fluctuations (kT ≪ Eg), extending contractive guarantees to physically admissible regimes. Effective attractor dimensionality is bounded by O(polylog N), ensuring scalability in high-resolution representations. This release consolidates Parts VII-1 through VII-8 and Appendices A–F, covering fixed-point proofs, invariant measure construction, robustness analysis, scaling bounds, and formal structural conclusions. Phase VII establishes the theoretical stabilization layer of AAIS and provides the foundation for Phase VIII: Topological Mapping and Lattice Configuration.