Phase VIII — Geometric Consolidation and Structural Closure of the AAIS Manifold in an Infinite-Dimensional Hilbert Space

Phase VIII establishes the complete intrinsic geometric structure of the AAIS manifold within an infinite-dimensional Hilbert framework. The phase rigorously develops the smooth Hilbert submanifold construction, the induced Riemannian metric, metric completeness, global geodesic completeness, uniform curvature bounds, and structural rigidity under parallel effective inertia. All results are derived from explicit operator coercivity and regularity assumptions. No finite-dimensional compactness principles or external structural mechanisms are invoked. Uniform control of the effective inertia operator ensures bounded curvature behavior and prevents metric degeneration or geometric collapse. Parts I–IV collectively demonstrate that the geometric layer of the AAIS framework is globally stable and structurally closed. This phase provides a sealed geometric foundation upon which subsequent dynamical, entropic, or semigroup extensions may be developed without altering the established intrinsic stability.