Stable-Neutral Geometry of Protected Critical Manifolds: Internal Freedom, Direction-Resolved Restoration, and Bounded Adaptation

We study how a structure can remain locally stable without freezing its internal degrees of freedom. Let M be a compact Morse-Bott critical manifold of a cost functional S, with Hessian kernel equal to TM and a uniformly positive restriction to the normal bundle. Rather than deriving this stable-neutral geometry, we determine its local dynamical and response consequences. The associated gradient flow is exponentially attracting toward M at every rate mu < lambda_perp; controls tangent to M preserve M, while bounded small normal forcing confines trajectories to a local O(epsilon/mu) tube. Retaining the full normal Hessian A_psi, rather than only its minimum eigenvalue, yields a direction-resolved response law: its eigenvalues determine transient recovery rates and A_psi^{-1} gives the leading-order normal displacement under sustained forcing. In a curved-manifold example, rates identified from unforced impulse recovery are frozen and predict held-out forced displacements to within the stated numerical tolerance, without refitting. The results are local and geometric; the origin, global accessibility, thermodynamic interpretation, and physical realization of M remain outside the present scope.