Gravitational Manipulation Theory v1.1: Dynamical Field Solutions and Self-Consistent Boundary Realization

Starting from the representative ansatz introduced in GMT v1.0, this work solves the coupled field equations of Gravitational Manipulation Theory (GMT) as a boundary-value problem and promotes the schematic chain Ω → χ → F(χ) → gμν from an assumed profile to a solved, self-consistent field configuration. The central result of v1.1 is that this chain can be closed, following the progression Field Solution → Stability → Backreaction → Self-Consistency (Representative → Solved → Stability Verified → Self-Consistent). The paper obtains numerical single- and double-wall solutions of the static reduced equations, extends them to finite wall separation and asymmetric boundary conditions, verifies their scalar-sector linear stability including the correct treatment of the translational zero mode, closes the scalar–metric backreaction loop to obtain a self-consistent solution, and quantifies the domain of validity of the v1.0 representative ansatz. These results demonstrate the existence of solutions for specified models and boundary conditions. They are not a global existence theorem and do not assert a complete coupled scalar–metric perturbation analysis, long-time nonlinear stability, experimental realisability, or observational admissibility. Observational confrontation is deferred to GMT v1.2. The phase convention is fixed as χ_N = 0 (normal/screened phase) and χ_G ≈ v_D (GMT-modulated phase). Theory-state tags [Exact], [Derived], [Effective], [Solved], and [Framework] are used throughout, with the explicit caveat that [Solved] ≠ [Exact]. The programme advances as:v1.0 (Can the framework close?) → v1.1 (Do the field solutions exist?) → v1.2 (Are they observationally allowed?).