Causal Exterior Ownership for a Moving Einstein–Scalar Quantum Sector

This ninth paper in the Schwarzschild Quantum Gravity series establishes a local causal exterior for the self-consistent Einstein–real-scalar quantum sector developed in the preceding papers. Beginning with the positive-coupling coherent quantum source and its associated nonlinear interior geometry, the investigation constructs a retarded exterior, derives the physical junction conditions across a moving timelike worldtube, and establishes first-order stationarity of a complete two-region Einstein–scalar action. A boundary-reseeded nonlinear characteristic fixed point produces a nonempty (C^2) exterior satisfying the scalar wave equation and every component of the Einstein equation with the inherited source normalization. The construction explicitly establishes the radial constraints, characteristic evolution, conservative-flux regularity bootstrap, and retarded constraint propagation. The exterior matches the interior induced metric, scalar trace, and normal scalar momentum while retaining a nontrivial jump in the second fundamental form. The resulting distributional Einstein tensor determines an effective surface layer with strictly negative proper-time energy density and positive angular pressure, satisfying (P=-σ/4) on the selected outward branch. A density-weighted weak formulation retains the regional volume measures and the induced interface measure. The corresponding local scalar surface action is reconstructed from the geometric junction tensor, and its metric and scalar Euler equations are verified on the physical interface. The effective surface layer violates the tangential-null energy condition, while the smooth bulk scalar retains its positive null contraction. The variational analysis incorporates both regional Einstein–Hilbert and real-scalar actions, oriented Gibbons–Hawking–York terms, the genuinely graph-induced scalar surface functional, finite external boundaries, and corner contributions. The moving-interface derivative reduces to an explicit normal first-jet constraint, which vanishes by the source-dependent physical clock and Einstein–scalar relations. On one selected physical collar, the complete corrected action has zero first right-sided shape derivative for every admitted edge-flat interface deformation. For a selected height, a separate theorem establishes zero right-quadrant joint first derivative under independently seeded admissible regional metric–scalar variations, including simultaneously nonzero interface metric and scalar tests. These results establish a mathematically specified local exterior, its nontrivial weak gravitational junction, and the variational response of the complete finite-collar system. Their scope is local and conditional on the stated boundary data and variation classes. Global causal continuation, asymptotic null infinity, maximal past history, and dynamical stability remain separate mathematical questions.