Characteristic Cone Geometry and Long-Range Gravity in a Constrained S3 Field

We derive an emergent effective metric for tangent perturbations of a constrained (S^{3})-valued field (\Phi:\mathbb{R}^{3,1}\to S^{3}) from the leading principal symbol of the linearized equations of motion. A spectral condition is stated to preserve Lorentzian signature. For a static spherical soliton, the resulting optical potentials fall as (r^{-6}) (massless) or (e^{-2mr}/r^{2}) (massive), implying short-range optical geometry at tree level rather than Newtonian long-range gravity. An instanton-suppressed scaling estimate is also given for vacuum energy.