CoreLumen Stage III: Response Embedding of Cosmological Perturbations

This document constitutes Stage III of the CoreLumen Stage Series (v1.0). Stage III formalizes the response-embedding principle of CoreLumen.The µ–Σ parameterization is interpreted as the low-energy projectionof a unified phase-induced response kernel rather than as a purelyphenomenological deformation of general relativity. The Structural Charter v1.0 remains strictly enforced:c_T = 1, c_s^2 > 0, Z_theta > 0.No additional propagating tensor or scalar degrees of freedom are introduced. Slip is interpreted as a derived mismatch indicator between Newtonand Weyl response channels, not as an independent physical degree of freedom. All constructions are confined to the quasi-static effective field theory regime.No ultraviolet completion is claimed.