CoreLumen Stage II : Reduction of Field Equations to Observable Response Functions

This document constitutes Stage II of the CoreLumen Stage Series (v1.0). Stage II performs the controlled linear perturbation analysis and quasi-staticreduction of the phase–curvature coupled effective action introduced in Stage I.Under explicit effective-field-theory ordering and stability conditions(Z_rho > 0, Z_theta > 0, c_s^2 > 0, c_T = 1),the scalar sector reduces to two effective response functions, µ(k,z) and Σ(k,z),governing modified Poisson equations at linear order. No additional propagating tensor degrees of freedom are introduced.The analysis is restricted to the linear quasi-static regime(aH