CoreLumen Stage VII : Observational Sensitivity of the Response Sector

This document constitutes Stage VII of the CoreLumen Stage Series (v1.0). Stage VII provides the observational projection and sensitivitycompletion of the locked Stage II–VI response structure.No new theory, degrees of freedom, or functional classes are introduced. Analytic log-sensitivity operators are defined,channel-direction geometry is established(RSD → µ, Weak Lensing → Σ with growth-induced corrections,BAO/Geometry → η),and an Euclid-like Fisher forecast is constructedto quantify detectability of the response amplitudes (µ0, Σ0). All analysis is confined to the quasi-static trust regionand the perturbative envelope verified in Stage VI.The Structural Charter v1.0 remains strictly enforced:c_T = 1, c_s^2 > 0, Z_theta > 0. Stage VII represents the completed observational sensitivitylayer of the CoreLumen program.