CoreLumen Stage VIII : Likelihood Interface for Cosmological Observables

This document constitutes Stage VIII of the CoreLumen Stage Series (v1.0). Stage VIII implements a linear-regime likelihood realization of thelocked Stage II–VI response structure and validates the Stage VIIprojection geometry at the level of explicit likelihood curvature. Using CLASS baseline matter power spectra and a growth-coupledµ–Σ response embedding, an Euclid-like weak-lensing configurationis constructed. Fisher curvature is compared against explicitGaussian mock-data realizations, demonstrating unbiased recoveryand quadratic scaling of the detection statistic. No new theoretical structures or degrees of freedom are introduced.All analysis remains confined to the quasi-static linear regimeand preserves the Structural Charter v1.0:c_T = 1, c_s^2 > 0, Z_theta > 0. Stage VIII establishes a validated observational interface forthe locked CoreLumen framework.