CoreLumen Cosmology VIII : Reconstruction of Cosmological Response Functions

This document records the reconstruction framework associated with theCoreLumen condensate cosmology program. Within the CoreLumen framework the physical vacuum is interpreted as acondensate medium described by the complex order parameter Ψ = ρ e^{iθ}. The phase structure of the condensate organizes the gravitational responseof spacetime and leads to a late-time cosmological attractor correspondingto vacuum-dominated cosmic acceleration. Building on the observational signatures discussed in CoreLumen Cosmology VII,this work outlines the conceptual reconstruction pipeline linking cosmologicalobservables to the effective parameters of the condensate vacuum model. In particular the reconstruction framework connects the following observables • background expansion history H(z)• growth of large-scale structure fσ8(z)• weak gravitational lensing observables to the effective cosmological response functions • dark-energy sector ρDE• gravitational response μ(k,z)• lensing response Σ(k,z) The purpose of this work is not to perform a full statistical parameterinference but to document the conceptual mapping between cosmologicalobservables and the condensate vacuum sector. This document is released in Zenodo archival mode as part of theCoreLumen Cosmology research series.