CoreLumen Observational Series IX : Growth–Lensing Consistency Test

This document defines the growth–lensing consistency test within theCoreLumen observational program. Modern cosmological surveys provide two complementary probes ofgravitational dynamics on large scales: the growth of cosmic structureand weak gravitational lensing. Within the standard ΛCDM framework basedon general relativity the scalar metric potentials satisfy Φ = Ψ, implying that the gravitational slip parameter η = Φ/Ψ is equal to unity. In the response-function formalism deviations from this relation can beparameterized using the effective cosmological response functionsμ(k,z) and Σ(k,z), which respectively modify the clustering and lensingresponses of gravity. Within the CoreLumen framework the physical vacuum is interpreted as acondensate described by the order parameter Ψ = ρ e^{iθ}. The phase dynamics of the condensate vacuum can generate smalllate-time deviations in the effective gravitational response. This work formulates an observational consistency test based on thecomparison between • galaxy clustering and redshift–space distortion measurements• weak gravitational lensing observations The joint analysis of these probes constrains the clustering response μ,the lensing response Σ, and the gravitational slip parameter η(z). This Zenodo archival document establishes the conceptual analysispipeline of the CoreLumen observational program and defines thegrowth–lensing consistency framework for future survey-based analyses.