CoreLumen Gravity VI : EFT Closure of Condensate Gravity

This work presents the effective field theory (EFT) formulation of theCoreLumen condensate gravity framework. Within the CoreLumen program the physical vacuum is interpreted as acondensate medium described by the complex order parameter Ψ = ρ e^{iθ}. In this picture the phase dynamics of the condensate vacuum organizesthe gravitational response of spacetime and modifies the effectivecosmological behavior at large scales. To connect the condensate gravity framework with cosmologicalobservations, the gravitational dynamics can be described througheffective response functions μ(k,z) and Σ(k,z), which respectively characterize the clustering response of gravityand the gravitational lensing response. This paper develops the effective field theory (EFT) formulation ofcondensate gravity and derives the response framework linking thecondensate vacuum sector with cosmological observables. Within the broader CoreLumen research program this work completesthe gravitational sector and establishes the theoretical interfacebetween the condensate vacuum theory and the cosmological andobservational analyses developed in subsequent papers. This document is released as a Zenodo archival version to recordthe structural EFT formulation of the CoreLumen condensate gravityframework.