CoreLumen Fundamental IV : Ultraviolet Completion of the CoreLumen Framework

This work presents a minimal ultraviolet completion of the vacuumcondensate underlying the CoreLumen framework. In the CoreLumen program the physical vacuum is interpreted as acondensate medium described by the order parameter Ψ = ρ e^{iθ}. Across the Vacuum, Gravity, and Cosmology series this condensatestructure organizes the effective description of vacuum filtering,gravitational response, late-time cosmic acceleration, andobservational signatures. The Fundamental Physics Series develops the microscopic basis ofthis framework. CoreLumen Fundamental I derived the condensate order parameter fromspontaneous symmetry breaking of a complex scalar field. CoreLumen Fundamental II established the quantum field theory of thephase sector and identified the conserved phase current governingthe coherent flow of the vacuum medium. CoreLumen Fundamental III interpreted spacetime geometry as themacroscopic propagation geometry of excitations in the phase-coherentvacuum condensate. The present work addresses the remaining microscopic question byconstructing a minimal ultraviolet completion of the condensatevacuum sector. We introduce a hidden-sector scalar field undergoing spontaneoussymmetry breaking. The resulting broken phase generates the condensateorder parameter Ψ = ρ e^{iθ} together with its Goldstone phase mode and conserved Noether current. At low energies the resulting theory reduces to the effectivecondensate description used throughout the CoreLumen Vacuum, Gravity,and Cosmology series. This construction therefore provides a concrete microscopic anchorfor the CoreLumen framework while preserving the phenomenologicalstructure of the existing program. This document is released as a Zenodo archival version and completesthe microscopic foundation of the CoreLumen Fundamental Physics Series.