A quasilocal multipole-projected source functional for the non-monopolar response sector of the VFT programme

The Vacuum Field Theory (VFT) programme replaces dark-matter halos by a baryonically sourced conformal scalar response. A central open problem is the status of the morphology- sensitive source sector: in its current operational form the corresponding response channel is represented by real-space projector constructions that subtract the spherical component of the baryonic source and retain only the aspherical residual. This paper introduces a quasilocal multipole-projected source functional QΣρ that provides the missing bridge between the op- erational Weg-3 construction and the programme-level higher-order response sector. We dene the functional, constrain its kernel, establish its structural properties, demonstrate its acti- vation logic on controlled and genuine-geometry toy models, derive the next-to-leading-order coupling-gradient coecient from the screening prole, and verify that the non-monopolar sector is parametrically suppressed for the nearly spherical Sun. An independent empirical bridge analysis on SPARC data further supports a broad, Yukawa-weighted, quadrupolar ra- dial accumulation law, consistent with the structure predicted by the quasilocal construction.