Verarmungsfeldtheorie (Vacuum Depletion Field Theory) as a Quantitative Research Programme: Theory Architecture, Empirical Gate, and Programme Status

We present the Verarmungsfeldtheorie (VFT) as a quantitatively ordered re- search programme in which the falsiable minimal core, the theoretically motivated but not fully isolated extensions, and the open closure problems are explicitly sep- arated. The programme is organised around a minimal conformal scalartensor response (model M0) with two parameters (α0,mχ) and a hard no-slip prediction, embedded in a hierarchical architecture with an environment-dependent gate and a morphology-conditioned operator family. We then construct a quantitative bridge from SPARC rotation-curve data to solar-system consistency and weak-lensing predictions. The SPARC-calibrated em- pirical gate Zα(x) is well described by a four-parameter logistic with an empirical oor zmin ≈0.015. Combined with a provisional Milky-Way environment mapping, this shows that pure solar-system closure by the coupling gate alone remains vi- able only in the low-coupling regime, α0 ≲ 0.17 0.18, while larger couplings leave open only a revised closure mechanism, since the present closure audit excludes the scanned class of smooth background-gated two-channel closures as physically non- trivial solutions. A dedicated closure audit over ∼150,000 hybrid-gate congura- tions shows that no smooth background-gated model simultaneously reproduces the SPARC-implied galactic response, satises the Cassini bound, and remains physi- cally non-trivial. The reason is structural: the scale gap between the SPARC-implied vacuum Compton wavelength (∼8 kpc) and AU-scale solar-system tests is so large that background-controlled mass amplication alone generically drives the model into the trivialized regime. This identies a structural no-go for the simplest closure class and motivates intrinsically local nonlinear screening mechanisms. A comple- mentary population-level viability test shows that a thin-shell-like locally nonlinear closure route remains viable across nearly the entire usable SPARC subsample, with non-empty closure windows typically of order 1 2 dex in the coupling-scale parame- ter. In the range sector, the SPARC audit reveals structured additional phenomenol- ogy beyond the amplitude-only baseline. Yet PCA and coverage-break tests show that this tted range freedom is not independently separable from the amplitude manifold in the current audit. The current data therefore support range-like struc- ture without establishing an empirically isolated second gate channel. Accordingly, 1no empirical claim of a second independently anchored screening gate is made in this paper. On the KiDS side, a methodologically robust matched-sample analysis yields a nonzero environment-dierential residual, but a ΛCDM-inspired benchmark shows that the strongest residual (Slice 9) is fully compatible with conventional broad environment-linked lensing structure. The physically normalized SPARC-scale core is negligible at the minimum radii accessible in current stacks. The bridge between the SPARC and KiDS sectors therefore remains architectural rather than observa- tionally closed, and KiDS is not retained as an independent VFT-specic empirical pillar in the current audit. The programme is narrower than before, but the empir- ically anchored core M0, Zα(E), and the Milky-Way mapping remains intact. Sharpening here means logical ordering of the existing elements, including the explicit withdrawal of speculative branches that do not survive the current tests not completion or cosmological closure.