Thin-shell coupling scale of the quadratic–quartic closure sector in Vacuum Depletion Field Theory

We report a thin-shell coupling-scale inference for the solar-system closure sector of the quadratic–quartic (QQ) potential family in Vacuum Depletion Field Theory (VFT). A companion paper mapped the geometry of the viable QQ closure band in dimensionless solver coordinates. Here, we bridge from solver space to the physical coupling scale χc/MPl using the two screened-branch observables that carry direct thin-shell meaning: the exterior charge-suppression proxy fts and the interior field displacement ∆u. This route does not depend on the absolute physical normalisation of the raw source-strength sweep parameter. Across all 237 strict QQ survivors, the inferred coupling scale lies in the range χc/MPl ≈ 3.8 × 10−10 to 8.4 × 10−9 , with every survivor satisfying the Cassini target χc/MPl ≲ 10−8. The QQ closure sector is therefore not only geometrically viable in solver parameter space but quantitatively consistent with the thin-shell coupling regime required by solar-system screening. This closes the coupling-scale side of the bridge; the absolute galactic source-amplitude normalisation remains an open calibration step.