A morphology-selective source operator for scalar–tensor gravity: population diagnostics on the SPARC sample

In scalar–tensor extensions of gravity the additional degree of freedom must be sup- pressed or otherwise rendered observationally negligible in regimes where General Relativity is well tested. Existing mechanisms (chameleon, symmetron, Vainshtein) typically trigger on local density or potential depth. Here we present a morphology-selective source operator and test its population behaviour; we do not claim a complete solar-system-consistent screening model in this work. The operator is a real-space spherical projector that removes the monopole component of the baryonic density and retains only the aspherical residual as the source for an additional scalar field χ. We implement this “Weg-3” operator on disk-only Newtonian potentials reconstructed from rotmod surface-brightness profiles of N = 175 galaxies in the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. A proof-of-concept on analytic density profiles confirms the expected hierarchy: a Hernquist bulge produces a coupling ratio consistent with numerical zero, a Plummer sphere is suppressed to∼10−2, and a thick exponential disk retains a response at∼10−1 . We cross-correlate an operational Weg-3 amplitude statistic with an independent stability diagnostic—a vertical-sweep tidal-anisotropy measure ∆A evaluated on the same potential grid. We treat ∆Aas a pipeline stability label; the main inference uses the outer regime (n= 119) where ∆A peaks are boundary-dominated. Galaxies in the upper decile of the Weg-3 distribution show a ∆A-outlier rate of 50%, compared with 5.6% in the remainder (odds ratio OR ≈16.8, Fisher exact p= 1.85 ×10−4). The association survives label-permutation tests, negative-control analyses, inclination stratification, and caliper-matched paired comparisons at the p<0.02 level. In the outer subset, all ∆A outliers occur in bulgeless systems (0/16 bulge-present), although the bulge-present subset is small and not statistically decisive on its own. We interpret these results as a reproducible indication of a non-trivial, morphology-dependent re- sponse structure at the operator level rather than as a detection claim, and we outline the steps needed to connect the operator to rotation-curve fits and solar-system constraints. The underlying theory preprint (VFT Paper v4) is archived on Zenodo (concept DOI 10.5281/zenodo.18817207); a companion differential weak-lensing analysis using KiDS is archived under 10.5281/zenodo.19017272.