The Constitutive Gravitational Framework X: Joint Galaxy–Solar-System Constraints on Constitutive Gravity Responses SPARC Response Shapes, Environmental Backreaction, and Certified Discrete Operators

Can a gravity response reproduce galaxies without creating a Solar-System tidalsignature that Cassini excludes? We find a quantitatively testable obstacle in fifteencommonly used single-scale responses. Applying the same nuisance-profiled fitting procedure to132 SPARC galaxies (2652 measurements), we reproduce the Paper IX median χ2/N = 1.932. Alleight transition functions previously classified as Cassini-viable in a different model and calibrationworsen the galaxy fits: their medians rise to 2.19–2.41, and each improves only 30–43 of 132galaxies (paired sign tests p<10-4). The RAR alternative improves the pooled objective and 90individual galaxies, while its median is slightly worse and its historical external-field quadrupoleremains problematic. Thus a sharper, acceleration-only interpolation is not an automaticsolution; the joint galaxy–Solar-System trade-off is exposed by a full-sample, common-pipelinecomparison. Two independent, complementary results constrain alternatives: a SPARC step/kinksearch finds no supported universal abrupt acceleration transition, and archived L = 40/42environmental-backreaction calculations change the historical solar quadrupole estimator by onlya few ×10−6 through λ≃0.18, far below the change conditionally needed for Cassini. Separately,a source-correlated certificate bounds the residual of a frozen 9460-row discrete gravity operatorby 1.974705 ×10−12; it does not certify the coupled physical solution. An observable-potentialaudit identifies why the historical coefficient cannot yet be equated with Cassini Q2. Theseresults provide reproducible model-specific constraints and identify two currently unproductiveroutes—simple transition sharpening and the explored backreaction branch—without claiming aphysical no-go theorem or a new Solar-System measurement.