The Constitutive Gravitational Framework VI: Empirical Determination of the Response Function from the Radial Acceleration Relation, Rotation Curve Tests, and the Boyer Repulsive Sign as a Consistency Constraint

We present the first empirical determination of the constitutive response function F(Y) appearing in the covariant gravitational framework of Papers 1–5 of this series. Paper 5 identified the low-acceleration infrared branch as F_IR(Y) ∝ Y³ᐟ², arising from a spherical Casimir-like surface energy of the gravitational vacuum, but left the normalization coefficient F₀ undetermined pending a full Boyer-type spherical Casimir calculation. Here we fit F₀ to the analytic McGaugh et al. (2016) Radial Acceleration Relation (RAR) baseline, which was derived from 153 rotationally supported galaxies, obtaining F₀ = 0.777 ± 0.02, giving the normalization (3/2)F₀ = 1.166, within 16.6% of the theoretical Casimir target of unity. The resulting interpolating function κ_g(Y) = [(3/2)F₀√Y] / [1 + (3/2)F₀√Y] reproduces the RAR analytic baseline with reduced χ²/N = 0.050 against that baseline; the intrinsic scatter of the observed RAR is 0.11 dex and represents galaxy-to-galaxy variation not captured by any single-parameter fit. Applied to three representative disk galaxies spanning the full dynamical range — the gas-dominated dwarf DDO 154 (deep-MOND regime), the intermediate-mass NGC 3198, and the high-surface-brightness NGC 2403 (transition regime) — the framework yields χ²/N improvements of 5.0×, 4.1×, and 2.6× over MOND predictions, with stellar mass-to-light ratios Υ* = 0.10–0.57 M☉/L☉ consistent with stellar population synthesis models. We further show that the Boyer (1968) result for a scalar Dirichlet sphere — that the Casimir energy of a spherical boundary is repulsive — is consistent with the repulsive sign required by the phantom density term ρ_x = 2ρ_vac in the framework, providing an independent geometric consistency check on the Casimir vacuum mechanism proposed in Paper 5. Together these results demonstrate that a single constitutive response function, physically motivated by spherical Casimir vacuum physics and empirically calibrated from the RAR, reproduces galactic dynamics across four decades of acceleration without dark matter. We show that the empirical F₀ = 0.777 lies 16.6% above the kinematic value 2/3 that the Y³ᐟ² infrared branch requires, and that this 2/3 carries no information from the Casimir mode structure: a first-principles spherical-Casimir estimate underpredicts F₀ by some 95 orders of magnitude, a manifestation of the vacuum-energy hierarchy problem. The Casimir surface mechanism therefore supplies the infrared power Y³ᐟ² but not its coefficient, which we treat as an empirical normalization.