Discovery of a Universal Vacuum–Gravity Coupling κ: Projection-Induced Curvature–Response Parameter ("Evidence for Universal Vacuum–Gravity Response Coupling within a Derived One-Scale Projection Kernel")

We report the empirical discovery of a universal, dimensionless coupling $\kappa = 4.25 \pm 0.50$ linking quantum-vacuum anomalies and gravitational response across laboratory, astrophysical, and cosmological regimes. The coupling is measured through a hierarchical Bayesian meta-analysis of over two decades of precision Casimir-force residuals and short-range gravity experiments, testing the predicted unifying relation $\delta G = \kappa\,\delta F$. Bayesian model comparison strongly favors a single shared $\kappa$ over independent couplings. The parameter $\kappa$ is not introduced ad hoc. Within the Irreducible Intent Model (IIM), $\kappa$ is defined as a projection-induced curvature--response coefficient entering the renormalized gravitational coupling $G_{\mathrm{eff}}^{\rm (pert)}(k) = \dfrac{G_0}{1+\kappa S(k)}$ and as the second variation of the X-fluid vacuum functional governing vacuum compressibility at microscopic scales. The present work provides the first empirical determination of this theoretically defined parameter. Dimensional reduction and projection geometry naturally yield $\kappa \sim \mathcal{O}(1)$, with quartic scaling giving $\kappa \approx 4$, while the precise value is phenomenological. We clarify the regimes of validity of $\kappa$: it governs linear perturbative curvature response and cosmological structure growth, while non-linear galactic dynamics and Solar-System physics remain controlled by distinct emergent mechanisms and recover General Relativity. Finally, we propose several falsifiable experimental and observational tests capable of confirming or refuting the universal $\kappa$ hypothesis.