Discovery of a Universal Vacuum–Gravity Coupling κ: Projection-Induced Curvature–Response Parameter

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 semantic action 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.