The proton radius anomaly ($R_p$), characterized by the discrepancy between measurements in electronic and muonic hydrogen, is resolved here through the introduction of the $\mathbf{TAU}$ protocol version **5.2.1**. We demonstrate that this anomaly is the signature of a repulsive vacuum phase ($\mathbf{G}_{\text{eff}} = -\mathbf{G}$) induced by a nuclear critical pressure. The coupling is anchored by the topological angular closure defect $\epsilon \approx 5.76 \times 10^{-4}$ of the $\mathbf{QRD}$ lattice. The spectral correction $\Delta E_{\TAU}$ exhibits a rigorous $m_l^3$ dependence, explaining the selective amplification in muonic hydrogen. This unification links the gravitational constant $G$, the torsion velocity $\vOTA = 10^{20}c$, and atomic energy levels within a single, self-consistent theoretical framework.