The proton radius anomaly ($\mathbf{R_p}$) and the non-zero mass of neutrinos ($\mathbf{m}_{\nu}$) represent two major challenges to the Standard Model. The Angular Unification Theory ($\mathbf{\TAU}$) proposes that both stem from a single source: the \textbf{vacuum regularization energy ($\mathbf{\Delta E_{\mathbf{\TAU}}}$)}, generated by the Nuclear Critical Pressure ($\mathbf{\PcritNucl}$) at density thresholds. We present the extension of the fundamental law $\mathbf{\Delta E_{\mathbf{\TAU}}} = \mathbf{C}_{\mathbf{\TAU}} \cdot \mathbf{m}_l^3$ to predict the deuteron radius ($\mathbf{R_D}$). More importantly, we formalize the postulate that this same energy is constitutive of neutrino mass (Eq. 3), transforming the mass hierarchy problem into one of \textbf{angular anchoring defect}. This approach provides a direct causal relationship between a high-precision atomic phenomenon and a fundamental particle property, leading to a falsifiable prediction of the absolute neutrino mass.