Paper1_Yukawa Hierarchy, Structural Neutrino Mass Law, and PMNS Structure

This paper formulates a $\beta$-organized mass program to address three fundamental open questions in particle physics: the hierarchy of visible fermion masses, the sub-eV neutrino sector, and the emergence of the PMNS matrix. While maintaining the Standard Model relation $m_f = y_f v/\sqrt{2}$, the framework introduces a structural law where the $\beta$ channel organizes the Yukawa spectrum via exponential ordering. The manuscript derives this Yukawa law step-by-step, demonstrating how the charged-fermion hierarchy is encoded and extending the logic to the neutrino regime without ad hoc scales. Finally, it explores the leptonic sector through a $\mu$-$\tau$-symmetric leading texture, providing a unified benchmark for mixing angles, the CP phase, and squared-mass differences.