Structural Origin of Electromagnetic Coupling and Mass Hierarchy

This work presents a structural formulation of the electromagnetic coupling, the electron mass scale, and selected charged-particle mass ratios using fixed structural ratios without introducing free parameters.The formulation is based on two constants,\[R = \frac{13}{6}, \qquad S = \frac{31}{24},\]together with sector-dependent structural indices \(\Psi\). In this revised version, each structural index is separated into a backbone component \(\Psi_0\) and a fixed residual fluctuation \(\delta\psi\), making explicit which part of each relation is common structural scaffold and which part is sector-specific residual correction.The inverse fine-structure constant is written as\[\alpha^{-1}= 4\pi\frac{3R^2}{S}\left(1+\frac{1}{\Psi_e^{\mathrm{eff}}}\right),\]yielding\[\alpha^{-1} \approx 137.035999177055.\]Using the same structural components, the framework gives fixed relations for\[\frac{m_p}{m_e}, \qquad\frac{m_n}{m_e}, \qquad\frac{m_\mu}{m_e}, \qquad\frac{m_\tau}{m_e}, \qquad\frac{m_\tau}{m_\mu},\]as well as a structural expression for the electron mass-energy scale,\[m_e c^2 \approx 0.510998950690048\ \mathrm{MeV}.\]The charged-lepton relations are expressed with fixed structural coefficients,\[\frac{m_\mu}{m_e}= K_c\,4\pi\frac{3R^2}{S}\left(1+\frac{1}{\Psi_\mu^{\mathrm{eff}}}\right),\qquad K_c=\frac{3}{2},\]and\[\frac{m_\tau}{m_e}= K_s(8RS)\left(1+\frac{1}{\Psi_\tau^{\mathrm{eff}}}\right),\qquad K_s=\frac{3}{4}.\]This paper is restricted to electromagnetic coupling, the electron mass scale, and charged-particle mass hierarchy. The Higgs mass, the electroweak vacuum expectation value, and the neutrino sector are not treated here and are reserved for separate work.No numerical fitting is performed. All quantities are obtained from fixed structural relations. A complete reference implementation is available at:https://github.com/yasuotanakaresearch/zero-parameter-structure