Structural Origin of Quark Masses

This work presents a zero-parameter structural formulation of the quark-mass hierarchy.Using the fixed constants\[R = 13/6, S = 31/24,\]the six quark masses are expressed through a unified structural relation,\[m_q/m_e=K_q(3R^2S)({8πu_qRu_q+1}{S})^n .\]Here, the coefficients \(K_q\) are generated from two structural indices,\[Ψ_d = 2, Ψ_u = 2R,\]and correspond to the six quark sectors \(u,d,c,s,t,b\).The formulation reproduces the observed quark-mass hierarchy across all three generations, including the light-quark scale, the charm and strange masses, the bottom mass, and the top-quark mass scale near \(173\,GeV\).The result is interpreted conservatively as a structural correspondence between fixed dimensionless ratios and the observed quark-mass spectrum. The top-quark value is not tuned to the latest central value, but is treated as an effective structural mass scale consistent with the known scheme dependence of top-mass determinations.A notable feature of the formulation is the structural asymmetry appearing in the second generation, where the charm and strange sectors follow different correction patterns. This is discussed as a possible transitional layer between the base and higher-order propagation sectors.No free parameters are introduced. No tuning is performed. All quantities arise from the fixed structural relations. A minimal Python implementation is provided for full reproducibility:https://github.com/yasuotanakaresearch/zero-parameter-structure