Structural Origin of Higgs, Electroweak, and Strong-Coupling Scale Relations

This work presents a zero-parameter structural formulation of Higgs, electroweak, Yukawa, and strong-coupling scale relations.Using the fixed ratios\[R=13/6, S=31/24,\]the Higgs-sector base structure is written as\[B_H=12Rα^2[1→2]=12Rα⁻²,α^2[i→ j]≡α²⁽ⁱ⁻ʲ⁾.\]The Higgs mass and electroweak vacuum expectation value are represented by\[m_H/m_e=1/2B_H+Ψ_H,/m_e=B_H-Ψ_v,\]with fixed structural integers \(Ψ_H=712\) and \(Ψ_v=6408\). The resulting structural values are\[m_H≈125.1116\,GeV,≈246.2210\,GeV,_e≈2.935012×10⁻⁶.\]The same sequence gives\[sin^2θ_W≈0.223215,_W≈80.36848\,GeV,_Z≈91.18752\,GeV,\]and the cross-sector boundary relation\[α_s(m_Z)=1-m_W/m_Z≈0.118646.\] The formulation introduces no observable-specific fitting parameters. The values are compared directly with representative Higgs, electroweak, and strong-coupling reference values, while the QCD running section is treated as an illustrative continuation from the structural boundary value at \(m_Z\). A minimal Python implementation is included in the paper and provided for full reproducibility:https://github.com/yasuotanakaresearch/zero-parameter-structure