Structural Origin of Neutrino Mass Relations

This work presents a zero-parameter structural formulation of neutrino mass relations.Using the fixed ratios\[R=13/6, S=31/24,\]together with the inherited electron-sector quantities \(α\) and \(m_e\), the neutrino mass spectrum is represented by\[{mν,n}{m_e}=B_ν(n+Φ_n),_ν=12Sα^2[2→0]=12Sα^4,=0,1,2.\]The branch factors are\[Φ_0=1,Φ_1=1/3R^2,Φ_2=1/R,\]and \(α^2[i→ j]≡α²⁽ⁱ⁻ʲ⁾\) is used as a compact structural-transfer notation. The resulting absolute masses are\[mν,0≈0.02246\,eV,ν,1≈0.02405\,eV,ν,2≈0.05529\,eV,\]with\[∑ m_ν≈0.10180\,eV.\]The corresponding mass-squared differences are\[Δ m₂₁^2≈7.418×10⁻⁵\,eV^2,Δ m₃₂^2≈2.478×10⁻³\,eV^2.\] The formulation introduces no neutrino-sector fitting parameters. The inputs \(α\) and \(m_e\) are inherited from the electron-sector structure, while the neutrino hierarchy is determined by the fixed ratios \(R\) and \(S\). A minimal Python implementation is provided for full reproducibility:https://github.com/yasuotanakaresearch/zero-parameter-structure