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The Complete Charged Fermion Mass Spectrum from E8 Boundary Geometry

Authors: Agyemang, Paul;

The Complete Charged Fermion Mass Spectrum from E8 Boundary Geometry

Abstract

All nine charged fermion masses are derived from the E8 root lattice with zero free parameters. Three structural formulae govern the complete spectrum. Leptons: m_{\tau}=v\epsilon_{E8}^{11/8}/\sqrt{2}=1790 MeV (0.75%), where e_{3}=11 is the third E8 exponent and rank(E8)=8; m_{\mu}=m_{\tau}\cdot4(1-2\epsilon_{E8})/63=105.5 MeV (0.13%); m_{e}=m_{Pl}\sqrt{\alpha_{G}} (Agyemang 2026g, 0.060%). Down-type quarks: m_{d}:m_{s}:m_{b}=|V_{us}|^4:|V_{us}|^2:e_{2}/N_{gen} (in units of m_{\tau}), giving 4.54, 90.2, 4177 MeV (all within 0.64\sigma). Up-type quarks: m_{t}=v(1-2\pi\epsilon_{E8}^2)/\sqrt{2} (Agyemang 2026, EPSILON); m_{u}=m_{t}|V_{ub}|^2=2.22 MeV (0.15\sigma); m_{c}=m_{u}\cdot e_{8}/|V_{us}|^2=1276 MeV (0.31 \sigma), where e_{8}=29 is the final E8 exponent.

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