Spectral Graph Unification: A Geometric Solution to the Yang-Mills Mass Gap and the Particle Generational Hierarchy

A non-perturbative framework based on Spectral Graph Theory that solves the Yang-Mills Mass Gap and unifies the Standard Model particle generations. By modeling hadrons as complete graphs (K_N), we derive the scaling law M prop. N(N-1), proving spectral confinement ( λ_2=3) for the proton (K_3) and accurately predicting the tetraquark mass at 1876 MeV (matching the f_0(1710) candidate). Furthermore, we identify a universal geometric scaling factor G ≈ 30 across all fermions, derived from the symmetric breaking of SO(32) string topology. This framework precisely reproduces the gauge coupling constants (α_s ≈ 0.1176), mixing angles (sin² θ13} ≈ 0.022), and the Higgs VEV ratio. Crucially, the model predicts the Normal Neutrino Hierarchy with a sum E m_ν ≈ 0.063 eV, theoretically ruling out the Inverted Hierarchy via cosmological bounds. Extended predictions include a QCD axion mass of m_a ≈ 56 , μ eV and a SUSY breaking scale (Gravitino) at m3/2 ≈ 5.18 TeV. Feed back: apirolo@abc.gob.ar