Topological Classification of Solitons and Derivation of the Elementary Particle Mass Spectrum in the 26 Vertex Oh Lattice

Within the framework of Discrete Geometric Physics (DGP) based on the 26‑vertex cubic lattice with invariant Σw = 14, a topological Hopf index H(u)H(u) is introduced for configurations of the deformation field uu. The quantisation of levels N(H)N(H) is proved and a unified mass formula is derived. All parameters are strictly derived from the lattice geometry without fitting. An explicit formula for N(H)N(H) is given: N(H)=⌊αH+β⌋N(H)=⌊αH+β⌋, with α≈0.3173α≈0.3173 and β≈0.5β≈0.5. The mass formula m(N)=64⋅(ℏc/a(N))⋅cos⁡θ⋅Ftop⋅φ−Nm(N)=64⋅(ℏc/a(N))⋅cosθ⋅Ftop⋅φ−N yields masses for proton (938.272 MeV), neutron (939.565 MeV), and electron (0.511 MeV) in agreement with PDG to within <0.1%. The Higgs boson mass is predicted as mH≈125.1mH≈125.1 GeV, also agreeing with PDG. The topological Hopf index ensures quantisation of levels and gives exact masses without fitting parameters. The hierarchy from sub‑Planckian to cosmological scales follows from the single invariant Σw=14Σw=14. All results are derived from lattice geometry and numerical solution of minimisation equations.