Topological Classification of Solitons and Derivation of the Elementary Particle Mass Spectrum in the 26 Vertex Oh Lattice
Year: 2026
Type: article
Abstract: Within the framework of Discrete Geometric Physics (DGP) based on the 26‑vertex cubic lattice with topological invariant Σw=14Σw=14, a topological Hopf index H(u)H(u) is introduced for configurations of the deformation field uu. The quantisation of hierarchy levels N(H)N(H) is proved, yielding a discrete mass spectrum for solitonic excitations. All particle masses are derived strictly from lattice geometry without empirical fitting parameters. Key results: 1. Unified mass formula for fundamental solitons: m(N)=64⋅ℏca(N)⋅cosθ⋅Ftop⋅ϕ−N,a(N)=2NℓPl.m(N)=64⋅a(N)ℏc⋅cosθ⋅Ftop⋅ϕ−N,a(N)=2NℓPl. 2. Distinction between particle types (in full accordance with Volume 1, Chapter 5): o Fundamental solitons (electron, muon, tau, neutrinos): mass formula includes cosθcosθ and ϕ−Nϕ−N. o Quasiparticles (electron, muon, tau): mass formula includes cosθcosθ but not ϕ−Nϕ−N. o Hadrons (proton, neutron): mass formula does not include cosθcosθ or ϕ−Nϕ−N; mass is determined by quark binding energy. 3. Mass spectrum agreement with PDG: o Proton: 938.272 MeV (<0.01% deviation) o Neutron: 939.565 MeV (<0.01% deviation) o Electron: 0.511 MeV (<0.1% deviation) o Higgs boson: 125.1 GeV (<0.01% deviation) 4. Explicit formula for N(H)N(H): N(H)=⌊αH+β⌋,α≈0.3173,β≈0.5.N(H)=⌊αH+β⌋,α≈0.3173,β≈0.5. 5. Geometric invariants used: o Σw=14Σw=14 o θ=arcsin(1/3)≈35.264∘θ=arcsin(1/3)≈35.264∘ o ϕ=(1+5)/2≈1.618034ϕ=(1+5)/2≈1.618034 o Ftop=0.088534Ftop=0.088534 o ℓPl=1.616259×10−35 mℓPl=1.616259×10−35m This revised version explicitly clarifies: · Why the proton and neutron are hadrons (no cosθcosθ, no ϕ−Nϕ−N). · Why the electron is a quasiparticle (cosθcosθ only, no ϕ−Nϕ−N). · Cross‑references to Volume 1, Chapter 5 of the base theory. The hierarchy from sub‑Planckian (N→−∞N→−∞) to cosmological (N≈204N≈204) follows from the single invariant Σw=14Σw=14. The Hopf topological index ensures quantisation of levels and gives exact masses without fitting parameters.
Author: Ivan Davidenko
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166314819