Standard Model from Knot Complements: Three Generations, Mass Hierarchy, and CP Violation

2025/11/18 by Salden, Alfons Hermanus · 1 voice

paper · doi:10.5281/zenodo.17642087

openalex publication_date 2025/11/18 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/01

Abstract

We derive the Standard Model particle spectrum from knot complement geometry. Key results: (1) Three generations from Thurston geometrization - only three stable knot classes (hyperbolic, toric, spherical) support particle states, (2) Mass hierarchy: electron (trefoil 3₁, m_e=0.511 MeV), muon (figure-eight 4₁, m_μ=105.7 MeV), tau (7₅ knot, m_τ=1776.8 MeV) with errors <5%, (3) CKM matrix from geometric overlaps between knot complement boundaries, predicting matrix elements with average error 8%, (4) CP violation via Jarlskog invariant J from knot braiding, predicting J≈3.6×10⁻⁵ (18% from observed value), (5) Higgs VEV v=246 GeV from vacuum defect network density, (6) SO(3) operator algebra forbids fourth generation via non-factorizable constraints. Quarks emerge as knot complement endpoints where defect lines terminate, with color charge from linking numbers and weak isospin from knot orientability. Framework naturally explains generation problem (why exactly three), mass ratios, mixing angles, and CP violation from pure geometry without free parameters.

Discussions

• How can it be as it should also operate in the complement space-time and that is why computer simulation is hyped BS: doi.org/10.5281/zeno... [bsky, 0 points, 0 comments]

Related

• The Preon Sector of the SLq(2) (Knot) Model
• α-π-Helix: Geometric Unification of Fundamental Constants
• A Possible SLq(2) Substructure of the Standard Model
• Solitonic Models Based on Quantum Groups and the Standard Model
• The Bohr Atom of Glueballs