The Primal Vacuum Structure: Complete Lagrangian Formulation and Unification of Fundamental Interactions

We present the complete mathematical formulation of the Primal Vacuum Structure (TVS), deriving all fundamental interactions from discrete icosahedral geometry with 23 torsional channels. The theory constructs the Master Lagrangian L_TVS unifying gravity, electromagnetism, weak and strong forces as different manifestations of vacuum torsion. Fermions emerge as topological knots spanning n channels (electron n=3, muon n=7, proton n=23), while bosons are torsional waves (photons n=0). We derive the complete Standard Model spectrum, fundamental constants including the proton-electron mass ratio (6π_TVS^5), dark energy density (Ω_Λ = 1637407/137³), and establish scale duality connecting Planck length to atomic scale via λ₀ = l_P · 23^18.43. The theory identifies six orders of prime resonances (23, 137, 1009, 9533, 113143, 1637407) governing geometric, electromagnetic, strong, leptonic, weak, and dark sectors. Predictions include modified Newtonian potential with oscillatory corrections and spacetime anisotropy of order 10⁻⁹.