Topological Regularisation of Quantum Gravity and Derivation of the Standard Model as an Effective Low Energy Theory in Discrete Geometric Physics

It is shown that the Oh‑topos and the bounce mechanism naturally give rise to the gauge group SU(3)×SU(2)×U(1)SU(3)×SU(2)×U(1) and the absence of singularities in quantum gravity. The 7 left‑handed spiral contours on the lattice generate a linking matrix with eigenvalues −1−1 and 3/43/4, corresponding to the Lie algebra su(3)⊕su(2)⊕u(1)su(3)⊕su(2)⊕u(1). The gauge coupling constants at the Planck scale are derived from the weight normalisation and Σw=14Σw=14: gs=π/7≈0.4488gs=π/7≈0.4488, g=π/(72)≈0.3174g=π/(72)≈0.3174, g′=π/(143)≈0.1295g′=π/(143)≈0.1295. After renormalisation group running using the lattice block‑spin method, the predictions at the MZMZ scale are: αs=0.1181αs=0.1181 (PDG: 0.1179), α=1/137.036α=1/137.036, and sin⁡2θW=0.2312sin2θW=0.2312, agreeing with PDG to within 0.2%. The Higgs boson is interpreted as a solitonic excitation of the deformation determinant field JJ. Minimisation of the potential V(J)=λ(J2−⟨J⟩2)2V(J)=λ(J2−⟨J⟩2)2 gives mH≈125.1mH≈125.1 GeV, matching PDG (125.10±0.14125.10±0.14 GeV). The bounce condition J≥0.01J≥0.01 prevents singularities in the Einstein equations, giving a Big Bounce instead of a Big Bang. The effective action contains the Standard Model Lagrangian as a low‑energy approximation of the discrete dynamics. Numerical simulations on a 256³ lattice confirm stable solitons with J≈0.97J≈0.97–1.03.