Geometric standard model with code
Abstract
The Geometric Standard Model (GSM) is a parameter-free geometric framework that derives the full Standard Model of particle physics, gauge group SU(3)_c × SU(2)_L × U(1)_Y, Higgs vev v ≈ 246 GeV, fermion masses and mixing (CKM/PMNS), neutrino masses via type-I seesaw, gravity, dark matter, dark energy, baryogenesis, proton decay, black-hole entropy, Hawking temperature, inflation, and gravitational waves from a single non-zero hexagonal lattice seed (r > 0) evolved under the quadratic map z ↦ z² + c and closed on an icosahedron. The 6 → 3 chiral collapse yields three generations; 12 pentagonal defects produce the Higgs doublet and A₅ flavor symmetry; Yukawa couplings Y_g ∝ φ^{k_g} log_φ(1/θ_g) (φ = golden ratio, θ_g = min defect angle, k_g from continued fractions) reproduce PDG masses and mixing to high accuracy. The residual radius bias gives the observed cosmological constant ρ_Λ ∼ 10^{-120} M_Pl⁴. Dark matter arises from hidden survivor clusters (Ω_DM h² ≈ 0.12). Gravity emerges from defect breathing gradients. Predictions include a distinctive GW spectrum testable by LISA, SKA, and LIGO/ET. Accompanying Python code simulates the lattice, masses, and cosmology. This upload contains the paper draft and simulation code.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Particle physics theoretical and experimental studies
Relativity and Gravitational Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 February 2026