UCT Geometric Unification from Microscopic to Cosmological Scales v3.5.0

UCT Geometric Unification from Microscopic to Cosmological Scales v3.5.0 A zero-parameter theoretical framework deriving fundamental physical constants from geometric principles. The theory connects particle physics, nuclear structure, and cosmology through mathematical primitives: kissing numbers (K₃=12, K₈=240, K₂₄=196560), the golden ratio φ, and transcendental constants π, e. Interactive verification: Google Colab Demo Key Results Fine Structure Constant α⁻¹ = 4π³ + π² + π = 137.036 Experimental: 137.035999177 ± 0.000000021 (CODATA 2022) Relative error: 0.0002% Baryon Mass Splitting Σ − Λ = K₃² × mₑ = 144 × 0.511 MeV = 73.58 MeV Experimental: 73.60 ± 0.10 MeV (PDG 2024) Relative error: 0.02% Cosmological Constant ρ_Λ/ρ_P = π⁻²⁴⁷ Addresses the 122 orders of magnitude discrepancy in vacuum energy predictions. v3.5.0: CKM-Electroweak Structural Relation |V_us| = sin²θ_W − 1/K₃² = φ/7 − 1/144 = 0.22420 Experimental: 0.2243 ± 0.0005 (PDG 2024) Relative error: 0.043% This establishes a geometric connection between electroweak mixing and CKM flavour structure. Verification Summary Metric Result Total predictions 50+ Physical domains 10 Free parameters 0 T3 predictions (7) 0.014% mean error Monte Carlo significance 4.4σ Rigidity test 42,674× degradation on ±1 perturbation T3 Predictions Observable Formula Relative Error α⁻¹ 4π³+π²+π 0.0002% m_τ/m_e (π⁷·ln10)/2 0.0003% m_p/m_e 6π⁵ 0.0019% m_μ/m_e 2π⁴+12 0.024% sin²θ_W φ/7 0.027% V_us m_s/m_d K₈/K₃ 0.000% Cross-Domain Applications Particle physics: Lepton mass ratios, quark mass ratios, mixing angles Nuclear physics: Hyperon mass splittings, baryon resonances Cosmology: Matter density Ω_m, spectral index n_s, dark matter fraction Molecular biology: Amino acid count (20), codon number (64) via Novgorodtsev Identity e^π − π ≈ K₈/K₃ = 20 Falsifiable Predictions Experiment Timeline Prediction JUNO 2026 Neutrino mass sum Σmν = 0.062 eV, normal hierarchy Belle II 2030 τ mass precision test Lattice QCD 2027 Tetrahedral T_d baryon structure CMB-S4 2028 Spectral index n_s refinement Package Contents UCT_Geometric_Unification.zip ├── Code/ │ ├── uct_ultimate_suite_v3_5_0.py │ └── uct_ultimate_suite_v3_5_0.ipynb ├── Data/ │ ├── results.json │ ├── certificate_alpha.json │ └── uct_ultimate_plots.png └── Paper/ └── UCT_Geometric_Unification.pdf (127 pages) Requirements pip install numpy scipy matplotlib python Code/uct_ultimate_suite_v3_5_0.py Mathematical Basis Constant Value Source K₃ 12 3D kissing number (Schütte & van der Waerden, 1953) K₈ 240 E₈ lattice (Viazovska, 2016) K₂₄ 196560 Leech lattice (Cohn et al., 2022) φ (1+√5)/2 Golden ratio π, e — Transcendental constants References CODATA 2022: Fundamental Physical Constants PDG 2024: Review of Particle Physics Planck 2020: Cosmological Parameters