Unifed Harmonic Soliton Model: Complete Mathematical Framework Python3 File and Complete PDF

This represents a mathematical framework that predicts Standard Model particle masses and charges through harmonic principles. The Unified Harmonic Soliton Model (UHSM) maps particle properties onto a log₂-based phase space using the Higgs boson mass (125.18 GeV) as reference, revealing systematic correlations across 15 orders of magnitude. Statistical validation against experimental data yields R² = 0.999957, χ²/dof = 0.086, and p = 4.76×10⁻²³. The model achieves 0.0279% mean error for particles above 1 GeV, with systematic deviations for lighter particles consistent with QCD and electromagnetic corrections to bare masses. Charge quantization emerges from a harmonic waveform (RMS error = 0.7109) incorporating the Pythagorean comma κ = 3¹²/2¹⁹ as a universal parameter. The mass generation formula integrates solitonic field theory, topological charge conservation, and quantum corrections. Comparative analysis shows superior performance to Standard Model approaches across all statistical metrics. The framework generates testable predictions for undiscovered particles at specific harmonic intervals and suggests harmonic mathematics as a fundamental organizing principle in particle physics.