G2 Geometry Predicts All Standard Model Parameters: A Zero-Free-Parameter Framework

This preprint presents a theoretical framework in which all Standard Model particle masses, mixing angles, and coupling constants are derived geometrically from a single G2 octonion field undergoing a topological vortex condensation in the early universe. The condensation produces exactly six active vacuum orientations at 60-degree intervals, from which precisely three stable particle loop sizes emerge — corresponding to the three observed generations of matter — with no free parameters beyond the Planck mass.

The framework yields over 30 numerical predictions matched against PDG experimental values. Three are independently verifiable with a pocket calculator and are presented on pages 11-12: the proton mass (predicted 939.0 MeV, measured 938.3 MeV, error 0.08%), the neutrino mixing angle theta_13 (predicted pi/21 = 8.571 degrees, measured 8.57 degrees, error 0.02%), and the hydrogen ionisation energy (predicted 13.6057 eV, measured 13.6057 eV, error 0.000%). Additional predictions include new particles accessible to existing LHC searches: a chi familon resonance at 94.6 GeV in the dijet channel, and supersymmetric partners at 391 GeV and 684 GeV.

The document is structured in four parts: an accessible introduction with the three verifiable predictions (Part 1, pages 1-14), the physical and geometric foundation (Parts 2 and 3), and the full mathematical derivations with the complete prediction table (Part 4)