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 adjustable parameters beyond two dimensionful anchors: the Planck mass (setting the scale sector) and the muon mass (setting the lepton sector via the Koide circle, itself derivable to about 0.35% from the Planck mass through the QCD scale). The framework yields 34 numerical predictions matched against PDG experimental values, of which 32 are computed directly from the Planck mass and the G₂ group integers. A machine-checkable verification script (verify.py) recomputes every value from these inputs and confirms all 34 pass, with a mean absolute residual of 0.29% and χ²/dof = 0.40 against a 1% tree-level floor. Where a one-loop correction is applied on top of a tree-level prediction, it is in every case a fixed formula from standard field theory evaluated with framework-derived inputs and no adjustable coefficient. Three predictions are independently verifiable with a pocket calculator. The proton-to-tau mass ratio is predicted at 0.52805 against a measured 0.52805 (error 0.00003%, with the QCD scale cancelling). The neutrino mixing angle θ₁₃ is predicted at π/21 = 8.571 degrees against a measured 8.57 degrees (error 0.02%). The hydrogen Rydberg energy is predicted at 13.6057 eV against a measured 13.6057 eV (error 0.000%), where the point is that the electron mass feeding the formula is itself geometric rather than measured. Additional predictions include new particles accessible to existing LHC searches: a χ familon resonance near 94.8 GeV in the dijet channel, and an inverted gaugino spectrum with a Bino near 391 GeV, a gluino near 914 GeV, and a wino near 1370 GeV. The document is structured in four parts: an accessible introduction with the pocket-calculator predictions (Part 1), the physical and geometric foundation (Parts 2 and 3), and the full mathematical derivations with the complete prediction table and verification script (Part 4).V15 -gluino removed. In the framework as well a gauge theory, the gluon is a connection, so the gluino should be excluded.
Quentin Duquesne (Mon,) studied this question.