Fermion Mass Derivations from Octonionic Geometry

AbstractWe present a unified geometric framework for calculating the masses of all Standard Model fermions. We demon-strate that the integer winding modes identified in our previous work [7] are Diophantine approximations of a fundamental Golden Ratio topology (𝑚 ∝ 𝜑𝑛 ). This geometric approach predicts charged lepton masses to within0.7 ppm. For quarks, we introduce a “Void Dynamics” model based on the Kepler-Hales FCC packing limit, which reproduces the full mass spectrum with an RMS error of 0.28%, effectively solving the heavy quark mass problem.Finally, we derive the neutrino mass spectrum from a dimensional coupling hypothesis, predicting a 1 ∶ 9 ∶ 49 mass ratio that aligns with global oscillation data.