The Mass Spectrum of the Standard Model from Discrete Scale Symmetry in a Fractal Spacetime

This paper presents a geometric solution to the mass hierarchy and parameter problems of the Standard Model, derived from the framework of the Golden K Hypothesis (GKH). A universal mass formula is derived from the theory's first principles, which are rooted in a pregeometric E8 lattice and the axiom of Discrete Scale Symmetry (DSS) governed by the golden ratio. The formula connects a log-periodic "bare" mass ladder, dictated by a conserved discrete scale charge (n), with a "phason dressing" correction determined by the particle's quantized internal phase angle on the E8 root lattice. It is demonstrated that this formula, using the electron mass as the sole calibration point, successfully reproduces the entire known mass spectrum—including charged leptons, electroweak bosons, all quarks, and neutrino oscillation parameters—with a precision consistently better than 1.5%. The paper concludes by discussing the model's falsifiable predictions for new particle resonances and a novel geometric explanation for the empirical Koide formula.