The Standard Model Derived: A Comparative Analysis of Parameter Frameworks and the Cascade Solution

For sixty years, theoretical physics has attempted to explain why the Standard Model parameters take their observed values. The approaches have been consistent in method and consistent in result: add structure — supersymmetric partners, extended gauge groups, extra dimensions, a string landscape — and explain nothing. Not one confirmed Standard Model parameter has been derived from first principles by any of these frameworks. This paper presents a systematic comparison of six major parameter frameworks against a seventh: the Resonance Theory, based on the Feigenbaum renormalization group. The comparison reveals a categorical distinction. Every existing framework either adds new structure, reduces parameters without explaining them, or fits without deriving. The cascade framework requires none of these. It adds no particles, no dimensions, no parameters, and no modifications to any existing equation. From two proven universal constants — α = 2.50291 and δ = 4.66920 — it derives seventeen Standard Model observables including the Weinberg angle, the fine structure constant, the strong-to-weak coupling ratio, the fermion mass hierarchy, and the Higgs boson mass. Most critically, the Koide sum rule Q = 2/3 — observed for 43 years without derivation — follows exactly and algebraically from the cascade bifurcation amplitude δ_K = √2, requiring no fitting of any kind. The distinction is not one of degree. It is one of kind. The Standard Model parameters are not free. They are outputs of the Feigenbaum renormalization group fixed point. The sub-atomic search is complete. Paper 46 of the Resonance Theory series.