The Cascade Energy Staircase: Dissolution of the Hierarchy Problem, the Cosmological Constant, and the Emergence of QCD from Electroweak Symmetry Breaking

We present the Cascade Energy Staircase: the discrete sequence of energy scales E_n = v/δ^n, where v = 246.22 GeV is the electroweak symmetry-breaking scale and δ = 4.6692… is the Feigenbaum bifurcation constant. This staircase descends from the electroweak scale at n = 0 through the QCD confinement domain at n = 4–5, the electron mass scale at n = 8, and terminates at the dark energy scale at n = 21, where v/δ^21 = 2.174 meV agrees with the measured ρ_Λ1/4 = 2.3 meV to 5.5%. The staircase geometrically dissolves both the Hierarchy Problem and the Cosmological Constant Problem: M_Pl/v = δ24.95 and v/ρ_Λ1/4 = δ20.96 are natural geometric depths, not accidents requiring fine-tuning. The ratio α_s/α_W = T² (Paper 44) locates the muon anomalous magnetic moment discrepancy at the QCD–EW interface and provides a cascade estimate of the hadronic vacuum polarization correction.