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The electroweak hierarchy problem asks why the Higgs vacuum expectation value (v = 246.2 GeV) is sixteen orders of magnitude below the Planck mass (M_P = 1.22 × 10¹⁹ GeV), requiring apparent fine-tuning of one part in 10³². We show that this framing rests on a false premise: the natural comparison scale is not M_P but √(M_P k_B T_CMB) = 1693 GeV, the geometric mean of the Planck mass and the CMB temperature, derived as the unique solution of the K_bdry/K_ent crossover condition. From this geometric mean, the observed Higgs VEV follows from standard one-loop Coleman-Weinberg corrections with a modest suppression factor, yielding v = 250.5 GeV (1.75% error) with zero free parameters. The K_ent barrier function provides a natural UV regulator replacing the artificial Planck-scale cutoff. We derive the critical density identity ρ_crit = N_SM M_P⁴/(12π² S_horizon), where N_SM = 118 is the Standard Model helicity count and S_horizon is the Bekenstein entropy of the cosmological horizon. This identity is proven algebraically independent of H₀ (the Hubble dependence cancels exactly through the Planck-unit identity l_P² M_P⁴ G = c⁴) and matches observation to 0.37% accuracy. The exact match requires N_SM = 12π² = 118.44, exceeding the naive count by 0.44 degrees of freedom. Three consequences follow: no new particles between the electroweak and Planck scales (consistent with LHC null results), the cosmological constant hierarchy is reduced from a 120-order-of-magnitude problem to a particle counting question, and the hierarchy is cycle-invariant under the bounce attractor (Paper 11).