Three-tier substrate hierarchy dc1 sea m₁ ≈ 2 meV/c² λ_dB ~ 1.3 mm n₁ ~ 7×10¹¹ m⁻³ Delocalized BEC Effective quantum m_eff ≈ 1.7 MeV/c² r_eff = 150 fm v_rot = 0.776 c L = ℏ exactly Coherence soliton ξ ≈ 97–110 μm E_min ≈ 13 meV ω₀ ~ 7.8×10⁹ rad/s Modon / lattice cell ν ~ 10⁹ ξ/r_eff Outer scale: determined by ℏ, c, ρ_DM ξ = (ℏ / ρ_DM · c)^1/4 ≈ 110 μm m₁ = ℏ/(c·ξ) ≈ 2 meV/c² Close-packing: n₁·ξ³ ≈ 1 → one vortex per coherence volume Inner scale: determined by α_mf and m_e (zero new parameters) m_eff = m_e / α_mf = 1.70 MeV/c² v_rot = c√(2α_mf) = 0.776 c r_eff = ℏ/(m_eff · v_rot) = 150 fm Angular momentum = ℏ Bridge equation (particle physics ↔ cosmology) ℏ · K · α_mf / (2m_e c) ≈ (ℏ / ρ_DM · c)^3/4 Satisfied within √2 If exact: zero-parameter connection between sin²θ_W, m_e, ρ_DM, and j₁₁