Unconditional Density Bounds for Quadratic Norm-Form Energies via Lorentzian Spectral Weights

For a real quadratic field ℚ(√d), we study the norm-form energy N = S_ζ² − d · S_L², where S_ζ and S_L are Lorentzian-weighted zero sums with w(ρ) = 2/(¼ + γ²). We prove three main results. (1) Spacelike spectral data: N < 0 unconditionally for all squarefree d > 1, as a consequence of a low-lying zero dominance theorem proved via explicit zero-counting. (2) Effective density bound: at each verified truncation level M, dens{N > 0} ≤ 2‖f_{S_L^{(M)}}‖_∞ · (W₁(ζ)/√d + ε_M), established unconditionally via Jacobi--Anger resonance analysis. At fixed M the bound is nontrivial only for sufficiently large d; the O(1/√d) rate requires M to grow with d, which in turn requires a uniform density bound that we establish under a computationally verified finite-rank condition on the resonance lattice. (3) Exact asymptotic: under the computationally verified hypothesis that the infinite resonance lattice Λ_∞ has finite rank (verified for M ≤ 20, where rank = 0), the sharp asymptotic dens{N > 0} = C(d)/√d + o(1/√d) holds. For d = 5, C(5) = 2 f_{S_L}(0) · 𝔼[|S_ζ|] = 0.1191; the constant depends on d through the zeros of L(s, χ_d), and C(d) = O(1/log d) as d → ∞. Appendix F tabulates the first 1000 zeros at 70 decimal places for L(s, χ₂), L(s, χ₃), L(s, χ₅), L(s, χ₆), L(s, χ₇), L(s, χ₁₀), L(s, χ₁₁), and L(s, χ₁₃), all rigorously certified by ARB interval arithmetic.