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 weighted sums over zeros of the Riemann zeta function and the quadratic Dirichlet L-function L(s, χ_d), formed using the Lorentzian weight w(ρ) = 2/(¼ + γ²). We prove unconditionally that N < 0 for all squarefree d > 1 (the "spacelike" property), that its Cesàro average is negative for all T > 0, and that the density of positive excursions satisfies an effective bound at each verified truncation level via Jacobi–Anger resonance analysis. Under a computationally verified hypothesis (resonance lattice rank zero at M = 20), the exact asymptotic dens{N > 0} = C(d)/√d + o(1/√d) is established, with C(5) = 0.1191. All computational results are certified using ARB interval arithmetic (python-flint). Supplementary data modules provide 200 zeros of L(s, χ₅) at 70-digit precision, 20 zeros each of zeros of L(s, χ₂); (s, χ₃); L(s, χ₆); L(s, χ₇); L(s, χ₁₀); L(s, χ₁₁); L(s, χ₁₃) at 20-digit precision, enabling full reproducibility of all numerical results. This is the first paper in the series "Persistent Heuristics."