A Conductor Census of 425,082 Goldbach–Frey Curves: Asymptotic Decomposition and Bandwidth Stability

Using the exact conductor formula Cond_odd(Jac(C)) = [rad_odd(p·q·N·(p−q))]² established in the preceding papers, we compute the conductor ratio ρ for every Goldbach pair (p, q) with p + q ≤ 10,000: a census of 425,082 curves. We decompose the mean conductor ratio into three components: a static term ρ_static depending only on N (6.5%), a boundary term ρ_boundary from p·q (66.0%), and a gap term δ from |p−q| (27.5%). The key empirical finding is bandwidth stability: σ(ρ) ≈ 0.33 is approximately constant over 2N ∈ [100, 10000], while ⟨ρ⟩ grows logarithmically. This implies the coefficient of variation σ/⟨ρ⟩ → 0 as N → ∞, providing a quantitative explanation for the high R² > 0.997 of the Band Shifting Law and connecting the conductor geometry to the Hardy–Littlewood prime pair density.