Using the exact conductor formula Condₒdd (Jac (C) ) = radₒdd (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 ρₛtatic depending only on N (6. 5%), a boundary term ρboundary 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.
Ruqing Chen (Tue,) studied this question.