We compute the true Artin conductor of the Jacobian of the Goldbach–Frey curve C: y² = x (x² − p²) (x² − q²), p + q = 2N, using Magma's genus-2 conductor algorithm. Across 10 test cases spanning 2N ∈ 10, 60, we establish three results: (a) every odd conductor exponent equals exactly 2 (tame semistable reduction) ; (b) the odd conductor support is precisely the set of odd primes dividing p·q·M· (p − q), where M = N; and (c) the radₒdd-proxy introduced in the preceding papers of this series equals the true odd conductor minus a single, explicitly computable correction term arising from |p − q|. The correction term is 2 log radₒddⁿew (|p − q|) /log (2N) and is verified to machine precision in all 10 cases (10/10 match). This validates the proxy framework underpinning the Band Shifting Law and explains why the BSL achieves R² > 0. 997: the proxy captures the full systematic content of the conductor, while the omitted difference term contributes only pair-dependent noise.
Ruqing Chen (Mon,) studied this question.