Dynamic Stability of the Goldbach Locus: Conductor Orbit Propagation and the Band Shifting Law in GSp(4)

We study the evolution of the Goldbach conductor distribution as the even integer N varies from 2¹⁰ to 2¹⁴. The static conduit factor rad_odd(N/2) fluctuates erratically, producing step-to-step jumps in Chen's ratio ρ exceeding ±3 units. Despite this apparent instability, we discover three rigidity phenomena: (1) The Band Shifting Law: ⟨ρ⟩ = 1.994ξ + 3.424 with R² = 0.9974, where ξ = 2log(rad_odd(M))/log N — the slope α ≈ 2 is algebraically exact from the discriminant. (2) Bandwidth constancy: the Goldbach ρ-band width is 1.09 ± 0.20, invariant under band shifting. (3) Non-emptiness under jump: all 513 even integers in [1024, 2048] have Goldbach pairs, despite conductor discontinuities. These results demonstrate dynamic stability: the Goldbach locus adapts to arbitrarily large conductor perturbations by reorganising its prime-pair content while preserving structural width. The corrected asymptotic form ⟨ρ⟩ = 2ξ + 4 − c/log N shows the law possesses asymptotic scale invariance, with local R² improving to 0.9994 at [2¹³, 2¹⁴].