Fractal-Spectral Structure of Goldbach Deviations: Long-Range Persistence and Amplitude Scaling

We investigate the structural properties of Goldbach deviations δ(N) = (G(N)-HL(N))/HL(N), where G(N) is the Goldbach representation count and HL(N) the Hardy-Littlewood prediction. Three principal findings emerge: (1) Scale Separation: the main term grows as N while the error grows as √N, ensuring asymptotic dominance; (2) Long-Range Persistence: the Hurst exponent H = 0.84 >> 0.5 indicates strong non-random structure; (3) Self-Similar Amplitude Scaling: the envelope coefficient κ ≈ C₂ = 0.6602 (twin prime constant) is stable across four orders of magnitude. These observations suggest that Goldbach deviations are governed by structured, arithmetically-driven dynamics rather than stochastic fluctuations. While not constituting a rigorous proof, these findings provide strong heuristic evidence for the structural stability of positive Goldbach counts at large N.