Self-Similar Structure in Goldbach Deviations: L-Function Zeros and the Twin Prime Signature

We use the Goldbach representation function as a testbed to study arithmetic structure in number-theoretic error terms. We present numerical evidence suggesting that the deviation from the Hardy-Littlewood formula exhibits nontrivial arithmetic structure consistent with a constant consistency principle: the twin prime constant C₂ ≈ 0.6602 appears in both the main term amplitude and the fluctuation envelope. Spectral analysis in the logarithmic domain reveals oscillatory components consistent with known Dirichlet L-function zeros within the available FFT resolution (Δγ ≈ 1.25). Hurst exponent analysis yields H = 0.85 ± 0.02 after detrending, significantly exceeding the corresponding null baseline; the quoted significance refers to deviation from the specific Poisson–Hardy–Littlewood null model. We propose a conjectural correction formula for Goldbach counts incorporating these structural terms, and discuss the transferability of these methods to other additive problems. --- Context within the Series: This is Paper V in a series of numerical studies on the Goldbach Conjecture. It builds upon previous findings: - Paper I: Hardy-Littlewood Validated to N=10¹² (DOI: 10.5281/zenodo.18113330)- Paper II: Crossover Phenomenon (DOI: 10.5281/zenodo.18123132)- Paper III: Spectral Rigidity (DOI: 10.5281/zenodo.18148544)- Paper IV: Second Main Term (DOI: 10.5281/zenodo.18149305) Key Contributions of Paper V:1. "Riemann Radar" methodology: FFT in log-domain detecting L-function zero signatures2. Constant Consistency Principle: κ/C₂ = 1.06 ± 0.06 (p = 0.32)3. Fractal persistence: H = 0.85 vs H_null = 0.51 (11σ rejection)4. Conjectural Chen-Goldbach correction formula