Chebyshev Bias in Goldbach Partitions: Analytic Derivation via Partial Summation and the Explicit Formula

We derive the Chebyshev bias in Goldbach partitions from first principles, conditional on the Generalized Riemann Hypothesis for L(s,χ3)L(s,χ3). A smoothed model proves Beven(x)=O(1/log⁡x)Beven(x)=O(1/logx), while a parameter-free heuristic predicts κ3=4κ3=4, matching empirical data to 5.8%. We detect the lowest zero of L(s,χ3)L(s,χ3) in Goldbach partition data via Lomb–Scargle periodogram (8.0379 vs 8.0397, 0.02% match). Three testable predictions are provided for mod-5, mod-7, and multiples of 3.