Windowed Phase Conditioning and Lag-One Covariance of Consecutive Prime Gaps

We study the lag-one covariance of consecutive prime gaps g_n = p_(n+1) - p_n in the window [10^10, 3x10^10), after local detrending and conditioning on the opening-prime residue modulo a primorial M. For each of seven moduli M in {6, 30, 210, 2310, 30030, 510510, 9699690} we obtain an exact decomposition A + X + Y + D = Cov that closes to within 10^-6. The residual correlation rho_resid remains negative at all seven scales, decreasing in magnitude from -0.0247 to -0.0103. The between-phase variance grows monotonically with M, accounting for up to 3.74% of Var(e). The non-D terms account for 60.4% of the lag-one covariance at the largest tested modulus, while between-phase structure accounts for 3.74% of the one-point variance. We report block-bootstrap 95% intervals for rho_resid that exclude zero at every scale. The results are finite-range and do not claim asymptotic laws. Source code, CSV results, run log and SHA256SUMS checksums are attached to this record.