Position Dependence of Phase-Decomposed Lag-One Covariance in Prime-Gap Data

We report the falsification of a preregistered prediction concerning the phase-decomposed lag-one covariance of consecutive prime gaps, together with a subsequent exploratory diagnostic. Earlier work established persistent negative lag-one dependence and an exact decomposition of the covariance of locally detrended gaps into A + X + Y + D. For a primorial modulus M, we define the non-D covariance share S(M) = (A + X + Y) / Cov(e_n, eₙ₊₁). A preregistered prediction that S(M) would not decrease at higher window positions was falsified: across three windows from 10^8 to 3×10^10, S(M) decreased for every tested modulus. In an exploratory fixed-count diagnostic using eight windows with approximately 10^8 gaps each, spanning prime locations from 10^8 to 10^13, both S(M) and |ρ_resid(M)| decreased monotonically with L = log p. The fixed-count design strongly disfavors a pure sample-size explanation. Over L ∈ [19.96, 29.93], logarithmic and power-law descriptions are similarly supported, while the reciprocal form is less supported at large moduli (Table A.6); the linear-in-L form is substantially disfavored. The results are reported as finite-range empirical trends, without an asymptotic interpretation or proposed theoretical mechanism.