Ab initio derivation of the Berry-Keating correction coefficient from the Conrey-Snaith triple correlation formula

The gap ratio statistic of Riemann zeta zeros converges to the GUE prediction as (T) = Rᵢnf + c/log² (T) with the empirical coefficient cₑmp = 1. 245 +/- 0. 040. We decompose c into two channels using the Conrey-Snaith formula for the triple correlation R₃ and the conditional gap probability Eᶜond from the Schur complement of the sine kernel. The delta R₃ channel, computed ab initio via Richardson extrapolation at L = 1000, 3000, 10000, and 30000, contributes cR3 = -1. 6, while the gap probability channel contributes cE = +2. 8 (inferred by difference), yielding c = cR3 + cE = +1. 245. Separately, we construct the Berry-Keating kernel and show that its Fredholm determinant gives the wrong sign, establishing that the kernel phase is the fundamental obstruction. The Conrey-Snaith route bypasses this because R₃ = |K|² is phase-immune.