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 <r>(T) = R_inf + c/log^2(T) with the empirical coefficient c_emp = 1.245 +/- 0.040. We decompose c into two channels using the Conrey-Snaith formula for the triple correlation R_3 and the conditional gap probability E^cond from the Schur complement of the sine kernel. The delta R_3 channel, computed ab initio via Richardson extrapolation at L = 1000, 3000, 10000, and 30000, contributes c_R3 = -1.6, while the gap probability channel contributes c_E = +2.8 (inferred by difference), yielding c = c_R3 + c_E = +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 R_3 = |K|^2 is phase-immune.