Chan's extended strong pair correlation conjecture

Let $F_\Delta(\alpha)$ denote the shifted pair-correlation function and let $w(\Delta)=4/(4+\Delta^2)$. Chan's extended strong pair correlation conjecture. For $|\alpha|\geq1$ and $\Delta=o(\log^{1/3}T)$,

$$F_\Delta(\alpha)=T^{-i\alpha\Delta}w(\Delta)(1+o(1)),$$

uniformly for $\alpha$ in compact intervals as $T\to\infty$. This longer-range pair-correlation input is used in the paper to derive Berry's variance formula in both the universal and non-universal regimes; the supplied text gives no resolution status.