Conjectural local statistics for shifted zeta-zero differences

Assume the Riemann Hypothesis, let $\gamma$ and $\gamma'$ range over imaginary parts of non-trivial zeros of $\zeta(s)$, and let $h$ be the shift parameter. For fixed $\alpha>0$, the shifted local pair-correlation conjecture.

$$\left(\frac{T}{2\pi}\log T\right)^{-1}\mathop{\sum_{0<\gamma\neq\gamma'\leq T}}_{|\gamma-\gamma'-h|\leq 2\pi\alpha/\log T}1\sim\int_{-\alpha+h\log T/(2\pi)}^{\alpha+h\log T/(2\pi)}\left(1-\frac{4}{4+h^2}\left(\frac{\sin\pi u}{\pi u}\right)^2\right)\,du.$$

This prediction is derived by convolving the preceding conjectural formula with a kernel and concerns the normalized number of zero pairs in a short shifted interval; it is open in the supplied text.