Conjectural pair correlation in short positive intervals

Assume the Riemann Hypothesis and let $\gamma,\gamma'$ range over imaginary parts of non-trivial zeros of $\zeta(s)$. For $0<\alpha<\beta\ll\log T$, the short-interval pair-correlation conjecture.

$$\left(\frac{T}{2\pi}\log T\right)^{-1}\mathop{\sum_{0<\gamma\neq\gamma'\leq T}}_{2\pi\alpha/\log T\leq\gamma-\gamma'\leq2\pi\beta/\log T}1\sim\int_\alpha^\beta\left(1-\frac{1}{1+(\pi u/\log T)^2}\left(\frac{\sin\pi u}{\pi u}\right)^2\right)\,du.$$

This gives a conjectural asymptotic for normalized zero-pair counts in short positive-difference intervals and is presented as a consequence of the preceding shifted pair-correlation conjectures; it remains unresolved in the supplied text.