  On the assumption of the Riemann hypothesis, we show that over a class of
sufficiently smooth test functions, a measure conjectured by Bogomolny and
Keating coincides to a very small error with the actual pair correlation
measure for zeroes of the Riemann zeta function. Our result extends the well
known result of Montgomery that over the same class of test functions the pair
correlation measure coincides (to a larger error term) with that of the
Gaussian Unitary Ensemble (GUE). The restriction of test functions remains
stringent, but we are nonetheless able to detect, at a microscopically blurred
resolution, macroscopic troughs in the pair correlation measure.
