For Haar-distributed U(N) matrices, the gap-ratio distribution approaches the sine-kernel limit with a leading correction of order N^{-4}, and this cancellation explains the (log(T/2π))^{-3} deviation seen in Riemann zeta zero spacing ratios.
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Distributions of consecutive level spacings of circular unitary ensemble and their ratio: finite-size corrections and Riemann $\zeta$ zeros
For Haar-distributed U(N) matrices, the gap-ratio distribution approaches the sine-kernel limit with a leading correction of order N^{-4}, and this cancellation explains the (log(T/2π))^{-3} deviation seen in Riemann zeta zero spacing ratios.