The sine beta process is a canonical random point process arising as the bulk scaling limit of eigenvalues from the Gaussian beta ensemble in random matrix theory. While the paper establishes that this process is tail trivial, meaning that remote events carry no information, a precise quantitative understanding of how correlations between distant portions of the point configuration decay remains elusive. Specifically, it is unknown whether one can establish explicit mixing rates or decay-of-correlation estimates for the sine beta process that are strong enough to drive a quantitative central limit theorem for smooth linear statistics, with an explicit error term in terms of the smoothness and support of the test function.