Dyson's bulk gap probability asymptotic conjecture

Let $E_\beta^{\rm bulk}(0;(0,s))$ denote the probability that an interval of length $s$ in the bulk contains no eigenvalues for the beta ensemble. Dyson's conjecture.

$$E_\beta^{\rm bulk}(0;(0,s)) \mathop{\sim}\limits_{s \to \infty} \exp\left(-\frac{\beta(\pi s)^2}{16}+\left(\frac{\beta}{2}-1\right)\frac{\pi s}{2}\right).$$

This is the large-$s$ asymptotic prediction for the bulk gap probability, with the asymptotic expansion understood to the displayed order.