Dyson's crank limiting-shape conjecture

Let $M(m,n)$ denote the number of partitions of $n$ with crank $m$, where the crank of a partition is the largest part if it has no ones, and otherwise is the number of parts strictly larger than its number of ones minus its number of ones. Let $p(n)$ denote the number of partitions of $n$, and set

$$\beta:=\frac{\pi}{\sqrt{6n}}.$$

Dyson's crank limiting-shape conjecture. As $n\to\infty$,

$$M(m,n)\sim \frac14\beta\,\operatorname{sech}^2\left(\frac12\beta m\right)p(n).$$

The conjecture describes the limiting shape of the crank generating function and was solved in the paper, although the supplied parser metadata does not give a resolution status beyond the paper's assertion that it solves Dyson's conjecture.