Desalvo–Pak ratio conjecture for the partition function

Let $p(n)$ denote the number of partitions of $n$. Desalvo–Pak's conjecture. For every integer $n\geq45$,

$$\frac{p(n-1)}{p(n)}\left(1+\frac{\pi}{\sqrt{24}n^{3/2}}\right)>\frac{p(n)}{p(n+1)}.$$

The coefficient $\frac{\pi}{\sqrt{24}}$ is asymptotically best possible, and the conjecture was subsequently proved by Chen, Wang, and Xie.