N^{3/2}-scale mixing conjecture in the maximal-current phase

Consider the simple exclusion process with open boundaries, with phase parameters $a$ and $b$, and let $t^N_{\mathrm{mix}}(\varepsilon)$ denote its $\varepsilon$-mixing time. Maximal-current mixing conjecture. When

$$\max(a,b)\leq 1,$$

including the triple point, $t^N_{\mathrm{mix}}(\varepsilon)$ is of order $N^{3/2}$ for every $\varepsilon\in(0,1)$, and cutoff does not occur.

The conjecture predicts the mixing scale in the maximal-current regime and contrasts it with the cutoff behavior expected in other phases. The supplied text gives no resolution.