Steady-state ratio conjecture for the doubly asymmetric simple exclusion process

Let $D=\textnormal{DASEP}(n,p,q)$ be parameterized by $t$ and $u$ as described above. For a partition $\lambda$ with $S_n(\lambda)\subseteq D$, let $S_n(\lambda)$ denote the set of permutations associated with $\lambda$, and let $\mu,\nu\in S_n(\lambda)$ be arbitrary permutations. Write $\textnormal{Pr}$ and $\textnormal{Pd}$ for the steady-state probability functions of the ASEP and DASEP, respectively.

Steady-state ratio conjecture. The following statements are equivalent: $t=1$; and, for all such partitions $\lambda$ and all permutations $\mu,\nu\in S_n(\lambda)$,

$$\frac{\textnormal{Pr}(\mu)}{\textnormal{Pr}(\nu)}=\frac{\textnormal{Pd}(\mu)}{\textnormal{Pd}(\nu)}.$$

That is, the ratio between steady-state probabilities does not change when moving from the ASEP to the DASEP. The preceding theorem proves this equivalence for $D=\textnormal{DASEP}(3,2,2)$; the conjecture proposes the corresponding result for general $n,p,q$.