Large-deformation limit conjecture for the ASEP ground state and current generating function

The partially asymmetric simple exclusion process is described using a deformed Markov matrix, with deformation parameter $\xi$ and system variables $\mathbf{x}$. For each positive integer $m$, let ${|\Psi^{(m)}(\mathbf{x};s)\rangle}$ be the twice deformed ground state vector, let $\mathcal{Z}^{(m)}(\mathbf{x};s)$ be its normalising function, and impose $s=\xi^{1/m}$. Let ${|\Psi_0(\mathbf{x};\xi)\rangle}$ and $F_0(\mathbf{x};\xi)$ be functions associated with the limiting state and generating function. Large-deformation limit conjecture. As $m$ tends to infinity, both the normalised twice deformed ground state vector and the scaled logarithm of its normalising function converge according to

$$\lim_{m\to\infty}\frac{{|\Psi^{(m)}(\mathbf{x};s=\xi^{1/m})\rangle}}{\mathcal{Z}^{(m)}(\mathbf{x};s=\xi^{1/m})}={|\Psi_0(\mathbf{x};\xi)\rangle},$$ $$\lim_{m\to\infty}\frac{\ln(\xi)}{m}\ln\left(\mathcal{Z}^{(m)}(\mathbf{x};s=\xi^{1/m})\right)=F_0(\mathbf{x};\xi),$$

where ${|\Psi_0\rangle}$ and $F_0$ are regular functions of $\mathbf{x}$. This conjecture is intended to connect the $q$KZ and Koornwinder-polynomial construction with the ground state and current-cumulant generating function of the deformed ASEP in the $m\to\infty$ limit; the supplied text does not indicate whether it has been resolved.