One uniqueness to rule them all

Let $A$ be the function defining the Zakharov–Shabat reflection coefficient, let

$$r(z)=-\I \int_\R \rmd u \, e^{\I z u}A(u),$$

and let $A_s$ be the associated operator, with kernel $K_s=A_s^2$. Consider the Riemann–Hilbert problem associated to the Zakharov–Shabat system with reflection coefficient $r$. One uniqueness to rule them all. The Riemann–Hilbert problem is uniquely solvable if and only if the determinantal point process with kernel $K_s$ is uniquely defined. The conjecture proposes an equivalence between uniqueness of the Zakharov–Shabat Riemann–Hilbert solution and uniqueness of the corresponding determinantal point process, linking the analytic and probabilistic descriptions.