Realization conjecture for rational inner functions of matrix argument

Let $\mathrm B_m$ and $\mathrm B_\alpha$ denote the matrix balls, and let $\mathop {\mathrm {Inn}}\nolimits(m,\alpha)$ be the space of all rational inner maps $F:\overline{\mathrm B}_m\to\overline{\mathrm B}_\alpha$. Let $\mathop {\mathrm {Char}}\nolimits(m,\alpha)$ be the space of characteristic functions determined by all possible elements of $\operatorname{U}(\alpha+mj)$ for $j=0,1,2,\dots$. Realization conjecture. Any rational inner function is a characteristic function of some colligation, namely

$$\mathop {\mathrm {Inn}}\nolimits(m,\alpha)=\mathop {\mathrm {Char}}\nolimits(m,\alpha).$$

This asserts that rational inner functions of matrix argument admit realization by colligations, identifying the function-theoretic and operator-theoretic classes. The supplied text gives no evidence resolving the conjecture.