Pole cancellation conjecture for Casselman and R-polynomial coefficients

Let $W$ be the Weyl group of a root system $\Phi$, let $u\leqslant v$, and let $m_{u,v}(\mathbf{z})$ and $r_{u,v}(\mathbf{z})$ be the corresponding Casselman and deformed Kazhdan–Lusztig coefficients. Define

$$S(u,v)=\{\alpha\in\Phi^+\mid u\leqslant v r_{\alpha}<v\}.$$

Pole cancellation conjecture. The functions

$$\prod_{\beta\in S(u,v)}(1-\mathbf{z}^{\beta})m_{u,v}(\mathbf{z}),\qquad \prod_{\beta\in S(u,v)}(1-\mathbf{z}^{\beta})r_{u,v}(\mathbf{z})$$

are analytic on all of $\widehat{T}(\mathbb{C})$. This conjecture asserts that the possible root-hyperplane poles of these coefficients are removed by the displayed product; the source gives no resolution.