Pole-constraint conjecture for stable-pairs descendent partition functions

Let $X$ be a nonsingular projective $3$-fold and let $\beta\in H_2(X,\mathbb Z)$ be a nonzero effective class. Let $d=\operatorname{div}(\beta)$ be the divisibility of the image of $\beta$ in $H_2(X,\mathbb Z)/\text{torsion}$. Pole-constraint conjecture. The poles in $q$ of the rational function

$$\mathsf Z_{\mathsf P}\Big(X;q\ \Big| \prod_{i=1}^r \tau_{k_i}(\gamma_i)\Big)_\beta$$

may occur only at $q=0$ and at roots of the polynomials $1-(-q)^m$ for $1\le m\le d$. The source presents this as part of the expected pole constraints; no resolution is supplied.