Denominator conjecture for local-curve stable-pairs descendent partition functions

Let $d$ be the degree, and let $\mathsf Z$ denote any of the degree-$d$ descendent partition functions covered by the paper's Theorems 1, 2, and 3.

Denominator conjecture. The denominators of these partition functions are products of factors of the form $q^k$ and

$$1-(-q)^r$$

for $1\leq r\leq d$.

Equivalently, the only conjectured poles in $-q$ occur at $0$ and at roots of unity of order at most $d$, with no dependence on the equivariant variables $s_i$. The conjecture is proved in the paper for descendents of even cohomology, while the unrestricted statement remains open.