Conjecture on pole cancellation in the Nekrasov instanton sum with adjoint matter

Let $p,q$ be positive coprime integers, let $b^2=p/q$, and let $\boldsymbol{Y}$ range over tuples of partitions with corresponding terms $Z_{\vec{Y}}$. Let $\epsilon_1$ and $\epsilon_2$ be the equivariant parameters, and let $m$ be the mass parameter. Pole-cancellation conjecture. The value $b^2=p/q$ is a removable singularity (or smooth point) of all terms $Z_{\vec{Y}}$ if $m$ or $\epsilon_1+\epsilon_2-m$ is in

$$\{k\epsilon_1\mid 0\leq k\leq \lceil q/p\rceil\}\cup\{k\epsilon_2\mid 0\leq k\leq \lceil p/q\rceil\}.$$

For other values of $m$, $b^2=p/q$ is a pole of at least one term $Z_{\vec{Y}}$. This conjecture seeks a complete characterization of the mass values for which all instanton terms avoid poles at positive rational $b^2$; the preceding examples motivate the stated intersection condition, while the general assertion is left unresolved in the source.