3 problems

Laurent-polynomial conjecture. For every degree $d$, $\Omega_{d[L]}$ is a Laurent polynomial in $q_0$, $q_1$, $q_2$, and $q_3$.

Higher-degree denominator conjecture. For every integer $d>1$,

Nekrasov–Okounkov conjecture. The generating series of these K-theoretic stable-pair invariants coincides with the Laurent expansion of the M2-brane index of $Z$.