Stable quotient polynomiality conjecture for local \u03b2c0^3

Let $K\mathbb{P}^3$ be the local projective three-space, let $T=I^{K\mathbb{P}^3}_1(q)$ be the mirror coordinate, and let $\mathcal{F}^{\mathsf{SQ}}_{g,a+b}[a,b](q)$ denote the stable quotient invariants, with $\mathds{G}_3$, $A_2$, $B_2$, $B_4$, and $C_1$ as defined in the source. Stable quotient polynomiality conjecture for $K\mathbb{P}^3$. For $g\geq2$, $\mathcal{F}^{\text{SQ}}_{g,a+b}[a,b](q)\in\mathds{G}_3[A_2,B_2,B_4,C_1^{\pm1}]$; $\mathcal{F}^{\mathsf{SQ}}_g$ has degree at most $2(3g-3)$ in $A_2$; and for $g\geq1$ and $k\geq1$, $\frac{\partial^k\mathcal{F}^{\mathsf{SQ}}}{\partial T^k}(q)\in\mathds{G}_3[A_2,B_2,B_4,C_1^{\pm1}]$. These assertions extend the polynomiality structure to local $\mathbb{P}^3$; the supplied text gives no evidence resolving them.