Stable quotient holomorphic anomaly and polynomiality conjecture for local b2c0^2

Let $K\mathbb{P}^2$ be the local projective plane, let $q$ be the degree variable, and let $T=I^{K\mathbb{P}^2}_1(q)$ be the mirror coordinate with $Q(q)=\exp(T)$. Let $\mathcal{F}^{\mathsf{SQ}}_g$ denote the genus-$g$ stable quotient invariants, and let $\mathds{G}_2$, $A_2$, and $C_1$ be the series and coefficient ring defined in the source. Stable quotient polynomiality conjecture for $K\mathbb{P}^2$. For the stable quotient invariants of $K\mathbb{P}^2$, (i) $\mathcal{F}^{\text{SQ}}_g(q)\in\mathds{G}_2[A_2]$ for $g\geq2$; (ii) $\mathcal{F}^{\mathsf{SQ}}_g$ has degree at most $3g-3$ in $A_2$; (iii) $\frac{\partial^k\mathcal{F}^{\mathsf{SQ}}}{\partial T^k}(q)\in\mathds{G}_2[A_2,C_1^{-1}]$ for $g\geq1$ and $k\geq1$; and (iv) $\frac{\partial^k\mathcal{F}^{\mathsf{SQ}_g}}{\partial T^k}$ is homogeneous of degree $k$ in $C_1^{-1}$. These structural properties are part of the holomorphic anomaly framework for local $\mathbb{P}^2$; the supplied text does not state whether this conjecture has been proved.