Rank formula conjecture for symplectic mapping groups of rational surfaces

Let $(X,\omega)$ be a rational symplectic surface with $8\leq\chi(X)\leq 11$, and let $Q(X)=\frac{1}{2}(\chi(X)-2)(\chi(X)-3)$. Let $r^+(X,\omega)$ denote the number of homology classes admitting $(-2)$ Lagrangian spheres. Rank formula conjecture.

$$Q(X)=r^+(X,\omega)+\operatorname{Rank}\bigl[\pi_1(\operatorname{Symp}_h(X,\omega))\bigr]-\operatorname{Rank}\bigl[\pi_0(\operatorname{Symp}_h(X,\omega))\bigr].$$

This is proposed as an extension of a formula known for rational surfaces with $\chi(X)\leq 7$. The source presents the extension as a speculation, and its general validity remains open.