Partition-function quiver description for equal-sign Hopf link conormal fillings

Let $L_{st}$ be a Lagrangian filling of the Hopf link conormal, with $s,t\in\{l,m,d\}$ and $|s|=|t|$. Let ${\mathsf{Z}}_{L_{st}}$ denote its skein-valued partition function, and let ${\mathsf{\Psi}}_{\mathrm{di}}^{(0)}$, ${\mathsf{\Psi}}_{\mathrm{di}}^{(1)}[a^2]$, ${\mathsf{\Psi}}_{\mathrm{an}}^{(-1,-1)}$, and ${\mathsf{\Psi}}_{\overline{\mathrm{an}}}^{(0,0)}[a^2]$ be the basic disk and annulus partition functions associated with the curves in the corresponding quiver description. Equal-sign filling partition-function conjecture. The partition function ${\mathsf{Z}}_{L_{st}}$ is generated by two basic disks on each Lagrangian component and two basic annuli that differ by a factor of $a^2$. In particular, ${\mathsf{Z}}_{L_{l^{+}l^{+}}}$ is obtained by inserting ${\mathsf{\Psi}}_{\mathrm{di}}^{(0)}$, ${\mathsf{\Psi}}_{\mathrm{di}}^{(1)}[a^2]$, ${\mathsf{\Psi}}_{\mathrm{an}}^{(-1,-1)}$, and ${\mathsf{\Psi}}_{\overline{\mathrm{an}}}^{(0,0)}[a^2]$ along the curves in the quiver description. This conjectural quiver description gives a proposed explicit form for the skein-valued partition functions of the equal-sign fillings; detailed formulas are provided in the source paper.