The geometric Cartan doubled Yangian conjecture for perverse coherent systems

Let $X$ be the local toric Calabi–Yau $3$-fold in the source, let $Y_\infty$ be the geometric Cartan doubled Yangian, and let $V:=H^*_c(\fM_\zeta^\chi,\varphi_W\mathbf{C})^\vee$ be the indicated cohomology vector space of the moduli space of stable perverse coherent systems. Let $D(\mathcal{SH})$ be the Drinfeld double constructed from the relevant Cohomological Hall algebra, and let the shifted affine Yangian have shift determined by $[\chi]$ and $\zeta$. Geometric Cartan doubled Yangian conjecture. The algebra $Y_\infty$ is isomorphic to $D(\mathcal{SH})$, it acts on $V$, and this action factors through an action of the shifted affine Yangian with the shift determined by $[\chi]$ and $\zeta$. This is an expected geometric construction and representation statement; the supplied source does not state a resolution.