The Markov-invariance conjecture for the relative weight grading in symplectic Khovanov cohomology

Let $L_{\wp_{\circ}}$ be the distinguished Lagrangian submanifold used to define symplectic Khovanov cohomology, and let $\beta\times\mathrm{id}$ be a braid-group action on it. The Floer group $HF^*(L_{\wp_{\circ}},(\beta\times\mathrm{id})(L_{\wp_{\circ}}))$ carries a relative weight grading. Markov-invariance conjecture. The relative weight grading is Markov invariant and recovers the relative second grading on $\mathrm{Kh}_{symp}(\kappa)$. The statement is presented after the paper's main theorem and is not accompanied here by an explicit resolution; its status is therefore left open.