Rigidity conjecture for the mirror of the canonical coisotropic brane

Let $Y$ be the complexified target and let $\widetilde Y$ be its mirror. Assume the canonical coisotropic brane on $Y$ has mirror brane $\widetilde{\mathcal B}_{cc}$, obtained as the corresponding object on $\widetilde Y$. Rigidity conjecture for the mirror canonical coisotropic brane. The brane $\widetilde{\mathcal B}_{cc}$ is always rigid. In the K3 example discussed immediately before the statement, its moduli space has dimension zero; the conjecture asserts that this rigidity holds generally for mirrors of the canonical coisotropic brane.