The trivial-center-deformation conjecture for untwisted elliptic algebras

Let $B_{V,\Psi}$ be an untwisted elliptic algebra, and let its center be denoted by $Z(B_{V,\Psi})$. A filtered deformation induces a trivial deformation of the center when the corresponding deformation of $Z(B_{V,\Psi})$ is trivial. Trivial-center-deformation conjecture. Any filtered deformation of an untwisted elliptic algebra $B_{V,\Psi}$ which induces a trivial deformation of the center is trivial. This is presented as a first step toward proving the surface construction in the untwisted case; it remains open, although the paper notes that the analogous statement for torsion twists would follow from the main conjecture.