Induced zesting conjecture for Drinfeld centers

Let $\mathcal{C}$ be a fusion category, and let an associative zesting of $\mathcal{C}$ induce a zesting on its center $\mathcal{Z}(\mathcal{C})$. Induced zesting conjecture. The induced zesting on the center $\mathcal{Z}(\mathcal{C})$ from an associative zesting of $\mathcal{C}$ is equivalent to an associative zesting on $\mathcal{Z}(\mathcal{C})$. In other words, the braided and ribbon zesting on the center are equivalent to the trivial one. This conjecture refines the preceding expectation that associative zesting of a fusion category induces a ribbon zesting of its center, extending the phenomenon established for the Mignard–Schauenburg modular isotopes. The general equivalence remains open.