The formal-dissection realization conjecture for derived-equivalent gentle and skew-gentle algebras

Let $A$ be a graded gentle or skew-gentle algebra, and let $\mathbf S=(S,\Sigma,\eta)$ be the graded surface associated to $A$. For a formal dissection $\Delta$ of $\mathbf S$, let $\mathbf A_\Delta$ be its associated formal differential graded algebra. Formal-dissection realization conjecture. For any graded associative algebra $B$ which is (perfect) derived equivalent to $A$, there exists a formal dissection $\Delta$ of $\mathbf S$ such that

$$B\simeq \mathrm{H}^\bullet(\mathbf A_\Delta)$$

as graded associative algebras. This conjecture is presented as a converse to the theorem that formal dissections yield graded skew-gentle algebras and that formal-generator endomorphism algebras are derived equivalent to graded skew-gentle algebras. Its general status is not specified in the supplied text.