Closure conjecture for graded gentle algebras under derived equivalence

Let $\mathbf S=(S,\Sigma,\eta)$ be a graded smooth surface with stops, and let $\mathcal W(\mathbf S)$ denote its partially wrapped Fukaya category. A formal generator is a generator of $\mathcal W(\mathbf S)$ whose associated endomorphism $A_\infty$ algebra is formal. Gentle-algebra closure conjecture. The class of graded gentle algebras is closed under derived equivalence. In particular, every formal generator of $\mathcal W(\mathbf S)$ is given by a formal dissection of $\mathbf S$. This is presented as the folklore smooth-surface case of the broader conjecture for graded orbifold surfaces; the paper notes that the analogous orbifold statement is known for disks with one orbifold point and stops, but the general closure claim remains open.