The graded clock condition characterization for gentle one-cycle algebras

Let $A=kQ/I$ be a graded gentle one-cycle algebra. Define $d_+$ (respectively, $d_-$) as the difference between the number of clockwise (respectively, counterclockwise) oriented relations and the sum of the degrees of the clockwise (respectively, counterclockwise) oriented arrows. The algebra $A$ satisfies the graded clock condition when $d_+=d_-$.

Graded clock condition conjecture. A graded gentle one-cycle algebra satisfies the graded clock condition if and only if it is derived equivalent to $\Gamma(p,q,0)$ for some $p,q>0$ or to $\Gamma'(0,q,q)$, which is Koszul dual to $\Gamma(0,q,0)$, for some $q>0$.

This conjecture characterizes the graded gentle one-cycle algebras satisfying the graded clock condition by their derived-equivalence classes. The supplied text does not state whether the conjecture has been proved or disproved.