Vanishing upper Serre dimension conjecture for finite-dimensional algebras

Let $A$ be a finite-dimensional algebra with finite global dimension. Write $\operatorname{Perf}(A)$ for its perfect derived category and $\operatorname{gldim} A$ for its global dimension.

Vanishing upper Serre dimension conjecture. The upper Serre dimension satisfies

$$\operatorname{\overline{Sdim}} \operatorname{Perf}(A)=0$$

if and only if

$$\operatorname{gldim} A=0.$$

This is posed after examples of finite-dimensional algebras with zero lower Serre dimension; the equivalence for all finite-dimensional algebras of finite global dimension is left open.