Rationality and nonnegativity conjecture for Serre dimensions

Let $A$ be a smooth and compact dg algebra over a field $\mathsf k$. Consider the lower and upper Serre dimensions of $\operatorname{Perf}(A)$.

Rationality and nonnegativity conjecture. The two Serre dimensions are rational numbers, and the upper Serre dimension is nonnegative:

$$\operatorname{\underline{Sdim}} \operatorname{Perf}(A),\qquad \operatorname{\overline{Sdim}} \operatorname{Perf}(A)\in\mathbb{Q},$$

with

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

The paper gives examples showing that the lower Serre dimension can be negative and notes that irrationality is unknown, so this conjecture remains open.