Finiteness conjecture for ultimate dimension under semi-orthogonal decompositions

Let $\mathcal T$ be a triangulated category with a semi-orthogonal decomposition

$$\mathcal T=\langle\mathcal A,\mathcal B\rangle.$$

Ultimate-dimension finiteness conjecture. If the ultimate dimensions of $\mathcal A$ and $\mathcal B$ are finite, then the ultimate dimension of $\mathcal T$ is finite. The source presents this as a hope needed to control Orlov spectra under semi-orthogonal decompositions; it is stated as conjectural and no resolution is given.