The semi-orthogonal decomposition conjecture for gaps in Orlov spectra

Let $X$ be a smooth algebraic variety, and let

$$\left\langle \mathcal A_1,\ldots,\mathcal A_n\right\rangle$$

be a semi-orthogonal decomposition of $\operatorname{D}^{\operatorname{b}}(\operatorname{coh} X)$. A gap conjecture for semi-orthogonal decompositions. The length of any gap in the spectrum of $\operatorname{D}^{\operatorname{b}}(\operatorname{coh} X)$ is at most the minimum of the maximal Rouquier dimension amongst the $\mathcal A_i$ and the maximal gap amongst the $\mathcal A_i$. This is proposed after a theorem giving an upper bound on gaps from generators of semi-orthogonal components; the conjecture remains purely conjectural in the source.