The finiteness conjecture for constructible sheaves on Alexandrov spaces

Fix a finite field $\mathbb{F}$. Let $X$ be a compact Alexandrov space, and let $D^b_c(\operatorname{Sh}_{\mathbb{F}}(X))$ denote the bounded derived category of constructible sheaves, whose cohomology sheaves restrict to local systems on the strata of the extremal stratification. The finiteness conjecture. For every $N\in\mathbb{N}$, there are only finitely many isomorphism classes of objects whose cohomology sheaves vanish outside $[-N,N]$ and whose restrictions to every stratum are local systems of rank at most $N$. This is a technical finiteness assertion intended to control constructible sheaf data on Alexandrov spaces; the source presents it as a conjecture, with no resolution supplied.