The bounded t-structure conjecture for negative K-theory

Let $E$ be a small stable $\infty$-category equipped with a bounded $t$-structure. Write $\mathrm{K}_{-n}(E)$ for its negative nonconnective $K$-groups. Bounded t-structure vanishing conjecture.

$$\mathrm{K}_{-n}(E)=0$$

for every $n\geqslant 1$. This is posed as a motivic and categorical generalization of Schlichting's conjecture; the paper establishes important special cases, but the general assertion remains open.