Antieau–Gepner–Heller connective K-theory conjecture for bounded t-structures

Let $\sC$ be a small stable $\infty$-category equipped with a bounded t-structure. A spectrum is connective when its negative homotopy groups vanish. Antieau–Gepner–Heller's connective K-theory conjecture. The K-theory spectrum $\K(\sC)$ is connective. This is one of the conjectures formulated for K-theoretic properties of bounded t-structures; the source supplies no resolution in the provided text.