K-theory non-detection conjecture for stable infinity-categories

Let $\mathcal{C}$ and $\mathcal{D}$ be small stable $\infty$-categories, and let $h_{n-1}\mathcal{C}$ denote their stable $n$-categorical truncations. Let $\mathrm{K}$ denote nonconnective algebraic $K$-theory.

K-theory non-detection conjecture. There is no natural number $n$ such that, for all such $\mathcal{C}$ and $\mathcal{D}$, an equivalence

$$h_{n-1}\mathcal{C}\simeq h_{n-1}\mathcal{D}$$

as stable $n$-categories implies

$$\mathrm{K}(\mathcal{C})\simeq\mathrm{K}(\mathcal{D}).$$

The conjecture is motivated by examples where stable higher-categorical truncations agree while algebraic $K$-theory differs; the authors note that Schlichting established the analogous $n=1$ phenomenon for triangulated categories.