Enhancement uniqueness conjecture for complicial t-structures

Let $\mathcal{C}$ be a stable presentable $\infty$-category with an accessible right complete $t$-structure that is compatible with filtered colimits and is $n$-complicial for some $n$. Let $h\mathcal{C}$ denote its homotopy category.

Enhancement uniqueness conjecture. The homotopy category $h\mathcal{C}$ admits a unique $\infty$-categorical enhancement.

The authors describe this as a wildly optimistic conjecture. The condition of being $n$-complicial is presented as critical, and examples without that condition have multiple enhancements; the general claim is not proved.