Quillen equivalence conjecture for the complicial and marked Kan model structures

Let $\mathfrak{K}_{n}$ and $\mathfrak{M}_{n}$ be the model categories of marked Kan complexes and marked complicial sets, respectively, and let $(i_{\Delta},-_{\Delta})$ be the adjoint pair between them. Quillen equivalence conjecture. The pair $(i_{\Delta},-_{\Delta})$ is a Quillen equivalence between $\mathfrak{K}_{n}$ and $\mathfrak{M}_{n}$. If true, this would imply that the authors' model is equivalent to the main cluster of geometric models of $(\infty,n)$-categories, in light of Loubaton's work.