Equivalence of n‑trivial complicial sets and established models of (∞,n)‑categories for n>2

Determine whether Verity’s n‑trivial complicial sets (weak complicial sets with all k‑simplices marked for k>n) are equivalent to established models of (∞,n)‑categories, such as Rezk’s Θn‑spaces and Barwick’s n‑fold Segal spaces, for all n>2.

Background

Complicial sets (stratified simplicial sets satisfying lifting properties) provide a proposed model for (∞,∞)‑ and, when truncated, for (∞,n)‑categories. For n=1 they recover marked quasicategories, and for n=2 various works (including Lurie and Gagna–Harpaz–Lanari) establish equivalence among major models.

Beyond n=2, the equivalence between n‑trivial complicial sets and other standard models (e.g., Θn‑spaces and n‑fold Segal spaces) has not been established, leaving a key comparison problem open in the landscape of higher category models.