The theory of bicategorical fibrations has been relatively well studied, e.g. by Baković and by Buckley. In particular, given a trifunctor $F : \mathcal K \to \mathbf{Bicat}$ from a bicategory $\mathcal K$ into the tricategory of bicategories $\mathbf{Bicat}$, there is an associated bicategory of elements $\int F$. However, the three-dimensional story appears to have been less developed so far.
Given a trifunctor $F : \mathfrak K \to \mathbf{Bicat}$ from a tricategory $\mathfrak K$, has the associated tricategory of elements been defined in the literature? For my purposes, I would be satisfied only having the construction for a trifunctor $F : \mathfrak K \to \mathbf{2\text{-}Cat}$ in which $\mathfrak K$ is a locally cubical tricategory.
