Coherence conjecture for higher-dimensional categories

A small lax $n$-category is a lax $n$-category whose underlying collection of objects and cells is small. A small Gray $n$-category is defined inductively: a small Gray $0$-category is a set, and a small Gray $(n+1)$-category is a small lax $(n+1)$-category strictly isomorphic to a sub-lax-$(n+1)$-category of the Gray $n$-categories.

Higher-dimensional coherence conjecture. Any small lax $n$-category is laxly $n$-equivalent to a small Gray $n$-category.

This extends the usual coherence results in dimensions two and three and is motivated by a Cayley-style argument for tetracategories and higher dimensions. The claim is presented as a conjecture, and no resolution is supplied here.