Is there a coherence theorem/conjecture for tetracategories (weak $4$-categories)? 


Todd Trimble mentions in his [notes](http://math.ucr.edu/home/baez/trimble/tetracategories.html) on tetracategories that his pasting definitions are essentially unambiguous due to the tricategorical coherence theorem of Gordon-Power-Street, and more than a decade has passed since then. 


Does the current state of the art have a coherence conjecture/theorem for tetracategories, or even all weak $n$-categories?



Coherence theorem for tetracategories, weak $n$-categories
Many things can be called a "coherence theorem", but I presume you're looking for one that's analogous to the GPS result that every fully-weak 3-category is equivalent to a [semistrict](https://ncatlab.org/nlab/show/semi-strict+infinity-category) one in which associativity and units are strict but not interchange. I don't think any theorem of this sort has been proven for $n\gt 3$, but recently there is at least a [proposal](https://ncatlab.org/nlab/show/associative%20n-category) for a class of semistrict $n$-categories that could in theory be the target of such a coherence theorem.


