The pseudoadjunction conjecture for bicategorical graphs and bicategories

A bicategorical graph consists of objects, arrows between objects, and 2-arrows between paths of arrows; regard bicategorical graphs as a locally discrete 2-category. A bicategory has 0-cells, hom-categories, weakly associative and unital composition, and specified associativity and unit isomorphisms. Pseudofunctors are weak structure-preserving maps between bicategories, and icons are the corresponding oplax transformations whose object components are identities.

Pseudoadjunction conjecture. There is a pseudoadjunction between the locally discrete 2-category of bicategorical graphs and the 2-category of bicategories, pseudofunctors and icons.

This is the weak, higher-categorical analogue of the strictification adjunction for 2-categories. The source refers to work of Campbell, Garner and Gurski on the higher structure, but does not state whether this pseudoadjunction has been established.