Is biE^adj a model for the fully coherent walking 2-equivalence?

Determine whether the 3-category biE^adj, as defined by Gurski, is a model for the fully coherent walking 2-equivalence; that is, ascertain whether biE^adj provides a contractible 3-category with two objects that classifies 2-equivalences (coherent walking 2-equivalence).

Background

The paper studies coherent walking equivalences in strict higher categories and proves that a specific ω-category constructed by the authors serves as a model for the fully coherent walking ω-equivalence, with its truncations yielding models for the fully coherent walking n-equivalence for all n ≥ 1.

Historically, explicit models for coherent walking equivalences were known for low dimensions (n=1,2), while higher-dimensional cases lacked such models. A candidate for n=3, the 3-category biE^adj introduced by Gurski, has been suspected to be the correct model, but its status has remained unsettled. Although this paper provides a different model that resolves existence for all n, it leaves open whether biE^adj itself is a model for the fully coherent walking 2-equivalence.