Beginning in the 60s, Arveson wrote a massively influential series of papers on subspaces of C*-algebras. A prominent focus of their papers was a proposed non-commutative formulation of the Choquet boundary. Since then, several watershed moments found this boundary to be key to uncovering intrinsic structural attributes for an operator space. At its core, Arveson’s boundary theory brings forth a link between operator spaces and C*-algebras. Combining with the wealth of structural results available for C*-algebras, this has introduced new depths to operator space theory. Here, I address a conjecture from one of Arveson’s final papers on this boundary and its connections to approximation theory. This is based on joint work with Raphael Clouatre.