Why it is a question
A15 §6: “Can a family of locally feasible interpretations fail to admit a globally feasible integration, even though a mathematically compatible global interpretation exists?” It distinguished “No joint representation exists” from “No feasible algorithm constructs or evaluates one”, and said “The second cannot establish the first.” CLAIM-197 is the record’s formal gluing result. Nothing in it is about cost.
The question is real if some class of local families admits global sections that are hard to find. Constraint-satisfaction problems with locally consistent instances suggest that it is. Whether anything communicative falls in such a class is the open part.
An answer is a model of context-indexed interpretations in which a global section exists and finding it is provably hard, or an argument that, for the covers the pragmatic-transport line uses, local consistency makes gluing cheap.