Local-to-global gluing burden

The local Hartogs bulks must assemble into one globally coherent three-dimensional carrier. Without this gluing, E_1 would contain many locally determined interiors but no physical space. The Book III problem is therefore a gluing problem: the local interiors must agree on overlaps, preserve their boundary/spectral data, and support a single carrier readout. This is the point where the famous external problem surfaces enter, not as prestige claims, but as names for the structural guarantees required by gluing.