When the two required invariant structures are incompatible under the source’s premises, no joint map can satisfy both restrictions. The impossibility concerns that shared realization. It does not assert that every pair of domains is incompatible or that either component ceases to be individually referenceable.

The distinction matters for arguments that assemble a large physical description from locally acceptable pieces. Local consistency is necessary but may not guarantee global compatibility. The proposed obstruction identifies the additional condition that such an assembly must check.

This is a source-attributed mathematical theorem within the adopted realization framework. It is not an observation of disconnected universes or an unrestricted prohibition on joining physical systems. The July source-era date identifies the documented formulation, with source review supplying the explicit restriction to incompatible invariant structures.