lin-0120
9.3 Compatibility is not effectivity
Local objects may agree on overlaps without arising from a global object in the declared model class.
For local models \(D_i\) and restrictions to overlaps \(J_{ij}\), compatibility means that the restricted models agree up to the declared coherence:
A compatible family is effective when there exists an admissible global model \(D\) whose restrictions recover the \(D_i\), with the required uniqueness or equivalence.
This separation is central to SID, RADAR, sheaf-structured argument systems, and distributed learning. A penalty on pairwise overlaps can reduce local disagreement while the compatible family remains outside the image of the global model class.
Localization diagnoses where a failure is witnessed. It does not guarantee that a local repair extends globally, that compatible repairs glue, or that the resulting global object lies in the admitted model class.