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Question
Can equations be locally well posed while their full realization requires more global structure?
What the note explains
Local spacetime geometry and the global organization of realizations answer different questions. The note investigates the latter without treating a reconstruction coordinate as an additional ordinary spacetime direction.
Example
Local solutions may agree on pairwise overlaps while their chosen identifications fail a triple-overlap compatibility test. Solving another local PDE does not by itself repair that coherence defect.
What the approach gains
The framework retains obstruction, sector, and comparison information that a single global presentation can suppress. It makes the choice of a mathematical carrier part of the reconstruction question.
Reading route
Read the author's prologue and Part I first. Use the contents and claim-status ledgers to enter later parts by question; this is a notebook to work through, not a short journal article.
Scope and limits
The source mixes definitions, conditional results, theorem schemas, conjectural mechanisms, and witness programs. Those labels remain binding; production readiness does not settle the open mechanisms.