Re-Phase Vol.1.5: Local-to-Global Compatibility

This volume formulates the local-to-global compatibility problem of Re-Phase. Vol.1.4 studied the static admissible set formed by intersecting compatible sets induced by observations or constraints. Vol.1.5 studies local admissible sets associated with selected local contexts and asks whether local compatibility implies global compatibility. The central point is that locally compatible constraints need not assemble into a single globally admissible configuration. In other words, local consistency does not generally guarantee global realizability. The volume introduces local contexts, local admissible sets, global compatibility, local-to-global compatibility obstruction, maximal compatible contexts, and structural information that can remain even when global compatibility fails. Examples include dimensional tolerance versus geometric realizability, a minimal discrete parity constraint, and phase closure failure.