Re-Phase Vol.1.6: Compatibility Propagation

This volume formulates compatibility propagation in the Re-Phase framework.

Vol.1.4 established the static admissible set formed by intersecting compatible sets induced by observations or constraints. Vol.1.5 introduced the local-to-global compatibility problem. Vol.1.6 studies the elementary refinement move that connects these structures.

A refined admissible set is obtained by intersecting the previous admissible set A_S with the newly added compatible set K_i(o_i).

The volume examines how a refinement move propagates through admissible structure, feature images, recoverability thresholds, and obstruction boundaries. It distinguishes feature-effective refinement, feature-preserving refinement, useful refinement, recoverability threshold crossing, existence collapse, and obstruction boundary crossing.

The term propagation in this volume does not refer to probabilistic belief propagation, Bayesian updating, or algorithmic message passing. It refers to the structural propagation of set-theoretic refinement through compatible sets, feature images, and local contexts.

This volume remains at the set-and-relation level of Re-Phase.