Bidirectional Graph Dynamics: Whole-Network Update Laws, Interfaces, and Invariants

A whole-graph theory for bidirectional updates, interfaces, and constraint control. This preprint formalizes a two-stage dynamical rule on graphs: a local proposal step followed by a global reconciliation step that enforces network-level consistency or constraint pressure. It introduces a cut-based interface formalism for whole–part communication and provides general monotonicity and bounded-drift results under explicit assumptions. Interference-like signatures arising from a specific instantiation are treated in a companion work and are not repeated here.