PhaseSync on a D-Operator Core: Retrofitting a Structure-Based Synchronization Protocol

PhaseSync is a BandOS component intended to synchronize structural state between entities without an explicit communication channel: state converges toward a target by following a drift-minimizing update, using only locally observable structure. Prior implementations used an ad hoc scalar drift function, hand-assembled from domain terms, and supported only one-to-one convergence toward a fixed target -- no entity could influence another. We replace this with the D-Operator (a vectorized, Kuramoto-type synchronization dynamics, previously implemented and verified independently), used unmodified as PhaseSync's core, with only a thin adapter mapping the domain's state (curvature, gravity) to and from the operator's vector representation. We show this adapter reproduces the prior one-to-one behavior as a special case (kappa=0) and additionally provides genuine multi-entity consensus (kappa>0), which the prior implementation never had. A later addition exposes the D-Operator's existing weighted-coupling support directly, giving PhaseSync partial synchronization over a sparse graph. Building this required correcting two real errors discovered during verification, both retained here rather than smoothed over.