D-Operator × StructuralTime: A Vectorized Synchronization Dynamics Coupled with Drift-Based Internal Time

Modern distributed systems, robotic control loops, and edge AI pipelines depend on external clock time to detect when something has changed. This paper introduces a combination of two components: (1) the D-Operator, a vectorized Kuramoto-type synchronization dynamics, and (2) StructuralTime, a drift-based internal time constructed from robust per-dimension change accumulation. We demonstrate, in a small five-agent toy system, that a regime change in the underlying dynamics (a sudden shift in the external target) manifests as a sharp jump in StructuralTime, allowing internal-time anomaly detection without external clocks. We also report a failure mode discovered while connecting the two components: because the D-Operator is designed to converge to an exact equilibrium, StructuralTime's per-dimension scale estimate collapses toward the floating-point noise floor, causing a genuine regime change to be amplified by six orders of magnitude. We introduce a minimum-scale floor as a fix and verify it numerically. This proof-of-concept is intentionally small in scope; scaling to real distributed or robotic systems is future work.