Simulation study demonstrates clock-free anomaly detection in a multi-agent system, suggesting drift-based internal time can identify regime shifts without external clocks.
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.
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ARIMOTO et al. (2026) studied this question.
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