Metric Mismatch and Rhythmic Integrity under Phase-Weighted Noise

This record reports an observational study of terminal behavior in a deterministic system subjected to heterogeneous perturbation mechanisms. Two distinct modes of intervention are examined: structural reconfiguration of the evolving trajectory and phase-weighted noise applied without modification of the system’s operating bounds. Despite the substantial differences between these perturbation mechanisms, the system consistently preserves coherent terminal behavior or transitions toward a newly formed stable trajectory. Classical similarity and performance metrics are observed to fail in characterizing this behavior, revealing a mismatch between metric-based evaluation and the system’s preserved rhythmic structure. The scope of the work is strictly observational. No theoretical interpretation or disclosure of system architecture is attempted. The results are presented to document the persistence of rhythmic integrity under perturbations of non-intuitive effect and to motivate further investigation into invariant properties governing deterministic system dynamics.