The Geometric Pre-Shatter: Predicting Cardiac Arrhythmia via Constrained Packing Dynamics (CPD)

Current cardiovascular diagnostics rely predominantly on one-dimensional (1D)temporal analysis of ECG signals. However, complex arrhythmias—often characterizedas "stochastic" or "chaotic"—are frequently artifacts of 1D observation sieves.This paper introduces Constrained Packing Dynamics (CPD), a topologicalframework that treats cardiac rhythms as a multidimensional kinematic flow. Byunfolding 1D RR-intervals into a 3D state-space manifold, we define the TopologicalYield (YT ) index. Our research using clinical data (MIT-BIH Record 106)demonstrates that a catastrophic collapse in YT precedes physical arrhythmia, identifyinga "Pre-Shatter" state where the heart’s geometric flexibility is exhaustedbefore clinical symptoms manifest. This provides a deterministic window for earlyintervention.