Additomultiplicative Cascades Govern Multifractal Scaling Reliability Across Cardiac, Financial, and Climate Systems

The generative mechanisms underlying multifractal scaling in complex systems remain a fundamental unsolved problem, limiting our ability to distinguish healthy from pathological dynamics, predict system failures, or understand how scale-invariant organization emerges across vastly different physical domains. We resolve this challenge by introducing threshold sensitivity analysis-an extension of Chhabra-Jensen's direct method-as a framework that classifies cascade types by examining how scaling reliability varies across moment orders <i>q</i>. Different <i>q</i> values systematically probe weak fluctuations (negative <i>q</i>) versus strong fluctuations (positive <i>q</i>), and the coefficient of determination (r2) of partition function regressions quantifies scaling reliability at each <i>q</i>. Analyzing r2(q) patterns in 280 cardiac recordings (healthy controls through fatal heart failure), 200 financial time series (global equity markets and currencies, 2000-2025), and 80 climate stations (tropical to continental zones, 2000-2025), we discover a universal diagnostic signature: symmetric expansion of valid scaling behavior under relaxed r2 thresholds, spanning both weak and strong fluctuations. This threshold sensitivity fingerprint-predicted by synthetic cascade simulations but never before validated empirically-uniquely identifies additomultiplicative cascades, hybrid processes that randomly alternate between additive stabilization and multiplicative amplification. Critically, this symmetric signature persists universally across domains: cardiac dynamics maintain consistent patterns across health and disease states, financial markets show varying robustness across asset classes (currencies more variable than US equities) while preserving a hybrid structure, and climate systems exhibit geographical variations (subtropical/continental stronger than tropical) without altering fundamental cascade type. These findings suggest that additomultiplicative organization is a unifying feature of complex adaptive systems, offering a resolution to decades of debate between additive and multiplicative models. The r2(q) profiling provides a mechanistic diagnostic capable of detecting early dysfunction, assessing system resilience, and revealing how environmental constraints shape-but do not determine-the fundamental principles governing multifractal complexity.