CAUSAL CONE GEOMETRY AS A UNIVERSAL PREDICTIVE FRAMEWORK FOR REGIME CHANGES IN COMPLEX DYNAMICAL SYSTEMS: APPLICATIONS TO EEG NEUROSCIENCE, FINANCIAL MARKETS, AND CLIMATE CHANGE

ABSTRACT We propose a universal geometric framework for predicting regime changes in complex dynamical systems, grounded in Einstein's causal cone formalism. The framework rests on the hypothesis that regime changes do not originate in the deterministic interior of the causal cone — where fixed rules govern behavior — but emerge on its surface, which we term the Frontier, before propagating inward. By modeling the system's state-space trajectory as a three-dimensional curve, we define the Frontier Index FI = τ/κ (torsion-to-curvature ratio) as a measure of proximity to and type of regime change: circular (gradual rule changes) or helical (irreversible paradigm shifts). We implement this framework as the FrontierDetector, a domain-agnostic computational module, and validate it across three independent domains with radically different temporal scales and generative mechanisms: (1) EEG theta-gamma coupling signals recorded via Muse 2 headset during cognitive sessions, where the FrontierDetector detects the transition to active learning states with non-reversible post-transition stabilization at a new equilibrium; (2) financial stress indicators from 2006-2009, where the TED Spread crosses the Frontier threshold 27 months before the September 2008 Lehman Brothers collapse while the VIX shows apparent calm — geometrically distinguishable from structural instability; (3) climate data from 1880-2024, where atmospheric CO₂ enters helical Frontier regime in 1964 — 60 years of uninterrupted irreversible motion — followed by sea level in 2007. The domain invariance of the framework provides evidence that causal cone geometry captures a fundamental universal property of complex dynamical systems near critical transitions.