The Dynamic Existence Threshold: Measuring Consciousness in Complex Systems

Abstract

Abstract Complex systems share a common failure mode: the breakdown of balance between integration and differentiation. This paper introduces the Dynamic Existence Threshold (DET), characterizing system state via integration (\((I)\)) and differentiation (\((D)\)) in a phase space where healthy function occupies a central balance zone. The DET predicts that critical events correspond to exits from this zone, producing measurable early warning signals. These predictions are tested across financial markets (6,785 trading days, 26 cascade events), space weather (9,802 days, 51 storm days), and human EEG (50 subjects, 136,394 epochs) using a five-layer architecture with zero-parameter tuning between domains. Six tests confirm the framework: (1) events cluster at \((I)\)--\((D)\) extremes; (2) events exit the balance zone faster than normal state changes (\((p = 0.0001)\)); (3) rising variance of \((|I - D|)\) provides early warning 5--30 days before events (2.0\((\times)\) elevation, \((p < 0.001)\)); (4) exit velocity discriminates events from normal (AUC 0.692--0.843); (5) in EEG, simple summation anti-predicts brain state (AUC 0.416) while \((R \times S)\) achieves AUC 0.909, demonstrating that the framework captures coordination rather than magnitude; and (6) total organizational information \((\Phi = I + D)\) is approximately conserved during critical transitions (within 1--14%), with components undergoing inverse exchange---connecting the static existence threshold to the dynamic framework.