The growing global interconnectedness of markets demands a shift in the evaluation of systemic risks, moving away from linear correlation models towards hybrid architectures capable of representing non-linear instabilities and extreme tail dependencies. This article presents CERN (Chaos-EVT Copula Risk Network), a novel framework for systemic risk monitoring at the company level. Unlike standard measures such as \(\varDelta \) CoVaR or SRISK, which exhibit limitations during regime transitions or extreme market conditions, CERN employs Chaos Theory through Largest Lyapunov Exponents ( \(\lambda \) ) to capture internal structural instability and Extreme Value Theory (EVT) through asymmetric copulas to model extreme tail spillover. Additionally, a Resilience-Adjusted Risk Factor (RARF) based on Environmental, Social, and Governance (ESG) dynamics is incorporated to quantify network connectivity, providing a multi-layered defense against contagion in global environments, such as the 2022 market correction. The findings demonstrate that CERN distinguishes between defensive central nodes (e.g., Verizon) and systemic triggers (e.g., Tesla), enabling effective mitigation of regulatory Type I errors (false positives). Comparative analysis reveals that while conventional models generate excessive signals or fail to differentiate during regime transitions, CERN maintains regime-neutral stability. The proposed framework provides robust instrumentation for macroprudential regulators, comprehensively addressing both market volatility and corporate governance stress conditions.