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This skill provides a comprehensive framework for scaling analysis based on the triad of Kolmogorov, Onsager, and Hurst theories. It allows developers and researchers to quantify the fractal nature of complex systems, ranging from fluid dynamics and network traffic to financial market regimes. By implementing robust algorithms like Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA), the skill helps determine if a system is persistent, anti-persistent, or purely stochastic, while providing the mathematical bridge between spectral exponents, Hölder regularity, and fractal dimensions.
