A Unified Framework of Fractal Chain Complex and the Revolution of Information Theory Mathematical Construction, Physical Breakthrough, and Cosmological Applications

his paper establishes a rigorous mathematical framework for fractal chain com?plexes, systematically elucidating the mechanisms by which fractal spacetime sur?passes the Bekenstein bound, resolves the black hole information paradox, andenables the construction of universe-scale quantum computing networks. A novelparadigm of fractal AdS/CFT duality is proposed, demonstrating the regulatoryrole of fractal dimensions DH on the degrees of freedom in boundary field the?ories and black hole thermodynamics. Through Monte Carlo lattice simulations(DH = 2.5, entanglement entropy growth SA ∝ A1.25) and LIGO-Virgo data analy?sis (signal with 2.7 confidence), the theoretical predictions are validated. This workprovides a cross-dimensional research paradigm for the fusion of quantum gravityand information theory.