THE DYNAMICAL FRAMEWORK OF HORIZON INFORMATION CORRELATION

This paper introduces a comprehensive mathematical and theoretical framework, designated as the Moath Xi-System, to provide a definitive resolution to the long-standing black hole information paradox. Utilizing the holographic principle, the system models the dynamic encoding, spatial distribution, and fast scrambling of quantum information directly across the degrees of freedom of the event horizon membrane. To prevent the mathematical and thermodynamic divergences inherent in classical and semi-classical models during the final stages of black hole evaporation, a non-zero quantum regulator is established at the Planck mass scale. We demonstrate through analytical derivation, rigorous methodology, and integrated numerical simulation that the horizon information correlation function converges asymptotically to a stable, finite quantum eigenvalue of zero. This framework successfully preserves quantum unitarity and determinism without inducing infinite back-reaction or division-by-zero singularities, offering a novel pathway toward reconciling general relativity with quantum mechanics.