The Multi-Scale Hierarchical Entangled Universe from Zero-Quantum World to Classical Ones

This work introduces a discrete, non-continuous mathematical paradigm formalizing the universe as a countably discrete digital matrix spanning the absolute interval [0, ∞). We reject the classical assumption that the Planck spacetime scale forms the fundamental floor of reality. Instead, we propose that the Planck fabric is an emergent property woven by a nested, self-similar hierarchy of infinitely small, subatomic, string-like informational units vibrating from absolute zero upward. By mathematically modeling multi-scale hierarchical fractional entanglement, we demonstrate how these sub-Planckian string-like particles undergo localized sub-sampling, state collapsing, and integration transformations to stitch themselves into macroscopic classical realities. Furthermore, we redefine standard Von Neumann and Shannon entropy metrics into a singular, scale-dependent information delta. This redefinition proves that thermodynamic entropy, vacuum fluctuations, and background noise are not fundamental physical constants, but rather mathematical artifacts of an incomplete observer constrained by specific spatial, temporal, and spectral sensing windows.