Theoretical Study of Hierarchical Information Propagation and Quantum Folding Structures over Finite Fields

Abstract

This work introduces the Hierarchical Information Propagation Model (HIPM), a framework in which information states are defined over finite fields and propagated through a multi-layer structure. The model formulates quantum-information “folding” as a hierarchical mapping and incorporates information resistance and nonlinear feedback, yielding an emergent entropy profile analogous to thermodynamic behavior. In specific parameter regimes, HIPM reproduces characteristic quantum-information features such as compactification, gauge-mediated feedback, and quasi-conservation laws, suggesting that the second law of thermodynamics may be understood as the reconfiguration of an underlying information phase. To ensure reproducibility, all simulation parameters, algorithms, and distinctions between reproducible and conceptual figures are systematically documented in the appendix.