Part II: Formal Structure of the Hierarchical Information Propagation Model

Mathematical Foundations of Hierarchical Folding, Nonlinear Gauge Symmetry, and Effective Geometric Deformation in Finite-Field Information Dynamics .

Abstract

This work develops the mathematical core of the Hierarchical Information Propagation Model (HIPM), independent of physical interpretation.
Information states are defined on discrete hierarchical spaces over a finite field, and inter-level propagation is formalized by mixed linear–nonlinear operators.
A nonlinear gauge symmetry associated with redundant internal representations is introduced.
Folding operations and their fixed points are defined algebraically.
We further derive the hierarchical Jacobian associated with inter-level maps and introduce an abstract effective metric structure induced by local deformation of these Jacobians.
Time and gravitational modulation are formulated as meta-hierarchical deformations without assigning any physical interpretation.
The formalism presented here provides the minimal structural backbone required for subsequent applications in higher parts of the framework.