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 .

Sasaki, Yuji

doi:10.51094/jxiv.2059

##article.authors##

Sasaki, Yuji Independent Researcher

DOI:

https://doi.org/10.51094/jxiv.2059

キーワード:

hierarchical information model、 finite field、 nonlinear gauge symmetry、 folding operator、 hierarchical Jacobian、 effective metric、 meta-hierarchical modulation

抄録

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.

利益相反に関する開示

The author declares no conflicts of interest associated with this study.

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引用文献

C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Jour-nal, 27, 379 – 423, 623 – 656, 1948.

R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM Journal of Research and Development, 5, 183 – 191, 1961.

H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, 2002.

S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta Mathematicae, 3, 133 – 181, 1922.

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 .