Hierarchical Information Propagation Model (HIPM) Part V

Structural Necessity of Three Layers and Four Variables

抄録

The Hierarchical Information Propagation Model (HIPM) has been proposed as a framework for describing hierarchical information flow across physical scales.
Within this framework, physical structures are understood as emerging from successive propagation, folding, and coarse-graining of information.
Dynamics, thermodynamics, time-scale separation, and phase behavior are treated as manifestations of this hierarchical process.
While previous studies focused primarily on expressive capability and conceptual unification, the present work addresses the structural necessity of the model itself.
We examine why HIPM adopts exactly three hierarchical layers and four core variables, and whether alternative configurations remain internally consistent.
By analyzing reduced and extended model variants, we show that fewer components fail to achieve hierarchical closure, while additional components introduce redundancy and instability.
We further identify a binary phase constraint emerging within the folding hierarchy, which acts as a structural selector for phase propagation toward coarse observables.
Numerical experiments are used solely as consistency checks, without phenomenological fitting.
These results suggest that the three-layer, four-variable architecture of HIPM constitutes a minimal and self-consistent structure for hierarchical information propagation.