Emergence of Three-Dimensional Space from Combinatorial Phase Structures in the Hierarchical Information Propagation Model: A Combinatorial Derivation within the Hierarchical Information Propagation Model

Sasaki, Yuji

doi:10.51094/jxiv.2997

##article.authors##

Sasaki, Yuji Independent Researcher

DOI:

https://doi.org/10.51094/jxiv.2997

キーワード:

Hierarchical Information Propagation、 Spatial Dimensionality、 Phase Modes、 Quotient Mapping、 Emergent Space

抄録

We present a minimal and combinatorial derivation of three-dimensional spatial structure within the framework of the Hierarchical Information Propagation Model (HIPM).
Starting from four fundamental variables, we show that ten unordered variable pairings naturally arise at a purely mathematical level.
Among these, four self-pairings correspond to invariant quantities and do not generate independent phase structure.
The remaining six mixed pairings define nontrivial phase topologies.
When these phase modes are projected through the folding layer of HIPM into the material observation layer, equivalence relations reduce them to three independent spatial axes.
As a result, three-dimensional space emerges without assuming spacetime dimensionality a priori.
This derivation relies only on combinatorial structure and hierarchical projection, and is independent of specific dynamical field equations.

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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Emergence of Three-Dimensional Space from Combinatorial Phase Structures in the Hierarchical Information Propagation Model

A Combinatorial Derivation within the Hierarchical Information Propagation Model