What question did this study set out to answer?

The research aims to establish the HIHT framework as an extended approach to model multi-mode recursive hierarchical systems.

February 26, 2026Open Access

Hierarchical Interaction Hyper-Tensors

Key Points

The research aims to establish the HIHT framework as an extended approach to model multi-mode recursive hierarchical systems.
Introduced the Hierarchical Interaction Hyper-Tensor framework as a generalization of the Depth-Propagation Tensor model.
Developed recursive propagation equations and conducted convergence analysis.
Explored emergent statistical metrics and functional-analytic embeddings.
Analyzed the irreducibility structure and operator growth bounds within the framework.
Established compactness in continuous limits and examined structural spectral regimes.
Provided a rigorous foundation for nonlinear multi-mode spectral theory.
Demonstrated convergence properties of recursive equations within the HIHT framework.
Identified the importance of compactness in continuous limits for theoretical applications.
Showed structural spectral regimes that characterize the behavior of multi-mode systems.

Abstract

This work introduces the Hierarchical Interaction Hyper-Tensor (HIHT) framework,a rigorous generalization of the Depth-Propagation Tensor (DPT) model tomulti-mode recursive hierarchical systems. The paper develops recursivepropagation equations, convergence analysis, emergent statistical metrics,functional-analytic embeddings, irreducibility structure, operator growthbounds, compactness in continuous limits, and structural spectral regimes.The framework provides a foundational base for nonlinear multi-mode spectraltheory and further developments within the WTDS series.

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