Hierarchical Interaction Hyper-Tensors

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.