Spectral and Phase Structure of Hierarchical Interaction Hyper-Tensors

This paper develops a nonlinear multi-mode spectral and stability theory for hierarchical interaction systems. Building on the Hierarchical Interaction Hyper-Tensor (HIHT) framework, the work establishes a nonlinear Perron–Frobenius structure, multi-parameter phase regimes, cross-mode stability boundaries, Jacobian stability analysis, Lyapunov constructions, and spectral growth surfaces. The theory provides a rigorous operator-theoretic and dynamical systems foundation for multi-mode hierarchical propagation.