Structural Turbulence in Finite Kernel Dynamics: Spectral and Lyapunov Stability Analysis (Companion to "A Deterministic Finite Geometric State Space…")

This manuscript provides a formal theoretical extension to the regime-based framework introduced in: "A Deterministic Finite Geometric State Space for Regime Decomposition Across Heterogeneous Black-Box Systems." The original article established the existence of a deterministic finite regime space constructed via geometric projection. The present work analyzes the dynamical properties of regime evolution within that space. Structural turbulence is formally identified with dominance convergence, entropy collapse, and spectral degeneracy of the empirical transition matrix. All results are permutation-invariant and do not disclose internal kernel geometry. This work serves as a theoretical companion paper and does not introduce additional structural details beyond those required for spectral and stability analysis.