Coefficient Dynamics and Stable Convergence Ratios in Fourth-Order Linear Recurrence Relations

This research paper investigates the coefficient dynamics and stable convergence limits within a specific family of fourth-order linear recurrence relations under a unitary initialization matrix. It demonstrates the mathematical behavior and trajectory shifts when the structural multiplier varies from 1 to 10. It also outlines the inverse prediction model for fixed ratio outputs and discusses potential software applications in digital filter stability and cryptography.