Rigorous Mathematical Derivation of Kinetic Tipping Points in Non-Hermitian Exceptional Point (EP2) Dynamics via NLS Smoothing and Third-Order Jerk Analysis

Rigorous Mathematical Derivation of Kinetic Tipping Points in Non-Hermitian Exceptional Point (EP2) Dynamics via NLS Smoothing and Third-Order Jerk Analysis A Predictive Kinetics Framework for Suppressing Ghost-State Formation and Preserving Microscopic Unitarity Dr. Theodor HeutschiIndependent Researcher, Lucerne, Switzerland Date: October 2026 Abstract Exceptional points of second order (EP2) in non-Hermitian quantum and optical systems represent singular phase transitions where eigenvalues and eigenvectors coalesce. Approaching an EP2 causes a divergence of the Petermann noise enhancement factor K(t), leading to non-unitary norm collapse and the emergence of negative-norm ghost states. In this paper, we establish a mathematically rigorous higher-order kinetics framework to identify the exact operative Tipping Point of EP2 dynamics prior to reaching the singularity. By applying Non-Linear Least Squares (NLS) smoothing to eliminate stochastic noise, followed by exact analytical differentiation up to the third derivative (Jerk, J(t) = d³K/dt³) and fourth derivative (Snap/Jounce condition d⁴K/dt⁴ = 0), we prove that the kinetic phase transition occurs significantly earlier than the EP2 peak. In an empirical time-series dataset of dynamic EP2 encircling, our framework pinpoints the Jerk Tipping Point at t = 3.033 ms (Petermann factor K = 5.973), providing an operational lead time of 1.967 ms before the EP2 singularity at t = 5.000 ms. We demonstrate how this early-warning boundary enables deterministic sub-critical feedback control, suppressing ghost-state formation and guaranteeing microscopic unitarity.