Robust Derivative-Order Spectral Geometry: Quantitative Near-Rigidity and Stable Finite-Window Packet Recovery

This paper develops a robust derivative-order spectral geometry, providing quantitative near-rigidity theorems and stable recovery results for derivative-order ladders. We show that small curvature defect implies proximity to rigid models and derive quantitative estimates for convergence to the canonical packet polynomial. Our analysis establishes stable finite-window packet recovery and a stable nullspace recovery theorem for annihilator polynomials, demonstrating that spectral ladders remain well conditioned under perturbations.