Improving on Popov: Machine-Certified Absolute Stability for High-Dimensional Lur'e Systems via Lean 4 & Comparator

High-dimensional Lur'e system stability analysis relies heavily on numerical matrix solvers, leaving safety-critical applications like aerospace EDL vulnerable to frequency-gridding gaps and floating-point drift. To eliminate these approximations, this paper introduces a five-module Popov multiplier framework mechanized via Lean 4 and Comparator. By systematically bridging sector invariants, frequency-domain conditions, and quadratic storage functions through the KYP lemma, we establish an exact, solver-free trajectory stability theorem that guarantees absolute asymptotic convergence across high-dimensional parameter spaces.