Waveform Dependent Breakdown of the Frozen State Approximation in an Optomechanically Parameterized Linear Gaussian System

This computational study examines the validity of the instantaneous frozen-state approximation in an optomechanically parameterized linear Gaussian system subjected to eight heterogeneous drive protocols and three nominal cooperativity targets. The analysis tests whether a scalar rate-based diagnostic, (\chi), can monotonically order the error between frozen covariance solutions and direct time-dependent covariance evolution. A post-run audit identified and corrected a temporal-window mismatch affecting a pulsed protocol, evaluated Gaussian quantum admissibility across all 24 drive/target cases, performed timestep-convergence checks on boundary cases, and quantified differences between nominal and realized coupling across waveform classes. Six drive/target cases were excluded from the final physical statistics because their covariance trajectories left the Gaussian quantum-admissible domain. After temporal alignment and physicality filtering, 11 pairwise (\chi)-error ordering inversions remained, distributed 5, 5, and 1 across nominal cooperativity targets (C_{\mathrm{target}}=50, 200,) and (1000). The results show that (\chi) retains substantial regime and ordering information, particularly at the highest target, but is not a sufficient monotonic predictor of frozen-state error across heterogeneous temporal protocols. The study also documents the finite quantum-admissible operating domain of the implemented generator and provides a fully archived computational provenance chain, including the locked model, post-run audit, figure source data, numerical outputs, execution records, and reproducibility materials.