# Claim 6: Classical LQR reproduces the exponential scaling law --- ## Setup Classical LQR meta-learning proxy from `experiments/figs_appendix_classical/fig_a1_a2_lqr_simplified.py` (Appendix B style simplified model). Seed 42. CPU local. ## Result Exponential saturation fit on adaptation gap vs \(K\): - \(A_\infty = 0.0029\) - \(\beta = 0.0420\) - \(R^2 = 1.0000\) (paper target \(R^2 \approx 0.99\)) Task-variance linear scaling: - \(G_\infty\) vs \(\sigma^2\): \(R^2 = 0.9674\) - \(G_K\) vs \(\sigma^2\): \(R^2 = 0.9860\) **Verdict:** Claim 6 reproduces. The same exponential saturation + linear variance scaling appears on a classical LQR landscape, supporting that Theorem 4.8 is geometry-driven rather than quantum-specific. Artifacts under `outputs/claim6/`. Official code in this workspace: https://github.com/nleclerc/metalearning-quantum-control (local clone). --- ````html LQR summary

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