Critical-Block Stability Sensitivity Ranking

Apply this after the black-box response estimator has produced gamma. Define three group levels: complete blocks, inter-block residual or feedback edges, and parameter tensors. At the coarse level, perturb each block output scale by plus or minus epsilon and recompute only the frequency-response assembly, not a full training run. Retain the top K blocks by sensitivity. At the second level perturb incoming residual edges or state couplings in those blocks, and at the third level perturb only the most sensitive tensors. Use the ranking to select one intervention: multiply the critical block output by r_j, impose a local spectral-norm cap, or assign that group a reduced learning rate. The paper contributes the multilevel sensitivity idea and measured component responses; the scale perturbation and neural interventions are the adaptation. The first cheap experiment is a four-block residual SSM on copy-memory, with one deliberately high-gain block. Compare exhaustive per-block perturbation, uniform regularization, and multilevel ranking. The prediction is that the top-ranked block should account for at least 70 percent of the margin reduction found by exhaustive search, while using substantially fewer response evaluations. Suppressing it should move gamma from above 1 to below 1 and remove long-horizon divergence without materially changing short-horizon loss.