Latent Perturbation Gain in Dynamical Systems: A Corrected Framework for Inference-Constrained Controllability

This work introduces a computational framework for quantifying perturbation sensitivity in latent dynamical systems. We propose a corrected functional, Γ*(t), designed to address key limitations of alignment-based measures, including magnitude degeneracy, coordinate dependence, and null correlation bias. The framework formalizes perturbation influence as a metric-corrected, null-subtracted, and energy-regularized gain functional. We derive its theoretical properties and demonstrate construct validity using synthetic stochastic systems with known controllability regimes. Across controlled simulations, Γ*: • predicts basin transitions and response magnitude • distinguishes controllable, uncontrollable, and noise-dominated regimes • collapses under null perturbation conditions These results establish Γ* as a falsifiable estimator of perturbation sensitivity in dynamical systems. This work is theoretical and computational in nature and does not claim empirical validation in biological systems. A clear pathway is outlined for future testing using neural data (e.g., EEG, TMS-EEG). All figures, datasets, and validation outputs are included as supplementary materials to support reproducibility and further investigation.