Version 3.1.1 provides formal clarifications to the nonlinear extension of the Adaptive Lag framework introduced in v3.1. The model replaces the previous linear tracking formulation with a state-dependent permeability function Phi(e) = Phi0 * exp(−gamma * e^2), yielding a bounded positive adaptive gain k(e) = Phi(e) / (R + epsilon), with R > 0 and epsilon > 0 ensuring strictly positive and finite gain under all admissible states. Under constant environmental drift and smooth permeability decay, the reduced one-dimensional tracking dynamics admit a saddle-node bifurcation. After nondimensionalization (gamma = 1), the analytically derived critical threshold is nu_c = (1 / sqrt(2)) * exp(−1/2) ≈ 0.4289. Deterministic phase diagrams and stochastic simulations (Ornstein–Uhlenbeck forcing) confirm the analytical boundary between stable tracking and divergence. A revised hazard formulation introduces state-dependent noise amplification, distinguishing constructive from destabilizing variance regimes. This framework does not claim universal collapse prediction. It formalizes a dynamical vulnerability mechanism under bounded feedback capacity in nonlinear control systems and complex adaptive systems. Community feedback, replication attempts, and critical evaluation are welcome. Nonlinear Dynamics Saddle-Node Bifurcation Complex Adaptive Systems Feedback Permeability State-Dependent Gain Adaptive Lag Control Theory Stochastic Forcing Ornstein–Uhlenbeck Process Systemic Fragility Transition Thresholds Feedback Saturation Dynamical Stability Hazard Modeling Constrained Control Systems