We present the Feedback Epistemic Equilibrium Law (FEEL), a formal stability theorem for artificial reasoning systems operating under corrective oversight. Standard control theory stabilises a plant using a controller assumed reliable by construction. FEEL removes this assumption: the feedback mechanism is itself a dynamical system with its own persistence, susceptibility to epistemic contamination, and potential for instability. We model the joint system as the affine recurrence Z_(t+1) = MZ_t + c where the block matrix M (A, -C; D, E)encodes intrinsic reasoning evolution (A) , corrective intervention (C), epistemic leak from reasoning into feedback (D), and feedback persistence (E), We prove that ρ(M) < 1 is necessary and sufficient for (i) existence and uniqueness of an equilibrium, (ii) global convergence from any initial condition, (iii) exponential stability with an explicit rate, and (iv) bounded epistemic-feedback disagreement. We characterise the failure regime ρ(M) >= 1, cataloguing divergence, oscillation, feedback amplification, and runaway correction cascades. We illustrate the criterion on a toy coupled system in which increasing the epistemic-leak strength alone — holding each subsystem’s standalone spectral radius fixed — drives the joint system through the predicted ρ(M) = 1 transition, confirmed across 200 random initial conditions. The result supplies a computable certificate for safe feedback in AI systems and identifies a structural gap in existing alignment frameworks: local stability of reasoning and feedback components does not imply global stability of their coupling.