Local Asymptotic Stability in the RHEA Adversarial Cognitive Harness

Abstract This paper presents an empirical dynamical analysis of the RHEA cognitive architecture using the RHEA Adversarial Cognitive Harness (v3). The harness evaluates reasoning systems under adversarial task conditions including deception traps, ambiguity cascades, corrupted information sequences, and multi-stage adversarial pressure. By instrumenting internal entropy and trust variables during task execution, the harness reconstructs the phase-space dynamics of the system. Using the collected trajectory data, we estimate a local equilibrium point and reconstruct the Jacobian matrix of the cognitive flow field near that equilibrium. Eigenvalue analysis of the reconstructed Jacobian reveals two negative real eigenvalues, demonstrating that the equilibrium corresponds to a locally asymptotically stable attractor. This result provides empirical evidence that the RHEA cognitive loop behaves as a regulated nonlinear dynamical system rather than a purely static inference mechanism.