Non-Hermitian Foundations for Autopoietic Cognitive Architecture: Extending the Internal State Dynamics Model

Classicalformulationsofcognitive-affectivedynamics, includingLyapunov-based stability frameworks, guarantee convergence to equilibrium: a property appropri- ate for many engineering applications but insufficient for systems that must learn, evolve, and maintain identity through change. This paper develops quantum foun- dations for a cognitive-affective architecture comprising three regimes: dynamic evolution(MDEI),stabilization(MCEE),andsymbolicmeasurement(MESN).This paper uniquely introduces the non-Hermitian Hamiltonianˆ Hef f= ˆ H−iˆ Γ, where the dissipative termˆ Γ models the system’s openness to its environment. The central contribution is the derivation of a self-referential floor: for any architecture containing a self-observing module (MESN), the effective dissipation rate is bounded below by an irreducible residue, Γef f ≥ε∞>0. This floor emerges fromtheback-actioninherenttoself-measurement—thesystemcannotobserveitself without disturbing itself. Consequently, all bound states have finite lifetime; the system cannot collapse into permanent stasis. Stability, for self-referential systems, is necessarily a pattern of bounded oscillation rather than convergence to rest. This result provides the formal foundation for autopoietic AI and motivates a dual-layer architecture: classical Lyapunov dynamics at the surface for compu- tational efficiency, non-Hermitian quantum dynamics at the core for autopoietic capacity. The operationalization of layer-switching mechanisms and empirical vali- dation constitute the ongoing research agenda.