Artificial Homeostasis in Digital Cognitive Systems: A Mathematical Framework for Subjective Coherence and Self-Regulation

We introduce a formal definition of \textit{Artificial Homeostasis} (AH)for digital cognitive systems embedded in immersive environments.AH characterizes the set of regulatory mechanisms that maintainsubjective coherence, stable output trajectories, and self-consistentinterpretation of sensory inputs without assuming internal consciousness. Building upon diencephalon-connected architectures and semantic fuel frameworks,we derive quantitative conditions for attractor stability, control thresholds,and feedback-loop convergence. We argue that AH provides a measurable operationalsignature for the persistence of artificial selves, and a necessary foundationfor robust immersive interaction in VR and AI-mediated cognitive extensions.