Recovery as a Viability Kernel: A Recursive Framework for Addiction Recovery

Current frameworks for understanding addiction recovery rely on linear outcome metrics, stage models, or additive resource inventories that inadequately capture what is distinctive about the recovery process. Meanwhile, dynamical systems approaches to addiction, while capturing nonlinearity, are missing what may be recovery’s most defining feature: that the system is continuously rewritten, not only by each recovery attempt but by the passage of time itself. This paper introduces viability theory, a branch of mathematics developed to study constrained dynamical systems, as a formal framework for addiction recovery, and extends it to account for the recursive, self-modifying character of the recovery process. We propose that recovery constitutes a viability kernel (i.e., safe zone): the set of states from which a person can maintain functioning within livable constraints over time, given the choices and strategies available to them. Recovery capital serves as the underlying resource base that determines both the shape of the viable safe zone and the menu of options available to the individual. Three features distinguish this framework from existing models. First, recovery is reconceptualized as a process of recursive self-modification, not a dynamic one. The way the person’s life evolves, the limits of what they can endure, and the choices they can actually make are continuously reshaped both by prior recovery experience and by the temporal evolution of the person’s physiological, social, and structural circumstances, thereby rewriting the viability safe zone itself. Second, the viability boundary (i.e., danger zone) is functionally unknown to the person operating within it, creating a condition of high epistemic uncertainty. Third, boundary violation produces catastrophic collapse rather than gradual degradation, consistent with the phase-transition dynamics observed in relapse. This framework unifies recovery capital theory, dynamical systems approaches to return to use, and the lived phenomenology of recovery under a single formal apparatus, while making explicit that recovery operates by a different principle than the linear and dynamical systems models that precede it.