The Geometry of Recovery: Accessibility Expansion, Insight, and Adaptive Change

Psychedelic compounds like psilocybin increase neural entropy and flexibility, but why this leads to adaptive recovery rather than disorganization is unclear. This paper proposes that the missing factor is accessibility—which futures remain reachable and recoverable within a landscape of possibilities. Entropy is a perturbative mechanism that temporarily reorganizes accessibility structure, expanding the set of reachable trajectories. Insight is the recognition of newly reachable futures, and psychological flexibility reflects expanded access to multiple viable pathways. Recovery occurs when systems regain access to constrained or collapsed pathways. Adaptive change requires perturbation to remain bounded by viability and recoverability constraints, offering a unified account of psychedelic-assisted change as restored reachability.

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Abstract

Psychedelic research has repeatedly linked compounds such as psilocybin to increased neural entropy, reduced network modularity, enhanced psychological flexibility, insight, and sustained improvements in well-being. Yet the relationship among these phenomena remains poorly specified. Entropy, plasticity, relaxed priors, and network reorganization describe important features of psychedelic states, but they do not fully explain why perturbation sometimes produces adaptive recovery rather than disorganization. This paper proposes that the missing explanatory variable is accessibility. Building on Persistence Geometry, this paper argues that adaptive systems are governed not only by what futures are possible, but by which futures remain reachable, viable, and recoverable from a given position within a landscape of possibilities. From this perspective, entropy is not the therapeutic outcome. It is a perturbative mechanism capable of temporarily reorganizing accessibility structure. Psychedelic perturbation may expand the set of reachable trajectories, allowing systems to explore futures that were previously inaccessible under ordinary constraints. Within this framework, insight is interpreted not as the acquisition of new information, but as the recognition of newly reachable trajectories. Psychological flexibility reflects expanded access to multiple viable futures. Recovery occurs when systems regain access to viable pathways that had become constrained, collapsed, or unreachable. This interpretation reframes psychedelic change as a process of accessibility expansion followed by exploration, selection, and stabilization. The framework also clarifies why increased entropy alone is insufficient. Adaptive change requires perturbation to remain bounded by viability and recoverability constraints; otherwise, exploration becomes destabilization rather than recovery. By linking entropy, flexibility, insight, and recovery through the geometry of reachable futures, this paper offers a unified account of psychedelic-assisted adaptive change and proposes a broader theory of recovery as restored reachability within persistence landscapes.