The Dodecahedral Lattice of the Twelve Loops: A Finite-Graph Model of Coherence, Stuckness, and Therapeutic Flow

This paper proposes a compact, testable state-space model for multi-domain human functioning by mapping twelve recurrent life domains ("loops") onto the twelve faces of a dodecahedron. The model's geometry provides a formal structure where faces encode the domains, edges represent lawful transitions between them, and vertices (where three faces meet) mark tri-junctions of high complexity. Dynamics on this finite graph are used to capture two clinically salient regimes: localization ("stuckness") versus delocalization ("flow"). These states are physically analogized by the Mott Insulator and Superfluid phases of the Bose-Hubbard Model, providing a bridge between psychological dynamics and quantum physics. The paper formalizes a simple Markov update rule with a small reset term (representing a "reboot") and defines a suite of operational metrics, including entropy, Gini, coverage, and a composite Stuckness Index. It further demonstrates how therapeutic interventions can be modeled as "edge-weight tuning" to bias the system out of a trapped state. The model yields falsifiable predictions regarding changes in system metrics and provides a reproducible user interface layer for daily logging and analysis, enabling independent replication across cases. Keywords Dodecahedron Graph Theory State-Space Model Computational Psychology Systems Theory Coherence Trauma Model Bose-Hubbard Model Localization Phase Transition Phenomenology Therapeutic Intervention Falsifiability Sacred Geometry Psychological Dynamics