Basis of Collapse A Geometric and Viability-Constrained Model of Systemic Phase Transitions in Complex Adaptive Systems

Abstract We present a geometric formulation of systemic collapse within a viability-constrained representation framework, integrating principles from representation-dependent detection (RDCH) and regime-dependent generative dynamics (PDAR). A complex adaptive system is modeled as evolving within a constrained state space defined by internal dynamics, representational structure, and viability filtering. Collapse is defined not as failure, but as a structural phase transition in which a system exits a metastable attractor due to deformation or loss of its constraint geometry. This transition induces multi-scale desynchronization, effective dimensional reduction, and reorganization toward lower-complexity regimes governed by local rather than global coordination. The framework establishes formally testable conditions for instability, identifies invariant structural signatures of collapse, and provides a unified description applicable across domains without reliance on domain-specific assumptions. Collapse is thereby reinterpreted as an intrinsic transformation of viability-constrained systems under constraint degradation.