The geometry of collective collapse: A model of regime competition, structural vulnerability, and existential potential

This paper proposes a formal model of collective system dynamics grounded in competition between organizational regimes. A collective system is represented as a set of possible dynamic regimes {R₀, R₁, R₂, ...} that compete to structure the system's observable evolution through replicator dynamics. When a single regime reaches dominance, collective behavior can be approximated as gradient descent on that regime's effective potential — a standard result from nonlinear dynamics applied here to organizational systems. The central contribution is the index Δ of collective vulnerability, which formalizes the distance between the active regime and a baseline viability regime R₀ through three independent and…