Existing AI systems for modeling human behavior operate at the level of individuals or detect events after they occur. As a result, they systematically fail to capture the collective dynamics that determine whether a group remains stable or transitions into escalation or breakdown. We propose a different foundation: a group of interacting humans constitutes a complex dynamical system in the precise mathematical sense, exhibiting emergence, nonlinearity, feedback loops, sensitivity near critical points, and phase transitions between qualitatively distinct regimes. The state of such a system is not located within any single participant; it is distributed across mutual influence loops and observable through the micro-dynamics of the body. We introduce BEHAVE (Behavioral Engine for Human Activity Vector Estimation), a formal framework that models collective dynamics as continuous behavioral fields defined over an interaction space derived from observable physical signals. Kinematic micro-signals (position, velocity, body orientation, gestural activity) are structured into a directed interaction graph and aggregated into a basis of behavioral fields capturing distinct, non-redundant axes of collective state. The framework rests on one theorem and two structural propositions characterizing the tension field, the field basis, and the criticality index. Perception and forecasting layers are implemented using neural models, enabling data-driven learning and approximation of system dynamics. BEHAVE is formulated as a computational system for learning, representing, and forecasting collective dynamics from data. A working pipeline is demonstrated on a 7-agent negotiation snapshot. The same fields, recalibrated, apply to crowd safety, crisis-team dynamics, education, and clinical contexts.