GEOMETRIC CYBERNETICS A Formal Stability Framework for Adaptive Systems, Swarm Intelligence, and Institutional Control Under Delay

AbstractWe introduce a formal framework for the analysis and control of adaptive dynamical systemsoperating under delay, uncertainty, and distributed interaction. The approach is based on therepresentation of system behavior as motion within a stability field defined over an extendedstate manifold.Rather than characterizing intelligence through symbolic representation or classification, wedefine it operationally as the capacity of a system to maintain navigability under increasinginstability, temporal lag, and informational load.The framework provides: (i) a state-space formulation incorporating delay and informationalvariables, (ii) an instability functional governing system behavior, (iii) a control law definedby descent along the instability gradient, and (iv) a distributed formulation applicable tomulti-agent systems.Potential applications include embodied navigation, swarm coordination, human–machineinteraction, systemic risk analysis, and adaptive governance under accelerated conditions.