Mathematic theory of agent control

<p dir="ltr">This paper presents a new formal theory of MetaMind — a generative meta-intelligence capable of creating self-reproducing chains of controlling agents. The theory establishes a rigorous mathematical foundation for the emergence, stability, and recursive evolution of agent populations that can, in principle, control arbitrary dynamical systems. Within the proposed framework, the generation operator ( \mathcal{G} ) acts on the probability measures over parameter spaces of agents and satisfies the average contractivity condition in the Wasserstein metric. Under these assumptions, the existence and uniqueness of an invariant distribution of agent parameters are proven, ensuring convergence of recursive generations toward stable meta-structures. Further results demonstrate that the MetaMind mechanism guarantees, with positive probability, the infinite emergence of "thinking" agents possessing adaptive and universal control capabilities. The paper also formalizes the conditions under which local learning rules of Robbins–Monro type converge and shows the theoretical advantage of meta-selection compared with random sampling. The framework provides a unified mathematical basis for constructing hierarchical systems of agents able to model, optimize, and control complex environments, forming a universal architecture for meta-intelligent self-organization. </p><p dir="ltr"><br></p>