Cybernetics of AI Companies

# Summary This theoretical paper models AI companies as cybernetic systems using advanced mathematical frameworks (homotopy type theory, category theory, and neural tangent kernels) to analyze feedback loops between observations, learning, deployment, and governance. The authors formalize how companies observe and intervene on data, how learning dynamics change under measurement, and what specifications must be preserved during updates—without claiming these results prove that actual AI firms necessarily consolidate or conduct universal surveillance. The work proposes a mathematical research program connecting organizational cybernetics with modern categorical mathematics rather than establishing empirical claims about real-world AI company behavior.