Manufacturing has passed through four widely recognized paradigms - mechanization, electrification, programmable automation, and Smart Manufacturing - each defined by the kind of work it shifted from humans to machines. In every case, one layer of industrial work remained fundamentally human: the coordinative cognition of production, comprising the interpretive, allocative, diagnostic, negotiative, and governance work exercised by engineers, planners, and operational managers. We argue that a fifth transition is now underway in which this layer, rather than the physical or routine-cognitive layers below it, is what foundation-model-based autonomous agents primarily redistribute. We name this paradigm Agent Manufacturing and define it operationally: a manufacturing system is an instance of Agent Manufacturing when its principal coordination mechanism is reasoning performed by foundation-model agents that can interpret open-ended goals, plan over long horizons, invoke tools and machines, and negotiate with other agents and humans. This is a narrower and more falsifiable definition than the existing literature on cognitive manufacturing or Industry 5.0 provides, and it distinguishes the paradigm sharply from classical multi-agent manufacturing systems, which were autonomous only within closed protocol spaces.