The Compact Company: An Actor-Graph Theory of the Firm in the LLM Era

This paper introduces the Compact Company as a distinct category in organizational theory. A Compact Company is an organizationally closed firm whose human core is minimized by cost or headcount while remaining sufficient to satisfy legal, governance, capacity, and probabilistic viability requirements. Most of its operational and regulatory variety is realized through an executable graph of human, software, LLM, agentic, and external actors. The concept treats compactness as an architectural property and separates it from small size, one-person entrepreneurship, virtual organization, lean management, and generic AI adoption. The paper develops a typed temporal actor graph and contributes four formal constructions. It defines an organizational-closure operator based on weak probabilistic bisimulation, represents the internal graph as a composite institutional actor, and preserves the distinction between a graph and a node. It defines the boundary of the firm as a transaction-attribution operator across authority, accountability, data regime, economic outcome, and control. It formalizes continuity and succession through the resilience of the authority-and-state graph to individual and correlated failures. It then formulates compactness as the minimization of the human core under viability constraints and establishes NP-hardness for a simplified core-design problem through reduction from Minimum Set Cover. This result supplies a lower bound on computational complexity and claims no new result in complexity theory. The economic mechanism of compactness arises from LLM-enabled reductions in the cost of semantic coordination, including the interpretation of incomplete instructions, task decomposition, context transfer, decision preparation, and the processing of standard exceptions. These reductions allow the human core to contract while the number and variety of controlled transactions expand. The paper positions an executable Digital Twin of the Organization as the most complete non-personal carrier of critical organizational state, policy, and execution for a compact digital firm. It concludes with an empirical program, explicit falsification criteria, a minimal compactness audit, and a design-based feasibility example involving Corezoid and Simulator.Company.