Principle of Minimal Architectures

This manuscript develops a structural framework for engineering systems under fundamental constraints. Departing from classical assumptions of global control, complete representation, and composability, it establishes that real-world systems—whether artificial, biological, or socio-technical—operate under conditions of incompleteness, dynamic constraints, and irreducible interactions. Within this regime, global coherence, full predictability, and exhaustive verification are not attainable in principle. The work introduces a series of results that collectively redefine the architecture of such systems. First, an operational form of incompleteness is established, showing that no system can fully represent or anticipate its own dynamics. Second, the absence of effective global control is demonstrated, implying that system-wide coordination cannot be guaranteed. Third, structural impossibilities—arising from limits of computation, verification, and interaction—are shown to constrain the space of admissible transformations. These results lead to two fundamental consequences: non-composability, where global behavior cannot be derived from local components, and non-consistency, where no unified coherent description of the system can be maintained. From these constraints emerges a minimal principle of organization. Systems can no longer be defined by objectives or global optimization, but only by their ability to maintain viable trajectories within dynamically evolving constraint fields. Viability thus replaces optimality as the primary criterion. Architectures must be local, distributed, and adaptive, operating without reliance on global representations or centralized control. The manuscript culminates in the formulation of the Principle of Minimal Architecture, which states that any realizable system under such conditions must be structured as a set of locally interacting components whose trajectories remain admissible only insofar as they satisfy evolving constraints. This principle is not prescriptive but structural: it defines the conditions of existence for architectures in open, complex environments. The proposed framework provides a unified perspective on contemporary limitations in artificial intelligence, including large language models, agentic systems, and multi-agent architectures, while extending beyond them to a general theory of systems under constraints. It suggests a shift from engineering systems for performance and control to engineering systems for viability and persistence under irreducible limits.