The DO–OAR Model: A Binary State-Space Framework for Adaptive Adversarial Systems. Conceptual Layers, Architectural Evolution, and the Case of the Patriot System in the Russia–Ukraine War

Modern adversarial systems, integrated air defenses, cyber-defense architectures, autonomous platforms, and precision-strike networks, are conventionally described through a binary distinction between offense and defense, with adaptation treated as an auxiliary modifier of each rather than as an independent structural dimension. This paper develops the DO–OAR model, a compact binary framework that separates the functional polarity of a system (Defense, Offense) from its adaptive-temporal dynamics (Observe, Adapt, Act, with a recursive closure bit through which every response becomes the next observation). The two dimensions are mathematically orthogonal, producing a six-bit state vector with sixty-four theoretical configurations that can be read graphically, layer by layer, as filled and empty capability markers. We situate the model within the intellectual history of adaptive-systems thinking, Boyd's OODA loop, Wiener's cybernetics, complex adaptive systems theory, and network-centric “kill web” doctrine, and argue that DO–OAR supplies a layer-resolved, domain-independent vocabulary that this literature has not consolidated into a single formalism. We then apply the framework to the most consequential live air-defense case of the current war: the employment of the Patriot system against Russian ballistic-missile and drone salvos in Ukraine. Reading Patriot's sensing, command, engagement, launch, and logistics layers through the DO–OAR lattice clarifies why the system's well-documented operational problems, terminal-phase discrimination failures against maneuvering warheads and decoys, and a severe industrial cost-exchange asymmetry against mass drone attack, are not isolated technical failures but predictable consequences of incomplete adaptive closure at identifiable architectural layers. The model's central claim is that architectural evolution should be measured as the elimination of empty adaptive bits within each layer, rather than as the accumulation of additional capability.