SORT-AI: Domain Architecture and Structural Diagnostics for Advanced AI Systems

Advanced artificial intelligence systems increasingly exhibit behaviors that are not adequately captured by component-local metrics, benchmark scores, or layer-specific monitoring. Such behaviors arise across coupling surfaces, control regimes, deployment boundaries, and emergent interaction patterns, indicating that the relevant analytical object is the composed system rather than the isolated component. This article introduces \emph{SORT-AI} as a \emph{Level-0 structural assessment architecture} for advanced AI systems and as the canonical domain reference within the SORT-AI research line. The framework organizes the AI domain along four main axes: \emph{Domain} as the problem space, \emph{Cluster} as the structural problem class, \emph{Application} as a recurrent structural problem form, and \emph{Structural Dimensions} V1 to V4 as the diagnostic grammar linking observed phenomena to structural causes, effect spaces, and decision surfaces. Below the application level, the architecture admits a further diagnostic decomposition into \emph{Scenario Classes}, \emph{Metric Sets}, and a \emph{Regime Classification} that distinguishes core, boundary, and overlap regimes. Applications are therefore treated not only as recurrent structural problem forms, but also as structured regime spaces. The current AI domain comprises 52 applications distributed across five clusters: Coupling, Learning, Control, Emergence, and Evidence. To make the domain paper self-contained at the level of AI-domain interpretation, a compact mathematical basis is provided using a closed set of 22 idempotent operators, a global consistency projector, a calibrated projection kernel, and a structured projection space in which AI systems are read as operator chains on structured execution states. Within this architecture, the Core-3 applications serve as three complementary structural coupling axes: \sortapp{AI.01} expresses physical/interconnect coupling, \sortapp{AI.04} logical/runtime-control coupling, and \sortapp{AI.13} semantic/agentic coupling. Runtime Control Coherence, represented by \sortapp{AI.04}, is used as the canonical example to illustrate how locally correct control mechanisms can generate globally incoherent behavior under scale. The paper further incorporates SORT-Sovereign as a meta-domain that projects technical structural findings into strategic, regulatory, and state decision spaces. In this form, SORT-AI is positioned as a reusable Level-0 structural assessment foundation for subsequent domain-specific analyses and application-level studies across the AI domain.