This article presents the development of a universal methodology for selecting and classifying Critical Objects of Attention (COAs) during crisis events, replacing static, standardized approaches with a dynamic, substantiated model. The authors propose formalizing criticality as an emergent property of the "world-governance-observer" system, where criticality is determined not by an object's intrinsic attributes, but by its role within crisis dynamics. Leveraging graph theory, information theory, and models of cognitive salience, a phase space of attention is constructed, equipped with a dynamic criticality function k(o, t) and an attentional energy functional L, enabling optimal selection of a compact subset of COAs. A five-stage methodology - DCSC (Dynamic Criticality Selection & Classification) - is introduced, implemented, and validated on a simulated cyberattack scenario. The model is unsupervised, interoperable with existing monitoring systems (e.g., SIEM, digital twins), and applicable across domains including cybersecurity, critical infrastructure management, and digital public governance. Keywords: critical attention objects, dynamic criticality, cognitive salience, crisis management, cybersecurity, attention functionality, DCSC methodology, mathematical modeling