A World Social Atlas on the AS-HFFH Coordinate System

This article introduces a global social atlas—referred to as the k-Atlas—that visualizes the dynamics of Social Curvature k for countries worldwide over the period 2006–2025. Rather than presenting static rankings or isolated indicators, the k-Atlas represents societies as trajectories evolving within a structured social space. The atlas is constructed within the AS-HFFH social coordinate system, a three-dimensional framework defined by Property Rights (P), Market Competition or Business Freedom (C), and Personal Freedom (A). These variables, grounded conceptually in classical political economy and operationalized using data from the Heritage Foundation and Freedom House, function as orthogonal axes that allow countries to be positioned coherently in a common measurement space at each point in time. The k-Atlas emphasizes trajectories rather than snapshots. Through k-Charts, it becomes possible to observe long-term drift, stability, structural breaks, and phase transitions in social systems—features that are often obscured in purely statistical or year-by-year comparisons. The article also addresses potential intuition traps arising from the geometric interpretation of k, particularly within Elliptic social space. Based on trajectory shapes, the article provisionally groups selected countries into several geometric patterns of social dynamics, illustrating the diversity of paths that societies may follow within a shared coordinate system. These groupings are not intended as ideological classifications, but as geometric descriptions of dynamic behavior. Together with related concepts such as the k-Circle, the k-Atlas contributes to the development of an approach provisionally termed Metric Sociology. It is hoped that this atlas can be extended, refined, and eventually expanded to cover all countries globally, serving as a useful resource for social research and education.