Vectorial Politics

This article develops, in axiomatic-deductive format, the theory of Vectorial Politics. Starting from a preliminary ontology that establishes the fundamental entities of the political field — actors, interests, emotions, institutions and narratives — a formal system of definitions, axioms, propositions and corollaries is deployed that recodes the classical political antagonism of Carl Schmitt through linear algebra and the geometry of n-dimensional spaces. The theory introduces formulas for political distance, political friendship, the conflict field, hegemonic accumulation, the Institutional Stability Index, narrative dissonance, subjective positioning and state stability, among others. The contributions of Mouffe, Agamben, Gramsci, Bourdieu, Kelsen and Schmitt are articulated within a unified quantitative framework that enables empirical measurement, cartographic visualization and dynamic simulation of contemporary political phenomena.