Differentiation, Geometry, and Information in the Structure of Reality

The Theory of Ontological Differentiation (TOD) proposes an ontological framework in which differentiation, relations, information, geometry, and persistence constitute distinct but coordinated dimensions of the organization of reality. The starting point is the postulate of self-differentiation, Ω₀ → Δ, which describes the emergence of the first distinction from an original undifferentiated condition. Alongside this foundation stands the independent axiom of the ontological primacy of relations. Differentiated reality is therefore understood not merely as a collection of independent entities, but as a structure in which relations participate in constituting configurations. A central aspect of the proposal is the distinction between difference and information. Difference (Δ) is not, in itself, identical to information. Information emerges when a difference leaves a recognizable trace through a transformation. This relationship is expressed by the general formulation I = T(Δ). Information is thus considered in relation to the traceability and transformation of differences, and to the possibility that they produce recognizable effects. The article further develops the principle of persistence, understood as the continuity of a configuration through change. Persistence is not reduced to the mere preservation of information: it concerns the criteria through which a structure can maintain its identity while its elements and relations undergo transformation. Another central topic is the relationship between geometry and information. Geometry is examined as a possible manifestation of the organizational properties of relational structure, whereas information concerns the preservation and transmission of differences. These dimensions are therefore connected, but not interchangeable. The article also addresses ontological entropy and the TOD hypothesis concerning the distribution of information between an overall structure and its substructures. The comparison with information theory, thermodynamics, the study of systems far from equilibrium, self-organization processes, and approaches to emergent geometry identifies areas of convergence and difference while keeping their respective descriptive levels distinct. The article's specific contribution is to propose an autonomous ontological framework that coordinates differentiation, the primacy of relations, information, geometry, and persistence without reducing them to a single quantity or to a linear causal sequence. It also examines operators, invariants, and validity conditions that may provide the basis for further mathematical development. The aim is to outline a formalization program in which TOD's ontological categories can be specified through mathematically assessable structures and, in perspective, compared with physical properties and systems.