Event Density: A Mathematical Formalization

This paper is ED‑05 in the Event Density Framework. This paper presents the mathematical core of the Event Density (ED) framework, a structural approach to reality grounded in becoming rather than objects, states, or trajectories. The formalism begins with a bare event domain and assigns non‑negative density values to finite configurations of events. These values represent how much becoming is present in a configuration, without presupposing time, geometry, causality, or probability. The paper introduces the minimal axioms governing event density—non‑negativity, a null baseline, monotonicity, and subadditivity—and shows how they capture the non‑linear, relational character of becoming. Morphisms between ED systems are developed to identify when two systems share the same underlying structure, providing a categorical perspective on ED. The framework is situated relative to measure theory, probability, point processes, causal sets, and statistical mechanics, clarifying both its generality and the commitments that distinguish it. Worked examples illustrate how ED can model simple counts, weighted systems, subadditive interaction, number‑theoretic structure, and temporal tension. This formalization provides the foundation for the broader ED research program and supports its applications in metaphysics, arithmetic, and temporal ontology.