Axiomatic Generative Ontology: Discrete–Aggregative Dynamics and Phase Cycles

This paper develops an axiomatic generative ontology formulated as a discrete–aggregative dynamical system. Existence is modeled as a finite-state relational process governed by five structural axioms: generativity, aggregation, dissipation, threshold transition, and cyclic closure. The system evolves through a discrete update rule defined on a state space X_n = (k_n, σ_n), where k_n represents structural accumulation and σ_n denotes phase orientation. A pressure function α_n determines threshold activation, which triggers phase inversion through a Heaviside transition operator. Under the finite-state condition, the system necessarily enters periodic cycles. This establishes existence as a structurally closed generative process rather than a static ontology. The framework provides a formal dynamical basis for phase alternation, structural stabilization, and cyclic recurrence in relational systems.