Distinction under Non-Closure and the Structural Foundation of Irreversibility

This paper develops a minimal axiomatic framework for understanding structural irreversibility. Rather than assuming time, causality, or discrete entities as primitives, it begins from the minimal condition that something is the case and derives the consequences of distinction under non-closure. From this basis, the paper establishes irreversibility as a structural consequence rather than an empirical asymmetry, and clarifies the conditions under which persistence, asymmetry, and non-reversibility arise. The work is intended as the first step in a broader program addressing the emergence of discrete regimes, continuity, and metric structure from a common formal basis.