Decay–Dynamic Equilibrium (DDE): The Foundational Theorem of the Law of Persistence

This working paper presents the Decay–Dynamic Equilibrium (DDE) theorem — the operational foundation of the Law of Persistence. DDE formalises how systems sustain continuity through alternating phases of decay and renewal, mediated by energy or information exchange within entropic boundaries. Whereas classical thermodynamics emphasises inevitable disorder, DDE reframes decay as the engine of renewal, showing that apparent loss is a necessary precondition for systemic persistence. The theorem models persistence as a dynamic balance between breakdown and regeneration, establishing the bridge between physical and informational processes that permit life, cognition, and technology to endure. This paper defines the conceptual and symbolic structure of DDE and clarifies its role as the mechanistic spine of the Law of Persistence and Synthetic Science (SS). Quantitative and algorithmic details are reserved for future empirical publications.