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What does it mean for something to persist? Physics and philosophy typically assume that systems persist through change: objects endure, states evolve, identities remain recognizable. This paper asks a more basic question: what structural conditions make persistence possible at all? The central idea is that persistence is not a given, but something that must be achieved. A system persists only if it can maintain its identity under transformation. This requires more than change — it requires a way to verify that identity has been preserved. From this starting point, the paper develops two main results. First, persistence requires a minimal three-part structure. A system must have a reference that defines its identity, a transformation that challenges that identity, and a relation that evaluates whether the transformation preserves it. This structure is called triadic closure. Simpler structures — involving only one or two components — cannot support genuine persistence. Second, this triadic structure must remain balanced. If identity dominates, the system collapses into stasis. If transformation dominates, it dissolves into incoherence. Persistence requires an exact structural equilibrium between identity and difference. The paper situates these results in relation to philosophical discussions of identity over time and to Peirce’s theory of triadic relations. It also outlines how these structural requirements constrain the kinds of mathematical frameworks that can describe persistent systems, pointing toward linear geometric structures. Overall, the paper proposes that persistence is not a primitive feature of reality, but a structural achievement requiring triadic closure and equilibrium.