The Level Mismatch: Why bounded systems mistake labels for identity — and the discipline that repairs the mistake

Abstract The Level Mismatch is a capstone orientation paper for the Identity-Persistence Program. It argues that many ancient and modern persistence problems arise from a single structural failure: sameness is declared at one level while the recurrence that actually governs behavior lives at another. A river, ship, organism, institution, database record, pharmaceutical solid form, or AI model may retain a stable label while its governing recurrence drifts beyond the declared bound. The paper does not introduce new formal results. Instead, it explains why the underlying forcing theorem, persistence calculus, finite-regime capacity theory, and coding theorem are repeatedly needed across philosophy, science, cognition, institutions, and engineering. It frames identity persistence as a declared-regime problem involving identity-bearing units, admissible transformations, quotients, invariants, governance, drift bounds, and explicit verdicts: PERSIST, BREAK, BRANCH, UNDEFINED, and REGIME-CHANGE. The paper also develops the ideas of selective persistence, meaning as what survives forgetting, purpose as directional selection over possible continuations, and discovery as invariant-finding followed by compression. Its central claim is structural rather than ontological: bounded systems require persistence structure to act coherently under change, but this does not settle final ontology.