Approximation Is Not Ontology_ Literal Branching, Metaphor, and the Deterministic Requirement in Quantum Foundations

Abstract This paper conducts a consistency audit of ontological claims made by the Many-Worlds Interpretation of quantum mechanics. Without proposing any alternative interpretation or modification to the formalism, the analysis examines whether claims of strict unitarity, determinism, and literal permanent branching are jointly admissible under unitary dynamics alone. The central result identifies a required but illicit substitution from approximate to exact orthogonality in decoherence-based branching accounts. Because unitary evolution preserves inner products, permanent branch separation cannot be derived dynamically without additional postulates. Modern “emergent” formulations avoid contradiction only by relinquishing literal ontological status, thereby reclassifying branching from physical ontology to descriptive metaphor. The paper draws no experimental conclusions and advances no new physics; it functions solely as an internal consistency audit of existing interpretive claims.