Closure Classes in the Quantized Dimensional Ledger: Structural Equivalence Beyond Phenomenology

This paper develops the formal notion of closure classes within the Quantized Dimensional Ledger (QDL), a structural admissibility framework in which physical representations are assigned integer charges in a 3L + 2F lattice and judged by a dimensional-closure criterion stronger than ordinary dimensional homogeneity. Building on prior work on admissibility-preserving transformations, the manuscript defines closure-equivalence as the relation generated by lawful transformations that preserve the admissible kernel on ledger space. It proves that closure-equivalence is an equivalence relation on the admissible sector and establishes a phenomenological non-identity result: two representations may agree over a declared observable regime while failing to belong to the same lawful structural class. A worked effective-field-theory example shows how a closure-complete admissible sector and a dimensionally homogeneous truncation can agree at low order while differing structurally because the truncation breaks admissibility preservation. The paper argues that closure classes refine underdetermination, sharpen model legitimacy, and provide the first mathematically definite selection object in QDL representation space.