This paper develops the first formal step required to extend the Quantized Dimensional Ledger (QDL) from operator filtering to representation governance. QDL has been introduced as a structural admissibility framework in which dimensional closure is stronger than ordinary dimensional homogeneity. The present paper argues that such a framework is incomplete if it governs only static objects. If admissibility is to function as a genuine structural criterion, then it must also govern the transformations by which representations are changed, reduced, truncated, calibrated, coupled, approximated, and deployed. A minimal formal scaffold is introduced consisting of a ledger space, ledger map, admissibility operator, admissibility-preserving transformation, and closure-equivalence relation. The main theorem proves that, for induced linear maps on ledger space, admissibility preservation is equivalent to invariance of the admissible kernel and therefore equivalent to quotient compatibility. A worked toy effective-field-theory truncation example then shows that a truncation can remain dimensionally homogeneous while failing admissibility preservation because it destroys the kernel relation required for closure. The paper concludes that admissibility-preserving maps are the first formal object required for extending QDL from operator filtering toward representation governance and, more cautiously, toward any longer-range QDL program of structural unification.
James D. Bourassa (Sat,) studied this question.