From Operator Filtering to Representation Governance: Admissibility-Preserving Maps in the Quantized Dimensional Ledger

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.