Quantized Dimensional Closure: Compton Realization and Operator Sector Selection

The Quantized Dimensional Ledger (QDL) represents physical quantities as integer-valued dimensional exponent vectors and tests constructed expressions against declared closure conditions. This paper develops quantized dimensional closure in two steps: first, by identifying a physical realization of the Quantized Dimensional Cell (QDC), whose isotropic dimensional form is length cubed times frequency squared; and second, by showing that modular QDL sectors can refine ordinary canonical dimensional analysis. For a massive excitation, the Compton wavelength and Compton frequency define a localization-frequency package whose product, wavelength cubed times frequency squared, has the same dimensional form as the QDC. This is a dimensional realization, not a dynamical derivation, and does not imply a universal minimum length, new dynamics, or a replacement for quantum field theory. Strict QDL closure is defined by a quotient map on a five-dimensional integer ledger lattice. Projected modular diagnostics are then used to prove covariance of sector separation under admissible projected-basis changes and to prove that QDL sector separation refines canonical dimension under sector-preserving maps. A worked example compares two dimension-six operators, a four-lepton operator and a charged-lepton dipole operator, which occupy distinct QDL sectors. This demonstrates classification information beyond ordinary dimensional homogeneity.