The Quantized Dimensional Ledger (QDL) treats physical theory construction as a problem of structural admissibility, closure completion, transformation stability, and residual survival. Physical quantities, fields, operators, constants, measurement chains, effective interactions, and dynamical maps must possess ledger representations, close in declared sectors, preserve closure under admissibility-relevant transformations, and pass residual-first empirical adequacy. This paper develops the QDL operator-governance layer: the claim that admissible operators and their renormalization maps must preserve declared QDL closure structure. The Standard Model Effective Field Theory (SMEFT) supplies the natural benchmark for this layer. SMEFT extends the Standard Model by adding gauge-invariant higher-dimensional operators, and at dimension six the Warsaw basis contains 59 baryon-number-conserving operator classes before flavor expansion and Hermitian-conjugation bookkeeping. The full three-generation dimension-six SMEFT parameter space contains 1350 CP-even and 1149 CP-odd real parameters, giving 2499 real parameters. One-loop renormalization of SMEFT operators is governed by an anomalous-dimension matrix. A nonzero matrix entry means that a source operator contributes to the running of a target operator. In QDL language, this is an admissibility-relevant transformation between operators. The paper formulates a finite, falsifiable QDL audit of SMEFT operator mixing. It introduces a projected two-component operator ledger Phi (O) = (a, b) and a modular QDL grade Delta (O) = 2a - 3b mod 6. The proposed operator-governance rule is: if gammaᵢj is nonzero, then Delta (Oᵢ) = Delta (Oⱼ). Equivalently, if Delta (Oᵢ) is not equal to Delta (Oⱼ), then gammaᵢj must be zero. This rule is not presented as an assumed truth. It is presented as a reproducible audit rule. Given an operator-grade table and a machine-readable anomalous-dimension matrix, the QDL zero mask and observed nonzero matrix mask define a matrix-level violation count V. The strongest audit result is V = 0. If V is greater than zero, the violations must be classified rather than hidden. The paper proves that QDL sector separation can refine canonical dimension under a declared modular projection, that sector-preserving maps imply a zero rule for direct operator mixing, and that the modular selection rule is equivalent to the matrix condition V = 0. It also supplies a worked benchmark: the four-lepton operator Qₗl has QDL grade 0 mod 6, while the lepton dipole operator QₑB has QDL grade 4 mod 6. Since the grades differ, QDL predicts that direct modular-grade-preserving one-loop mixing from Qₗl to QₑB is forbidden. The paper supplies a dependency-light Python audit artifact that reads operator-grade and anomalous-dimension CSV files, computes modular grades, audits nonzero entries, reports violations, and writes a reproducible violation table. It does not claim that the full 59 x 59 class-level or 2499 x 2499 flavor-expanded SMEFT anomalous-dimension matrix has already passed QDL closure. A full validation requires a machine-readable matrix in a declared basis and convention. The contribution of this paper is narrower and technical: QDL operator governance is converted into a finite, falsifiable, executable SMEFT matrix-audit standard.
James D. Bourassa (Fri,) studied this question.