QDL Flavor Closure as a Conditional Rank Theorem and Common-Scale Hierarchy Audit: Three Generations, Yukawa Depth, CKM Leakage, and PMNS Neutral-Flavor Closure

The Quantized Dimensional Ledger (QDL) program treats physical theory construction as a problem of structural admissibility, closure completion, transformation stability, and residual survival. Earlier QDL spectrum-selection work conditionally recovered the one-generation Standard Model chiral matter package from the gauge and primitive field seed SU(3)c x SU(2)L x U(1)Y, Q, L, H, under Yukawa closure, hypercharge neutrality, and anomaly cancellation. A second spectrum-selection layer conditionally selected the Standard Model gauge seed itself under explicit color-triplet, chiral weak-doublet, single-hypercharge-ledger, Higgs-doublet, and minimality closure axioms. Those spectrum results left an important negative result: gauge and anomaly closure alone do not select the number of generations. One complete Standard Model generation is anomaly-closed, and any integer number of identical complete generations remains anomaly-closed. Therefore the observed value Ngen = 3 must arise from a deeper flavor-layer condition. This paper consolidates the QDL flavor-selection and flavor numerical-closure sequence into a bounded standalone manuscript. The first layer formulates generation number as a rank-completion problem in the Yukawa and charged-current mixing sector. A complete flavor sector must support nontrivial mass-rank structure, intergenerational charged-current mixing, and irreducible CP-complete flavor structure. For N generations, a unitary quark mixing matrix contains N(N - 1)/2 physical mixing angles and (N - 1)(N - 2)/2 physical CP-violating phases. Thus N = 1 has no mixing and no CP phase, N = 2 has one real mixing angle but no irreducible CP phase, and N = 3 is the minimal number supporting both nontrivial mixing and irreducible CP violation. QDL flavor closure therefore selects Ngen = 3 under the declared condition that a complete admissible flavor sector must support mass-rank closure, charged-current mixing closure, and irreducible CP closure. The second layer formulates numerical flavor closure. Once the Standard Model gauge seed, one-generation chiral matter package, and three-generation flavor rank have been selected, the remaining flavor problem is numerical. The Yukawa matrices Yu, Yd, Ye, and, depending on neutrino mechanism, Ynu, MR, and Mnu must be treated as admissibility-preserving maps whose singular values, ratios, basis-mismatch matrices, and CP invariants satisfy dimensionless closure conditions. The third layer develops the first QDL flavor-depth ledger. The top quark is treated as the saturated scalar-fermion closure mode, y_t^(0) = 1, so all other charged fermions are residual projections below the top channel. The electroweak-flavor suppression seed is rho_QDL = alpha / sin^2 theta_W, approximately 3.15 x 10^-2. Its powers organize the charged-fermion Yukawa hierarchy: rho_QDL is of order 10^-2, rho_QDL^2 is of order 10^-3, rho_QDL^3 is of order 10^-5, and rho_QDL^4 is of order 10^-6. The charged-fermion hierarchy is represented as y_f^QDL = q_f rho_QDL^d_f, where d_f is flavor depth and q_f is a rational projection factor. This manuscript treats the q_f values as declared first-pass projection factors, not as uniquely derived constants. Their deeper derivation remains open. A common-scale hierarchy audit is included. Using representative electroweak-scale running Yukawa values at mu = MZ, the QDL table is compared at hierarchy level. The common-scale audit shows that the QDL depth assignments reproduce the correct charged-fermion tiers, typically within factors of order unity, but not as a precision fit. This is the correct status: QDL presently supplies a flavor hierarchy architecture, not a completed precision theory of fermion masses. The fourth layer interprets CKM mixing as Cabibbo leakage: square-root flavor-depth leakage between up-type and down-type residual Yukawa ledgers. QDL gives lambda_C^QDL = (5/4) sqrt(rho_QDL), approximately 0.222, close to the observed Cabibbo/Wolfenstein value near 0.225. The remaining CKM hierarchy is represented by |Vus| approximately lambda_C, |Vcb| approximately (5/6) lambda_C^2, and |Vub| approximately (5/18) lambda_C^3. The fifth layer treats neutrinos as a neutral residual ledger rather than as ordinary charged-flavor depth modes. PMNS mixing is large because the neutral sector is rank-democratic, corrected by the same residual seed rho_QDL. QDL proposes sin^2 theta_12 = 1/3 - rho_QDL/2, sin^2 theta_23 = 1/2 + rho_QDL/2, and sin^2 theta_13 = (13/18) rho_QDL/(1 + rho_QDL), yielding approximately 0.318, 0.516, and 0.022. The neutrino mass-splitting hierarchy is represented by Delta m^2_21 / |Delta m^2_31| approximately rho_QDL, approximately 0.0315. This paper does not claim a final precision flavor theory. It does not derive all Yukawa eigenvalues, rational projection factors, CKM and PMNS phases, Majorana phases, absolute neutrino masses, or a complete common-scale renormalization-group fit. Its contribution is bounded but significant: QDL moves from generation-number selection to a common-scale hierarchy audit linking three generations, Yukawa depth tiers, CKM leakage, Cabibbo mixing, PMNS neutral-rank closure, and the neutrino mass-splitting ratio through one electroweak-flavor seed.