QDL Spectrum Selection as a Conditional Standard Model Theorem: Gauge Seed Minimality, Hypercharge Closure, Anomaly Cancellation, and One-Generation Matter Completion

The Quantized Dimensional Ledger (QDL) program formulates physical theory construction as a problem of structural admissibility, closure completion, transformation stability, and residual survival. This paper presents a conditional QDL spectrum-selection theorem for the Standard Model. It does not claim to derive the Standard Model from no assumptions. Instead, it shows that under explicit Standard Model-facing QDL closure requirements, the Standard Model gauge seed and one-generation chiral matter package arise as a minimal closure-complete admissible package. Starting from the gauge seed SU(3)c x SU(2)L x U(1)Y and primitive field seed {Q, L, H}, where Q is a quark doublet, L is a lepton doublet, and H is a…