The Standard Model as a Minimal Closure-Stable Projection: A Conditional QDL Admissibility Theorem for One-Generation Chiral Gauge Structure

This preprint formulates a conditional structural-admissibility theorem for the one-generation Standard Model chiral gauge sector within the Quantized Dimensional Ledger (QDL). Relative to a declared Standard-Model-like color-weak representation skeleton, the paper organizes dimensional admissibility, chiral orientation, hypercharge-kernel closure, anomaly-residue cancellation, and minimality as components of a single closure-stability test. The main result is that, within the declared candidate class, the familiar one-generation Standard Model hypercharge pattern is a minimal closure-stable survivor of the residue grammar, up to overall normalization and interchange of the two color-antitriplet singlet labels. In integer normalization, the Standard Model hypercharge vector is y = (1, -4, 2, -3, 6; 3), corresponding to the usual assignments for Q, u^c, d^c, L, e^c, and H. The proof uses standard anomaly-cancellation conditions for SU(3)_C^3, SU(3)_C^2 U(1)_Y, SU(2)_L^2 U(1)_Y, U(1)_Y^3, mixed gravitational-U(1)_Y, and the global SU(2) condition, then interprets the surviving hypercharge ray as a QDL closure-kernel result. The paper does not claim to derive the full Standard Model, the gauge group, gauge couplings, fermion masses, Yukawa matrices, CKM or PMNS structure, the Higgs potential, neutrino physics, dark matter, quantum gravity, or a complete ultraviolet completion. Its contribution is a bounded theorem-level formulation showing how standard chiral gauge-theory consistency requirements can be expressed as a structural persistence test in QDL language.