Reference-Centered Generalization Bounds for Modern Pre-Normalized Decoders: Explicit Constants and a Vacuity Threshold

We derive an explicit reference-centered uniform generalization bound for pre-normalized decoders, including grouped-query attention, rotary maps, RMS normalization, and SwiGLU, and ask when such a bound can be nontrivial at all. The bound has two moving parts: a transport coefficient, which carries an early parameter perturbation through the residual stack, and a covering-entropy term. We prove a sharp threshold ${\kappa }_{\star }=0.1085$ for the normalized stage coefficient of the truncated-Dudley objective: at or above it, the optimized certificate must equal its range cap, and in a stronger regime improvements in stage-cover constants drop out of the objective altogether. On a frozen public 1.1B checkpoint, a norm-matched Jacobian audit gives a median ${\log }_{10}$ transport of $40.58$ for the product of separately estimated sublayer norms but only $3.66$ for the directly estimated composite. Three SmolLM2 checkpoints (135M–1.7B parameters) reproduce the separation, with median paired gaps of $46.17$–$54.23$ decades against $36.84$ on the 1.1B reference; all operator norms in this audit are finite-search lower estimates. We find that, within this covering-and-transport proof structure, the obstruction sits in stagewise transport rather than in the cover constants, and our results point to direct, direction-aware composition bounds rather than further tightening of stagewise constants.