Proposition: Finite-width packet diagnostic

Let an isometry $W:{\mathbb{C}}^2\to L^2(\mathbb{R})$ embed two orthonormal packets with disjoint supports, each within distance $\ell$ of its centre $x_j$. For a static dephasing interval $t$, comparison with the two-centre kick model gives trace-distance error at most

Proof. Disjoint supports give

The conjugated state difference is bounded by twice this norm. Integrate the generator residual, propagate it contractively, and divide by two.