The tested perturbation and its theorem-level consequence

On the ordered one-excitation sector, the script uses a detuning operator $D_M$ with memory-label eigenvalues $-1,+1$ and zero radiation-sector entries. The unit-duration event propagator is

Since ${\Vert D_M\Vert }_{\infty }=1$, each event has $h_j=10^{-4}$. This perturbation stays in the initial energy sector; extending $D_M$ by zero on other sectors gives a bare-energy-conserving finite-space perturbation.

With exact preparation, collection, and the ideal decoder in this specified matrix model, Theorem thm:B6 gives

Equation (eq:diagnosticrobust) is an analytical consequence of the specified detuning and norm budget. The script does not compute the actual perturbed recovery optimum or print the perturbed decoded diamond distance.