A complete recurrent comparison

For a frozen deletion of $k$ coordinates of magnitude at most $w$, the corresponding matrix difference satisfies

Gatewise quantities, not only packed-tensor density, enter the certificate. Training-induced changes require their own residuals.

If $D=\text{norm}{z-z^{\prime }}_{\infty }$, the accuracy interface is

The proof is the signed-margin and Markov-inequality argument recorded in Psy01-A and Psy03-A CheungPsy01A,CheungPsy03A. A small numerical perturbation bound alone does not prove strictly improved accuracy.