Integrated residual certificates

This is the residual accounting form compared with En01-B CheungEn01B. It supplies a quantitative certificate only after the target dynamics and residual $r$ are supplied. It does not convert record equality into residual equality.

Normalization of a rare branch requires a probability lower bound. For positive blocks of traces $p,\hat{p}>0$ with $\Vert \hat{\sigma }-\sigma {\Vert }_1\le ϵ$,

Thus small unconditional block error alone does not uniformly control every normalized conditional state.