Certificates, comparisons, and the resulting release

For input dimension $d$, normalized Choi operators give

An already certified diamond error is added without another factor $d$. These are channel-certificate comparisons with Hawk02-E and Hawk04-A CheungHawk02E,CheungHawk04A,Watrous. They do not prove a scheduler, geometric route, or lateness invariant.

A flagged cutoff

is deterministic and CPTP. For a state commuting with $P$, its trace-distance error in the common enlarged space is the discarded probability. That equality need not hold for states with low–high coherences. Compare En02-E thm:cutoff CheungEn02E.

An exhaustive finite-graph programme with $N\le 20$ additionally needs a finite schedule/gate catalogue, horizon and register bounds, exact or validated arithmetic, and complete failure outcomes. There are continuously many instruments even on a small graph. No new computation or certificate execution is reported.