A finite semidefinite upper certificate

This is a sufficient finite certificate in the semidefinite channel-norm framework WatrousSDP. No numerical optimization or floating-point feasibility check is reported as executed.

If $\hat{H}$ is an approximation with $\Vert H-\hat{H}{\Vert }_{\infty }\le \xi$, a feasible domination matrix for $\hat{H}$ becomes one for $H$ after adding $\xi I$. For output dimension $k$, this increases $t$ by at most $k\xi$. A rigorous numerical certificate must price this slack and certify positive semidefiniteness, rather than trust a printed decimal.