Conditional endpoint certificate

Fix coordinates in which the selected abstract cone is ${\mathcal{L}}_m$. A target is an anchored pair

Use the comparison norm $\Vert (t,x){\Vert }_{\ast }=|t|+\Vert x{\Vert }_2$.

A compatible realization must declare:

• actual source and receiver coordinates $a_{n,\zeta },b_{n,\zeta }$;

• a finite complete channel ${\Gamma }_{n,\zeta }:\mathcal{B}(M_0)\to \mathcal{B}(M_0\otimes F_{n,\zeta })$;

• an ideal complete target ${\Theta }_{n,\zeta }(X)=X\otimes {\sigma }_{n,\zeta }$;

• matching factorizations, encoder and decoder allowances, physical edge availability, and all resource counts.