An exact dilation and its resource meaning

This is an existence statement for a unitary dilation. It is not an exact-synthesis claim for arbitrary matrix entries in a fixed discrete gate library. After readout, any retained fine index is classical implementation history. It must either be explicitly available to the controller or remain outside its observation boundary.

For a horizon $T$, retaining all fine indices requires at most $Te$ bits. Storing all geometry labels additionally requires at most $(T+1)\lceil {\log }_2|\mathsf{G}|\rceil$ bits. These are sufficient reserves, not optimal adaptive-memory bounds. No spectator is charged against them.