Proposition: Implementability of A–C

The specified programmes are deterministic CPTP maps with the stated laboratory peaks.

Proof. Occupation-label readout determines actual occupied rails. No supplier-side operation or hidden emission record is used. At most $m=0,1,2$ memory qubits coexist with the next atomic packet. Every gate acts on existing memory and an existing incoming rail. Every measurement has both outcomes and its declared feedback. Padding and consumed rails are destructively removed. Finalization leaves exactly one output, or allocates one recyclable slot for fixed-output preparation. Instrument completeness proves trace preservation and includes all references.