Theorem: Reference-preserving target-adapted transport

For every initial payload–reference state ${\rho }_{A_{0}E}$, after tick $j$ the state is

under the fixed register identifications. Thus the complete logical payload channel is exactly the identity, including its arbitrary reference. The report is forwarded without changing its joint law. Arrival is at developed time $t_{\mathrm{d}}+\ell$, or host time $T_{\mathrm{d}}+\ell /c$. All dependency routes stay in the regular part.

Proof. Initially the assertion is the preparation. At hop $j$, a SWAP moves the entire current payload factor, including its correlations with $E$, into the next independent blank and leaves the previous factor blank. Induction proves the formula. The final statement follows at $j=n$.

A classical copy preserves diagonal records and their joint correlations; it is not cloning an arbitrary unknown quantum state. The chosen spacings and tick durations make every cross dependency null in the developed chart and therefore causal in the host.