Lemma: Exact chain transport

Successive adjacent SWAPs along this chain move the unknown payload factor to the final station and return all preceding payload factors to blank. The identity holds on all payload–reference operators.

Proof. A SWAP exchanges complete tensor factors and all their correlations. Induction over the chain moves the original factor one step at a time; each factor left behind is the original blank. The resulting factor permutation gives the identity on every matrix unit, including a reference.