The chain and its permission contract

Fix distinct $x_A,x_B\in U$, and let

The source event is $(T_d,x_A)$; the prescribed null destination is

Choose $m\ge 1$, and install the target-adapted sites

Thus $x_0=x_A$, $x_m=x_B$. Set

Each site carries a $p$-qubit payload register $A_j$. The payload may be the surviving $XQ$ of (eq:probe-prep), so $p=p_X+1$.

Prepare $A_1,\dots ,A_m$ in a fixed blank state $\omega =|0\cdots 0⟩⟨0\cdots 0|$, independently of $A_{0}E$. At tick $j$, apply SWAP to $A_{j-1}{A}_j$, and identities elsewhere.

A two-site SWAP across the tick is an admitted block primitive with causally embedded endpoint dependencies. No continuous-time Hamiltonian implementing that primitive within the tick is asserted.