Theorem: Buffered certificate and payload transport

Under Assumption ass:permissions, the finite route implements

where ${\mathcal{U}}_{0\to n}$ is exact payload-factor transport and ${\omega }_{\mathrm{blank}}$ contains the returned blank payload registers. The identity is complete and reference preserving. The protocol satisfies the physical-containment certificate of Theorem thm:containment.

For a fixed clock–catalogue input independent of the payload, the payload communication has a unit signalling witness. This is a declared transport operation, not gravity-generated entanglement.

Proof. Proposition prop:table gives the subnormalized branches. A classical copying isometry copies their already orthogonal history labels; it does not copy an unknown quantum state. Lemma lem:swap gives the exact payload action in every branch. Keeping every history and summing every branch proves (eq:transport) on matrix units and reference extensions.

All local operations lie on regular timelike station worldlines. Every communication path has speed $1/2$, and every control arrives before its declared use. Thus every complete dependency has its required future-causal implementation.

Finally use payload inputs $|0⟩⟨0|$ and $|1⟩⟨1|$ on one payload qubit, with all other input data identical. Their final receiver states have trace distance one, attaining the maximum signalling contrast. The host metric is unchanged and supplies no entangling interaction. Pre-existing reference entanglement is preserved, not attributed to gravity.