A timing contract that really is additive

At a deadline $t$, the reduced destination task channel can be written

where ${\omega }_{\ast }$ is a declared failure state. On failure the message may still survive elsewhere; that register belongs to the complete protocol output, not to the reduced destination task.

For a route of $\ell$ edges, the protocol uses $\ell$ Bell pairs and $2\ell$ Bell-outcome bits. A sequential implementation can recycle local workspace, but supplier holdings and perfect storage are separate resources. There is no unknown-state duplication.