A product-formula simulation certificate

Combining Theorem thm:tail, Proposition prop:trotter, and Theorem thm:signal-stability certifies the Hamiltonian route at Target A, including reference systems.

It does not automatically give Target B at the target Hamiltonian time: assigning every small nonlocal block gate an arbitrarily short geometric duration can violate the physical communication bound. A causal routing implementation needs a separate clock and latency certificate. More efficient local-Hamiltonian simulation algorithms use Lieb–Robinson decompositions HaahHastingsKothariLow; no efficiency claim from that literature is needed for our elementary estimate.