= Full-evolution comparison for truncated dynamics
{title2=$\|\tau_t^H(A)-\tau_t^{H_j}(A)\|\leq\sum_{Y\notin H_j}\int_0^{|t|}\|[\tau_\sigma^H(A),h_Y]\|d\sigma$}
A Duhamel comparison can bound truncation error using <commutators> evolved under the full Hamiltonian. This avoids assuming that a black-box <Lieb-Robinson bound> for $H$ also holds for every truncation. Polynomial shell weights and exponential distance suppression make the sum over omitted shells convergent. Comparing two truncations through the full evolution bounds their difference.
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