= Almost-exponential locality of filtered Hamiltonian terms
{title2=$\|A^{(Z,d)}\|\leq O(\|h_Z\|d^{\alpha+1}e^{-cd/(\log(cd))^2})$}
In a <telescoping local-shell decomposition>, split the <spectral filter> integral at a time proportional to the shell distance. A <Lieb-Robinson bound> controls short times, while the two-sided almost-exponential <spectral filter> tail controls long times. Polynomial shell-weight growth then gives the displayed decay. The estimate is asymptotic at large distance; small shells retain the elementary operator-norm bound. The <evenization of a nonnegative bandlimited filter> can supply the two-sided tail from a one-sided existence statement.
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