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Assume \\[ |{\\rm Riem}(x)| \\lesssim r(x)^{-p} \\quad \\text{as } r(x)\\to\\infty. \\]\n  If $p>3$, curvature is spectrally short-range: $L$ exhibits regular low-energy scattering and zero energy is not singular. At the critical decay \\[ |{\\rm Riem}(x)| \\sim r^{-3}, \\] dispersion and curvature balance. 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Let $(M,g)$ be asymptotically flat and let $L=\\Delta_L$ denote the spatial Lichnerowicz operator acting on symmetric $2$-tensors. Assume \\[ |{\\rm Riem}(x)| \\lesssim r(x)^{-p} \\quad \\text{as } r(x)\\to\\infty. \\]\n  If $p>3$, curvature is spectrally short-range: $L$ exhibits regular low-energy scattering and zero energy is not singular. At the critical decay \\[ |{\\rm Riem}(x)| \\sim r^{-3}, \\] dispersion and curvature balance. 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