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In the compact momentum support setting, we prove that $\\|p_{0}^{\\frac{18}{5r} - 1+\\beta}f\\|_{L^{\\infty}_{t}L^{r}_{x}L^{1}_{p}} \\lesssim 1$, where $1\\leq r \\leq 2$ and $\\beta >0$ is arbitrarily small, is a continuation criteria. 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