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Using the Wold representation for non-Gaussian density fields, \\delta(\\rvec) = \\int f(|\\rvec - \\rvec^\\prime|) \\Delta(\\rvec^\\prime) d^3 \\rvec^\\prime, we find conditions on \\Delta and f for which \\phi must have a Gaussian one-point distribution, while \\delta can be non-Gaussian. 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