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For the unit shift, we prove $S_1^\\varphi(x)\\ll x\\exp{-(1/2-o(1))\\sqrt{\\log x,\\log_2 x}}$. More generally, put $A=\\log_3 x+\\log_4 x-\\log 2$, $G=\\sqrt{\\log x,A}$, and $V=\\log x/G$. For every fixed integer $J\\ge 1$, uniformly for $1\\le h\\le \\exp{G/\\sqrt{J}}$, we obtain $S_h^\\varphi(x)=D_{h,>Y_J}^\\varphi(x)+O_J(x\\exp{-\\sqrt{J},G+o_J(V)})$, where $Y_J=\\exp{\\sqrt{J},G}$. 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