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For every $0<p<\\infty$, we prove that the Toeplitz operator $T_\\mu^{\\mathrm{ph}}$ induced by $\\mu$ on pluriharmonic Fock space belongs to $\\Sp_p$ if and only if $z\\mapsto\\mu(B(z,r))$ belongs to $L^p(\\C^n)$ for one, or equivalently every, $r>0$; this is also equivalent to Schatten membership of the corresponding holomorphic Toeplitz operator $T_\\mu$. For $n\\geq2$, this settles a conjecture of Jaguzovi\\'c and Vujadinovi\\'c, and the result includes the range $0<p<1$ in every dimension. 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For every $0<p<\\infty$, we prove that the Toeplitz operator $T_\\mu^{\\mathrm{ph}}$ induced by $\\mu$ on pluriharmonic Fock space belongs to $\\Sp_p$ if and only if $z\\mapsto\\mu(B(z,r))$ belongs to $L^p(\\C^n)$ for one, or equivalently every, $r>0$; this is also equivalent to Schatten membership of the corresponding holomorphic Toeplitz operator $T_\\mu$. For $n\\geq2$, this settles a conjecture of Jaguzovi\\'c and Vujadinovi\\'c, and the result includes the range $0<p<1$ in every dimension. 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