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One distinguishes between ``true'' $CP$-violating triple-product (TP) asymmetries which require no strong phases and ``fake'' asymmetries which are due to strong phases but require no $CP$ violation. So far a single true TP asymmetry has been measured in ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}}$. A general discussion is presented for $T$-odd TP asymmetries in four-body …