Measurement of the time-integrated $CP$ asymmetry in $D^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ decays using opposite-side flavor tagging at Belle and Belle II

We measure the time-integrated $CP$ asymmetry in $D^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ decays reconstructed in $e^{+}{e}^{-}\to c\bar{c}$ events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 and 428 fb${}^{-1}$, respectively. To infer the flavor of the $D^0$ meson, we exploit the correlation between the flavor of the reconstructed decay and the electric charges of particles reconstructed in the rest of the $e^{+}{e}^{-}\to c\bar{c}$ event. This results in a sample which is independent from any other previously used at Belle or Belle II. The result, $A_{CP}(D^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0)=(1.3\pm 2.0\pm 0.2)\mathrm{\%}$, where the first uncertainty is statistical and the second systematic, is consistent with previous determinations and with $CP$ symmetry.