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First measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math> -odd moments in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn…

First measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math> -odd moments in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn…

We report the first measurement of the $T$-odd moments in the decay ${D}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ from a data sample corresponding to an integrated luminosity of $966\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected by the Belle experiment at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. From these moments we determine the $CP$-violation-sensitive asymmetry ${a}_{CP}^{T\text{-odd}}=[\ensuremath{-}0.28\ifmmode\pm\else\textpm\fi{}1.38(\mathrm{stat}.{)}_{\ensuremath{-}0.76}^{+0.23}(\mathrm{syst}.)]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which is consistent with …