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Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> -even fraction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><…
A determination of the $CP$-even fraction ${F}_{+}$ in the decay ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is presented. Using $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\psi}(3770)\ensuremath{\rightarrow}D\overline{D}$ data collected by the BESIII detector, one charm meson is reconstructed in the signal mode and the other in a $CP$ eigenstate or the decay $D\ensuremath{\rightarrow}{K}_{S,L}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. Analysis of the relative rates …