Evidence for<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:mtext mathvariant="normal">−</mml:mtext><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup></mml:math>Mixing

We observe evidence for ${D}^{0}\mathrm{\text{\ensuremath{-}}}{\overline{D}}^{0}$ mixing by measuring the difference in the apparent lifetime when a ${D}^{0}$ meson decays to the $CP$ eigenstates ${K}^{+}{K}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and when it decays to the final state ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$. We find the relative difference of the lifetimes ${y}_{CP}$ to be $[1.31\ifmmode\pm\else\textpm\fi{}0.32(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.25(\mathrm{syst})]%$, 3.2 standard deviations from zero. We also search for a $CP$ asymmetry between ${D}^{0}$ and ${\overline{D}}^{0}$ decays; no evidence for $CP$ violation is found. These results are based on $540\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data recorded by the Belle detector at the KEKB ${e}^{+}{e}^{\ensuremath{-}}$ collider.