Evidence for direct<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>violation in the decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mo stretchy="false">(</mml:mo></mml:msup><mml:msup><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>S</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>and measurement of the CKM phase<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

We present a new measurement of the unitarity triangle angle ${\ensuremath{\phi}}_{3}$ using a Dalitz plot analysis of the ${K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay of the neutral $D$ meson produced in ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{D}^{(*)}{K}^{\ifmmode\pm\else\textpm\fi{}}$ decays. The method exploits the interference between ${D}^{0}$ and ${\overline{D}}^{0}$ to extract the angle ${\ensuremath{\phi}}_{3}$, strong phase $\ensuremath{\delta}$, and the ratio $r$ of suppressed and allowed amplitudes. We apply this method to a $605\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data sample collected by the Belle experiment. The analysis uses three decays: ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}D{K}^{\ifmmode\pm\else\textpm\fi{}}$, and ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{D}^{*}{K}^{\ifmmode\pm\else\textpm\fi{}}$ with ${D}^{*}\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{0}$ and ${D}^{*}\ensuremath{\rightarrow}D\ensuremath{\gamma}$, as well as the corresponding charge-conjugate modes. From a combined maximum likelihood fit to the three modes, we obtain ${\ensuremath{\phi}}_{3}={78.4}^{\ifmmode^\circ\else\textdegree\fi{}}\genfrac{}{}{0}{}{+10.8\ifmmode^\circ\else\textdegree\fi{}}{\ensuremath{-}11.6\ifmmode^\circ\else\textdegree\fi{}}\ifmmode\pm\else\textpm\fi{}3.6\ifmmode^\circ\else\textdegree\fi{}(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}8.9\ifmmode^\circ\else\textdegree\fi{}(\mathrm{\text{model}})$. $CP$ conservation in this process is ruled out at the confidence level $(1\ensuremath{-}CL)=5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, or 3.5 standard deviations.