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Measurement of the branching fraction and search for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:math> violation 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:mn>0</mml:mn></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><…
We measure the branching fraction for the Singly Cabibbo-suppressed decay $D^0\rightarrow K^0_S\,K^0_S\,\pi^+\pi^-$, and we search for $CP$ violation via a measurement of the $CP$ asymmetry $A^{}_{CP}$ and also the $T$-odd triple-product asymmetry $a_{CP}^{T}$. The later two measurements are complementary. We use 922~fb$^{-1}$ of data recorded by the Belle experiment, which …