We observe $D^0-bar{D}^0$ mixing in the decay $D^0rightarrow K^+pi^-$ using a data sample of integrated luminosity 976 fb$^{-1}$ collected with the Belle detector at the KEKB $e^+e^-$ asymmetric-energy collider. We measure the mixing parameters ${x}^2 = (0.09pm0.22)times 10^{-3}$ and $y = (4.6pm3.4)times 10^{-3}$ and the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates $R_D = (3.53pm0.13)times 10^{-3}$, where the uncertainties are statistical and systematic combined. Our measurement excludes the no-mixing hypothesis at the 5.1 standard deviation level.
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