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We present measurements of the
time-dependent $CP$-violating
asymmetries in $B^0 \rightarrow K^0_S K^0_S K^0_S$ decays based
on 384 million $\Upsilon(4S)$
decays collected with the BABAR detector at the PEP-II
asymmetric-energy $B$ Factory at SLAC.
We obtain the $CP$ asymmetry parameters
$C = 0.02 \pm 0.21 \pm 0.05$ and
$S = -0.71 \pm 0.24 \pm 0.04$, where the first
uncertainties are statistical and the second systematic.
These results are consistent with standard model expectations.
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