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A search for $CP$ violation in $D^0 \to \pi^-\pi^+\pi^0$ decays is reported,using $pp$ collision data collected by the LHCb experiment from 2015 to 2018corresponding to an integrated luminosity of 6$fb^{-1}$. An unbinnedmodel-independent approach provides sensitivity to local $CP$ violation withinthe two-dimensional phase space of the decay. The method is validated using theCabibbo-favoured channel $\D^0 \to \K^-\pi^+\pi^0$ and background regions ofthe signal mode. The results are consistent with $CP$ symmetry in this decay.

Search for $CP$ violation in the phase space of $D^0 \to \pi^-\pi^+\pi^0$ decays with the energy test