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In this paper we document the modifications introduced to the previous version of the Resonance Chiral Lagrangian current ({\it Phys.Rev.} {\bf D86} (2012) 113008) of the $\tau^\pm \to \pi^\pm \pi^\pm \pi^\mp \nu_\tau$ decay which enable the one dimensional distributions measured by the BaBar collaboration to be well modeled.
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