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We analyze a 37 pb$^{-1}$ data sample collected with the SND detector at theVEPP-2000 $e^+e^-$ collider in the center-of-mass energy range 1.05--2.00 GeVand present an updated measurement of the $e^+e^- \to \omega \pi^0 \to\pi^0\pi^0\gamma$ cross section. In particular, we correct the mistake inradiative correction calculation made in our previous measurement based on apart of the data. The measured cross section is fitted with the vector mesondominance model with three $\rho$-like states and used to test the conservedvector current hypothesis in the $\tau^-\to\omega\pi^-\nu_{\tau}$ decay.

Updated measurement of the $e^+e^- \to \omega \pi^0 \to \pi^0\pi^0\gamma$ cross section with the SND detector