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We prove that the set of singular times for weak solutions of the homogeneousBoltzmann equation with very soft potentials constructed as in Villani (1998)has Hausdorff dimension at most $\frac{|\gamma+2s|}{2s}$ with $\gamma \in[-4s,-2s)$ and $s \in (0,1)$.

Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials