  In this paper we analyze the singular set in the Stefan problem and prove the
following results:
  - The singular set has parabolic Hausdorff dimension at most $n-1$.
  - The solution admits a $C^\infty$-expansion at all singular points, up to a
set of parabolic Hausdorff dimension at most $n-2$.
  - In $\mathbb R^3$, the free boundary is smooth for almost every time $t$,
and the set of singular times $\mathcal S\subset \mathbb R$ has Hausdorff
dimension at most $1/2$.
  These results provide us with a refined understanding of the Stefan problem's
singularities and answer some long-standing open questions in the field.
