  Solid modules over $\mathbb{Q}$ or $\mathbb{F}_p$, introduced by Clausen and
Scholze, are a well-behaved variant of complete topological vector spaces that
forms a symmetric monoidal Grothendieck abelian category. For a discrete field
$k$, we construct the category of ultrasolid $k$-modules, which specialises to
solid modules over $\mathbb{Q}$ or $\mathbb{F}_p$. In this setting, we show
some commutative algebra results like an ultrasolid variant of Nakayama's
lemma. We also explore higher algebra in the form of animated and
$\mathbb{E}_\infty$ ultrasolid $k$-algebras, and their deformation theory. We
focus on the subcategory of complete profinite $k$-algebras, which we prove is
contravariantly equivalent to equal characteristic formal moduli problems with
coconnective tangent complex.
