  Solid partitions are the 4D generalization of the plane partitions in 3D and
Young diagrams in 2D, and they can be visualized as stacking of 4D unit-size
boxes in the positive corner of a 4D room. Physically, solid partitions arise
naturally as 4D molten crystals that count equivariant D-brane BPS states on
the simplest toric Calabi-Yau fourfold, $\mathbb{C}^4$, generalizing the 3D
statement that plane partitions count equivariant D-brane BPS states on
$\mathbb{C}^3$. In the construction of BPS algebras for toric Calabi-Yau
threefolds, the so-called charge function on the 3D molten crystal is an
important ingredient -- it is the generating function for the eigenvalues of an
infinite tower of Cartan elements of the algebra. In this paper, we derive the
charge function for solid partitions. Compared to the 3D case, the new feature
is the appearance of contributions from certain 4-box and 5-box clusters, which
will make the construction of the corresponding BPS algebra much more
complicated than in the 3D.
