  Recently Ooguri and Yamazaki proposed a statistical model of melting crystals
to count BPS bound states of certain D-brane configurations on toric
Calabi--Yau manifolds [arXiv:0811.2801]. This construction relied on a set of
consistency conditions on the corresponding brane tiling, and in this note I
show that these conditions are satisfied for any physical brane tiling; they
follow from the conformality of the low energy field theory on the D-branes. As
a byproduct I also provide a simple direct proof that any physical brane tiling
has a perfect matching.
