  We compute the leading (first-type Landau) singularities of a certain
four-loop 7-point graph that is related to the 7-point ``ziggurat'' graph by
the graphical moves familiar from equivalent circuit theory. We find perfect
agreement with a subset of the ``heptagon symbol alphabet'' that has appeared
in the context of planar $\mathcal{N}=4$ super-Yang-Mills theory. The remaining
heptagon symbol letters are found in its subleading Landau singularities, which
we address in a companion paper.
