  We solve the Landau equations to find the singularities of nine three-loop
7-point graphs that arise as relaxations of the graph studied in
arXiv:2211.16425. Along the way we establish that $Y{-}\Delta$ equivalence
fails for certain branches of solutions to the Landau equations. We find two
graphs with singularities outside the heptagon symbol alphabet; in particular
they are not cluster variables of ${\rm Gr}(4,7)$. We compare maximal residues
of scalar graphs exhibiting these singularities to those in $\mathcal{N}=4$
super-Yang-Mills theory in order to probe their cancellation from its
amplitudes.
