  In this paper, we investigate the relationship between pinch point
singularities observed in energy- and momentum-resolved spectroscopy and
topologically non-trivial gapless points. We show that these singularities are
a universal signature, and that the Berry flux encoded must be $n\pi$ for an
$n-$fold pinch point under suitable symmetry protection. Our results apply to
most systems and are independent of their microscopic details. Hence they
provide a new way to identify topological phases without requiring detailed
knowledge of the microscopic model. Our work can be readily applied in
spectroscopy experiments on various platforms.
