  We study discrete Lorentzian spectral geometry by investigating to what
extent causal sets can be identified through a set of geometric invariants such
as spectra. We build on previous work where it was shown that the spectra of
certain operators derived from the causal matrix possess considerable but not
complete power to distinguish causal sets. We find two especially successful
methods for classifying causal sets and we computationally test them for all
causal sets of up to $9$ elements. One of the spectral geometric methods that
we study involves holding a given causal set fixed and collecting a growing set
of its geometric invariants such as spectra (including the spectra of the
commutator of certain operators). The second method involves obtaining a
limited set of geometric invariants for a given causal set while also
collecting these geometric invariants for small `perturbations' of the causal
set, a novel method that may also be useful in other areas of spectral
geometry. We show that with a suitably chosen set of geometric invariants, this
new method fully resolves the causal sets we considered. Concretely, we
consider for this purpose perturbations of the original causal set that are
formed by adding one element and a link. We discuss potential applications to
the path integral in quantum gravity.
