  Exomoons are predicted to produce transit timing variations (TTVs) upon their
host planet. Unfortunately, so are many other astrophysical phenomena - most
notably other planets in the system. In this work, an argument of reductio ad
absurdum is invoked, by deriving the transit timing effects that are impossible
for a single exomoon to produce. Our work derives three key analytic tests.
First, one may exploit the fact that a TTV signal from an exomoon should be
accompanied by transit duration variations (TDVs), and that one can derive a
TDV floor as a minimum expected level of variability. Cases for which the TDV
upper limit is below this floor can thus be killed as exomoon candidates.
Second, formulae are provided for estimating whether moons are expected to be
'killable' when no TDVs presently exist, thus enabling the community to
estimate whether it's even worth deriving TDVs in the first place. Third, a TTV
ceiling is derived, above which exomoons should never be able to produce TTV
amplitudes. These tools are applied to a catalog of TTVs and TDVs for two and
half thousand Kepler Objects Interest, revealing over two hundred cases that
cannot be due to a moon. These tests are also applied to the exomoon candidate
Kepler-1625b i, which comfortably passes the criteria. These simple analytic
results should provide a means of rapidly rejecting putative exomoons and
streamlining the search for satellites.
