Impossible moons -- Transit timing effects that cannot be due to an exomoon

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.