With their smaller radii and high cosmic abundance, transiting planets around cool stars hold a unique appeal. As part of our on-going project to measure the occurrence rate of extrasolar moons, we here present results from a survey focussing on eight Kepler planetary candidates associated with M-dwarfs. Using photodynamical modeling and Bayesian multimodal nested sampling, we find no compelling evidence for an exomoon in these eight systems. Upper limits on the presence of such bodies probe down to $sim0.4M_{oplus}$ in the best case. For KOI-314, we are able to confirm the planetary nature of two out of the three known transiting candidates using transit timing variations. Of particular interest is KOI-314c, which is found to have a mass of $1.0_{-0.3}^{+0.4}M_{oplus}$, making it the lowest mass transiting planet discovered to date. With a radius of $1.61_{-0.15}^{+0.16}R_{oplus}$, this Earth-mass world is likely enveloped by a significant gaseous envelope comprising $geq17_{-13}^{+12}$% of the planet by radius. We find evidence to support the planetary nature of KOI-784 too via transit timing, but we advocate further observations to verify the signals. In both systems, we infer that the inner planet has a higher density than the outer world, which may be indicative of photo-evaporation. These results highlight both the ability of Kepler to search for sub-Earth mass moons and the exciting ancillary science which often results from such efforts.
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