Asterodensity profiling (AP) is a relatively new technique for studying transit light curves. By comparing the mean stellar density derived from the transit light curve to that found through an independent method, AP provides information on several useful properties such as orbital eccentricity and blended light. We present an AP survey of 41 Kepler Objects of Interest (KOIs), with a single transiting candidate, for which the target star's mean stellar density has been measured using asteroseismology. The ensemble distribution of the AP measurements for the 31 dwarf stars in our sample shows excellent agreement with the spread expected if the KOIs were genuine and have realistic eccentricities. In contrast, the same test for the 10 giants in our sample reveals significant incompatibility at 4σ confidence. While extreme eccentricities could be invoked, this hypothesis requires four of the KOIs to contact their host star at periastron passage, including the recently claimed confirmation of Kepler-91b. After carefully examining several hypotheses, we conclude that the most plausible explanation is that the transiting objects orbit a different star to that measured with asteroseismology—cases we define as false-positives. Based on the AP distribution, we estimate a false-positive rate (FPR) for Kepler's giant stars with a single transiting object of FPR 70% ± 30%.
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