The Kepler light curves used to detect thousands of planetary candidates are susceptible to dilution due to blending with previously unknown nearby stars. With the automated laser adaptive optics instrument, Robo-AO, we have observed 620 nearby stars around 3857 planetary candidates host stars. Many of the nearby stars, however, are not bound to the KOI. In this paper, we quantify the association probability between each KOI and detected nearby stars through several methods. Galactic stellar models and the observed stellar density are used to estimate the number and properties of unbound stars. We estimate the spectral type and distance to 145 KOIs with nearby stars using multi-band observations from Robo-AO and Keck-AO. We find most nearby stars within 1 of a Kepler planetary candidate are likely bound, in agreement with past studies. We use likely bound stars as well as the precise stellar parameters from the California Kepler Survey to search for correlations between stellar binarity and planetary properties. No significant difference between the binarity fraction of single and multiple planet systems is found, and planet hosting stars follow similar binarity trends as field stars, many of which likely host their own non-aligned planets. We find that hot Jupiters are ~4x more likely than other planets to reside in a binary star system. We correct the radius estimates of the planet candidates in characterized systems and find that for likely bound systems, the estimated planetary candidate radii will increase on average by a factor of 1.77, if either star is equally likely to host the planet. We find that the planetary radius gap is robust to the impact of dilution, and find an intriguing 95%-confidence discrepancy between the radius distribution of small planets in single and binary systems.
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