Imaged companions in our Kepler control sample, showing magnitude differences in the Kepler band as functions of projected (left) on-sky or (right) physical separations (measured with respect to the primary). Circle markers are colored and sized by the RUWE values of the primary star; black square markers indicate systems that did not have RUWE values available in Gaia DR3. The cutoff for on-sky separations to be included in our sample was roughly twice the Kepler pixel size (∼8″).