The experimental basis for the purported proof of heliocentricity is vast. Fortunately we collected up all of the submissions to our "can you prove heliocentricity?" challenge which began December 25, 2015.
Experimentation and Heliocentricity
Argument from Ignorance
Popular science (SciPop) doesn't have any positive confirmation for the hypothesis that nuclear decay rates have always been constant. What's a paradigm to do in a situation like this? Go for negative confirmation.