I will. In the sense of "proven" meaning demonstrated as necessarily true by rigorous logical argument -- or in the sense of "proven" meaning that, by any means, any possible contradictory claims have been presumptively eliminated -- heliocentrism is NOT "proven". It is a theory. The purpose of a theory is to explain facts. Heliocentrism explains facts, that is: the specific polar coordinates, wrt the earth, of the sun and the other planets at specific times.
It is logically possible that other theories might explain the same facts, and explain them better. Indeed it is an historical fact that other theories HAVE at times explained these facts and explained them better, even though heliocentrism prevailed in the end.
Even though (nearly) everyone thinks that heliocentrism actually IS true, and will continue to prevail, and will not be replaced by any substantively divergent theory, this does not change its status as a theory.
I suggest that, in principle, the theory could become an observed fact. This would require stationing an observatory above the plane of the solar system, located above the sun, so that it would remain stationary with respect to the sun. From that vantage point, the motion of the earth could be observed and recorded. At the end of a year, we would have taken the theory and reduced it to an observed fact. The tape which recorded the observations could be played for anyone who wanted to see the evidence. Not only that, the observation could always be repeated, as desired.
Seems to me that our trips to the Moon, and probes to other planets prove the theory quite well. If it was false we could not have made it. Let's remember that very accurate measurements had to be made to accomplish these tasks. In addition, present day instruments I think can certainly verify it (and have verified it) in various ways.