My theory is that if stars were as far away as mainstream cosmology claims they would be impossible to see. It would be physically impossible to generate a light that bright by any claimed mechanism. Intuitively this is obvious, but has anyone gone to the trouble of proving it?
It should be easy to prove, and this would in turn disprove the theory of the earth orbiting the sun in the manner claimed since there is generally no parallax effect and that in turn would expose mainstream cosmology as the hoax that it has always obviously been.
One test might be to look at the night sky at opposite ends of the earth. And compare the parallax effect of the planets with that of the stars. If there is a parallax effect in the planets but not the stars, this means the stars are far away. If there is a parallax effect in both this means the stars are close by. If there is no parallax effect in either then further investigation will be needed.
Another possibility is that the stars are close by but no parallax effect is observed because the stars are all roughly equally distant from the earth. But this would not conflict with the idea that the earth is orbiting the sun.
Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years
If stars are that far away, then any observed effect is going to be so tiny that you will need to be an expert in astronomy to be able to tell if it is "legit". I think Allen does not trust astronomers, and is only willing to fully accept results of experiments he can understand, in the same way that a vaccine skeptic might want to understand the medical studies himself rather than trust the conclusions of a medical expert.