There are several ways to verify parts of this theory.

The most promising is to research the claimed relative large eccentricity orbit anomaly of the moon.  This can be done by comparing the moons measured orbit data with calculated data.

This can make it possible to determinate whether such data is consistence with each other.. This theory that the Moon has a eccentricity anomaly that builds up during a 4½ years period, where after it cancel out the following 4½ years period.
 
We might also be lucky also to observation that stars in galaxies at the edge of the visible universe explode almost simultaneously. The reason why we can see this all of the time is that after a while exploding galaxies will not be transparent.

The final evidence is that this theory could have solved the underlying cause of many mysteries.
 

Normally, detection of a single mystery often leads to very large well-founded scepticism.

In this case, sees a wide range of mysteries to be solved in a very simple way, without in any way appear to be in conflict with any known true knowledge, and which, incidentally, is not and probably cannot be disproved, - Nor not mathematically.

Finally, further contributions to this theory from others could further strengthen it, including such mathematical contributions. For example here