So, just using a 1/r relation for potential energy, and the ratio of perhelion to aphelion, this thing has only ~3% of the potential energy at the outermost poi

So, just using a 1/r relation for potential energy, and the ratio of perhelion to aphelion, this thing has only ~3% of the potential energy at the outermost point in is orbit compared to the innermost point. That's practically miraculous on its own, isn't it? The paper authors are actually arguing for a Planet X which has had periodic encounters much weaker than that at a distance of a few hundred au.