In my other post titled "Short period comets - proof of Planet X's recent passage", I discussed that whatever event or reason is used to explain the Kuiper cliff, or the nudging of the leftover debris in the Kuiper Belt, it must be an event which occurred less than 10,000 years ago, since we know for a fact that some short period comets have minimum lifetimes of only 10,000 years.
I agree. The non-Planet X explanations for the Kuiper belt require that the belt be established billions of years ago in a singular or at least non-periodic event.
I do not agree that the existence of short period comets is proof of a periodic Planet X-like perturbation.
Consider, for example, the Trojan asteriods in Jupiter's orbit. These asteroids are in resonance with Jupiter's orbit, and have trajectories around the L4 and L5 Lagrange points. That is why they are still there, and have not either crashed into a planet or been ejected from the solar system.
- Only an actual Lagrange point is stable. The vicinity of a Lagrange point is only quasi-stable. A single asteroid at the L4 Lagrange point may well stay there forever, but all the other asteroids near the L4 Lagrange point are therefore potentially in unstable orbits (although it may take thousands, millions, or billions of years for these orbits to decay).
- A Lagrange point only technically exists for an infinitesimally small mass between two larger masses. Obviously the asteroids themselves, while certainly possessing very small masses, are not infinitesimal. Also the Solar system is certainly not a 2-body problem. Therefore the `Lagrange points' in the Solar system are not true Lagrange points, only approximations thereof. Therefore even objects directly at the so-called `Lagrange points' are potentially in unstable orbits.
- It is impossible to analytically solve the 3-body problem, let alone a 1000-body problem. Therefore even in a Solar system consisting of only the Sun, Jupiter, and a single Trojan asteroid it is impossible to say whether or not that asteroid is in a stable orbit. Obviously our Solar system is more complicated than this.
Indeed, it is far more likely, in my opinion, that the occasional small perturbations from neighbouring small-body asteroids and such is responsible for sporadically generating short period comets than a periodic massive perturbation from an elliptical planet. Such a planet would probably leave several large, and easily observed, holes in the Kuiper and asteroid belts (if it came that close).