How to loop a confined particle system setup up with collisions and zero deaths

Question

In a particle simulation where no particles die, is there a way to get the initial particle position to match the end position so that the simulation forms a loop? I have a particle simulation where the particles collide with the inner walls of a cube. I have searched for techniques for looping particles but only found techniques that loop particles that at some moment die off. In this particular case no particles die. The only way I imagine that the loop can work in this case is if each particle's initial position matches its final position. I am not sure but maybe one of the possible solutions would be to use the Sverchok addon to cache the particle's positions at the beginning of the simulation (frame 1) and then somehow interpolate frame 1's location values with the simulation's final frame's (frame 100) position values. I still haven't figured out how to do this and I am guessing that this would have to be done over a range of frames so that the initial and final positions "blend". Attached is an image illustrating the setup.

The following is my first attempt at a solution using Sverchok. It only works for a very small count of particles. For a count of 10 particles I am getting choppy motion and crashes. I still don't know why.

Answer 1

The solution I found for this was to bake the cyclic polylines generated from the particles and then pass those baked geometries' data to a curve zero-twist frame node. For looping the particles, the curve's T parameter was randomly offset for each particle and controlled by the scene's frame count. This is the result: https://sketchfab.com/3d-models/simple-density-explainer-animation-8a73b2d51f7747ef8701bf3056a827c2