Conjecture on main simple choreographies in the equal mass Newtonian N-body problem

Let $N\geq 3$ and consider the equal mass Newtonian $N$-body problem. A main simple choreography is a simple choreography that is not derived from a given simple choreography by traveling around it multiple times, by a continuation of the angular momentum, or by a combination of both. The trivial circle solution is the rotating $N$-gon.

Main choreography conjecture. For every $N\geq 3$, there is a main simple choreography solution different from the trivial circle solution. The number of such distinct main simple choreographies grows rapidly with $N$.

This conjecture arises from numerical discoveries and predicts that the Newtonian problem has many genuinely distinct simple choreographies beyond the rotating $N$-gon. The supplied text does not state a resolution, so its status remains open.