4 problems

Generalized Marchal's conjecture. For any odd number of bodies, the $n$-gon choreography and the $n$-body figure eight are in the same continuation class.

Marchal's conjecture. The three-body equilateral triangle of Lagrange and the three-body figure eight are in the same continuation class.

Minimum-period conjecture. The minimum of $T$ among all figure-eight choreographic solutions is attained within the series $\alpha$; consequently,

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…