Marchal's conjecture on the continuation class of the Lagrange triangle and figure eight

Let the three-body problem be considered with its equilateral triangle of Lagrange choreography and its figure-eight choreography. Two periodic orbits are in the same continuation class if one can be reached from the other by continuous variation of the energy.

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

This conjecture formalizes Marchal's proposed connection between the equilateral-triangle family and the figure-eight choreography; the source presents it as a motivation for numerical continuation studies, without asserting a resolution.