Order-preservation conjecture for equal-mass three-body syzygies

Let three equal masses be released from rest in a scalene triangular configuration whose side lengths satisfy

$$r_{12}<r_{13}<r_{23}.$$

Let $r_{ij}(t)$ be the distance between masses $i$ and $j$, and let $t$ be the instant of first syzygy. Equal-mass order-preservation conjecture. Under Newtonian attraction, the inequalities persist throughout the motion up to first syzygy:

$$r_{12}(t)<r_{13}(t)<r_{23}(t).$$

This is suggested by the preceding minimizer theorem, which establishes the corresponding inequalities for the relevant variational minimizers. The broader assertion for every equal-mass release from rest in such a scalene shape is presented as a conjecture, with no resolution supplied here.