In this paper, we show that there is a Cantor set of initial conditions in the planar $4$‑body problem such that all four bodies escape to infinity in a finite time, avoiding collisions. This proves the Painlevé conjecture for the $4$‑body case, and thus settles the last open case of the conjecture.
"Non-collision singularities in a planar 4-body problem." Acta Math. 224 (2) 253 - 388, June 2020. https://doi.org/10.4310/ACTA.2020.v224.n2.a2