3 problems

Nonuniqueness conjecture. For $d\geq 2$, uniqueness is not guaranteed in general for the constrained approximate optimal transport map problem.

Low-density Jacobian conjecture. Separatrices in the pushforward density follow from the intrinsic difficulty of capturing the correct slope, or Jacobian determinant, of $S$ in reg…

Multimodal Langevin-sampling conjecture. The observed separatrices further demonstrate the difficulty of sampling from multimodal distributions with Langevin dynamics.