The disk obstruction conjecture for traversing boundary concave vector fields

Let $D^{n+1}$ be the standard $(n+1)$-disk, and call a vector field traversing if all of its trajectories are appropriately traversing, with no closed trajectories. A vector field is boundary concave when its boundary tangencies have the concave orientation described in the paper.

Disk obstruction conjecture. The standard $(n+1)$-disk $D^{n+1}$ does not admit a traversing boundary concave vector field.

This conjecture extends the observed obstruction for the $2$-disk, contrasting with the existence of boundary generic concave non-vanishing fields on $D^3$ that are not traversing. Its status is not resolved in the supplied text.