The $\frac{3\pi}{2}$-open spanning path conjecture

Let $S$ be a finite point set in general position in the plane. A spanning path of $S$ is a plane straight-line path containing every point of $S$. Such a path is $\alpha$-open when all angles relevant to its openness are at most $\alpha$.

$\frac{3\pi}{2}$-open spanning path conjecture. Every finite point set in general position in the plane has a $\frac{3\pi}{2}$-open spanning path.

This is the paper's concluding formulation of the conjectured bound for spanning paths in general position. The paper establishes a non-tight bound of $\frac{5\pi}{4}$ and leaves the stated existence claim unresolved.