North Pole maximal directed discrepancy conjecture for Polar Coordinates

Let $n\in\mathds{Z}^+$, and consider the point configuration called Polar Coordinates with parameter $n$. For a direction on the sphere, let the directed Discrepancy be the discrepancy measured in that direction. North Pole maximal directed discrepancy conjecture. Polar Coordinates with parameter $n$ has maximum directed Discrepancy in the direction of the North Pole. This conjecture asserts that the North Pole is a worst-case direction for the directional discrepancy of this highly symmetric point configuration; the paper proposes it based on observations and seeks evidence toward a proof.