The third critical probability conjecture for relative covariance in random orientations

Let $p_3(n)$ denote the third critical probability at which the relative covariance of paths in $\vec G(n,p)$ changes sign, where $p_1(n)<p_2(n)<p_3(n)$ are the three critical probabilities conjectured to exist for $n\geq 27$. Third critical probability conjecture. For all $n\geq 27$,

$$p_3(n)<1/2.$$

This is part of the paper's conjectural description of the sign changes of the relative covariance; the supplied source gives no evidence that this assertion has been resolved.