Three sign changes in the relative covariance for random orientations of $G(n,p)$

Let $G(n,p)$ be the random graph on $n$ vertices in which each edge is present independently with probability $p$, and orient every present edge independently and uniformly at random. Fix distinct vertices $s,a,b$, and let

$$R_n(p)=\frac{\mathbb{P}(a\not\to s,\ s\not\to b)-\mathbb{P}(a\not\to s)\mathbb{P}(s\not\to b)}{\mathbb{P}(a\not\to s,\ s\not\to b)}.$$

The three-sign-change conjecture. For $n\ge 27$, the relative covariance $R_n(p)$ changes sign at three critical probabilities $p_1(n)<p_2(n)<p_3(n)$.