Mundici's conjecture on sums of squared Farey gaps

Let $Q$ be an integer greater than $1$, let $S_2(Q)$ denote the sum of the squared distances between consecutive elements of the $Q$-th Farey sequence, and define

$$C(Q):=\frac{S_2(Q)Q^2}{\log Q}.$$

Mundici's conjecture. One has

$$C(Q)<3$$

for all $Q>1$.

This conjecture concerns the normalized sum of squared consecutive spacings in Farey sequences. It was proposed after checking the first $1000$ values of $Q$; the supplied source gives no resolution, so its status remains open.