Ghorbani's determinant conjecture for Seidel matrices

Let $G_n$ be a simple graph on $V_n=\{v_1,\dots,v_n\}$, and let $S(G_n)$ be its Seidel matrix. Let $\det(S(G_n))$ denote its determinant. For a uniformly chosen graph on $V_n$, consider the proportion of graphs satisfying the determinant inequality below. Ghorbani's conjecture. The proportion of graphs $G_n$ on $V_n$ satisfying

$$\det(S(G_n))\geq n-1$$

tends to $1$ as $n$ tends to infinity. This conjecture is presented as an investigation of Haemers' Seidel-energy conjecture. The source paper proves the asserted asymptotic statement, so the conjecture is resolved.