The symmetric determinant magnitude conjecture for random sign matrices

Let $M_n^{\mathrm{sym}}$ be an $n\times n$ symmetric random sign matrix.

Symmetric determinant magnitude conjecture. With probability $1-o(1)$,

$$|\det M_n^{\mathrm{sym}}|=n^{(1/2-o(1))n}.$$

Nguyen's and Vershynin's least-singular-value results, together with the semicircle law, confirm this conjecture, so it is solved.