Polynomial singularity bound conjecture for random regular digraphs

Let $M$ be a uniform random element of the set of $n\times n$ zero-one matrices with every row and column sum equal to $d$. Polynomial singularity conjecture. There are absolute constants $C,c>0$ such that, for every $3\leq d\leq n-3$,

$$\pr\big(\det(M)=0\big)\leq Cn^{-c}.$$

The conjecture extends the paper's polynomial singularity estimate to all nontrivial degrees in the stated range. It is presented as an open conjecture in the supplied text.