Komlós' singularity probability conjecture for random Bernoulli matrices

Let $A_n$ be an $n$ by $n$ random matrix whose entries are independent Bernoulli random variables. Komlós' singularity probability conjecture. The probability that $A_n$ is singular satisfies

$${\bf P}(A_n\text{ is singular})=\left(\frac{1}{2}+o(1)\right)^n.$$

This conjecture asserts that the elementary obstruction coming from equal or opposite rows or columns gives the correct exponential order of the singularity probability. The source gives no resolution status.