The satisfiability threshold conjecture for random k-SAT

Let $F$ be a uniformly random proper $k$-SAT formula with $n$ variables and $cn$ clauses, where each clause contains $k$ distinct variables, each possibly complemented, and clauses may be repeated. Write $F(n,cn)$ for this random formula, and let a property hold almost surely when its probability tends to $1$ as $n\rightarrow\infty$.

Satisfiability threshold conjecture. For each $k$ there exists a threshold density $c_k$, such that for any positive $\varepsilon$, for all $c<c_k-\varepsilon$, $F(n,cn)$ is almost surely satisfiable, and for all $c>c_k+\varepsilon$, $F(n,cn)$ is almost surely unsatisfiable.

The conjecture asserts a sharp limiting satisfiability transition analogous to the known $2$-SAT threshold. For large $k$, satisfiability and unsatisfiability density bounds are asymptotically equal, but the existence of the threshold remains open in the source.