Random $k$-SAT satisfiability threshold conjecture

For given $n$, $k\geq2$, and $p$, let $F_k(n,p)$ be the random $k$-SAT formula obtained by including each of the $\binom{2n}{k}$ possible $k$-clauses independently with probability $p$. Satisfiability conjecture. For each $k\geq2$, there exists $c_k>0$ such that for every $\varepsilon>0$:

• if $p\leq(1-\varepsilon)c_kn^{-1/(k-1)}$, then with high probability $F_k(n,p)$ is satisfiable;
• if $p\geq(1+\varepsilon)c_kn^{-1/(k-1)}$, then with high probability $F_k(n,p)$ is unsatisfiable.

This asserts a sharp satisfiability threshold at the stated scale, a central problem in random constraint satisfaction and average-case complexity. The supplied text does not report a resolution.