The MAX-SAT and SAT equivalence conjecture

Let $F(n,cn)$ be a uniformly random $k$-SAT formula with $n$ variables and $cn$ clauses, and let $f(n,cn)$ denote the expected maximum number of satisfiable clauses. For a fixed density $c$, consider the limiting expected satisfiable fraction and the limiting probability of satisfiability.

MAX-SAT and SAT equivalence conjecture. For any $c<0$,

$$\lim_{n\rightarrow\infty}\frac{f(n,cn)}{cn}=1$$

if and only if

$$\lim_{n\rightarrow\infty}\Pr\bigl(F(n,cn)\ \operatorname{is\ satisfiable}\bigr)=1.$$

The conjecture is intended to formalize a connection between the MAX-SAT limiting function conjecture and the usual satisfiability threshold conjecture. The source provides no resolution status beyond presenting it as a conjecture.