The maximum-satisfiable-clauses scaling conjecture for random K-SAT

Let $N(n,m)$ be the maximum number of clauses that can be satisfied by one assignment of $n$ variables in a random K-SAT instance with $m$ clauses, and let $c^*_K$ be the threshold from the linear phase transition conjecture. Maximum-SAT scaling conjecture. Assuming the linear phase transition conjecture holds, for every $c>c^*_K$ the limit

$$\lim_{n\rightarrow\infty}{N(n,cn)\over cn}$$

exists and is smaller than one. This conjecture concerns the limiting fraction of clauses satisfiable above the threshold; the source attributes it to earlier work and does not report a resolution.