The maximum-feasible-subset scaling conjecture for random K-LSAT

Consider the random K-LSAT linear program with $n$ variables and $m$ constraints, with all auxiliary variables $\psi$ set to zero. Let $N(n,m)$ be the maximum cardinality of a feasible subset of the constraints $C_j$, and let $c^*_K$ be the K-LSAT threshold introduced in the source. Maximum-feasible-subset scaling conjecture. For every $c>0$, the limit

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

exists. Moreover, this limit is strictly smaller than one for every $c>c^*_K$. The conjecture is presented as an open analogue of the maximum-SAT conjecture for the generalized linear-programming relaxation.