The linear phase transition conjecture for random K-LSAT

Let $c^*_K$ be the constant introduced in the source's theorem for the optimal value ${\cal LP}(n,c)$ of the random K-LSAT linear program, and consider the corresponding feasibility problem obtained by setting all auxiliary variables $\psi_j$ to zero. K-LSAT linear phase transition conjecture. With high probability as $n\rightarrow\infty$, the random K-LSAT problem with $cn$ constraints is satisfiable if $c<c^*_K$ and is not satisfiable if $c>c^*_K$. The preceding theorem proves the analogous linear transition for the relaxed optimization problem, but not for feasibility with all $\psi$ variables fixed to zero; the source states that this feasibility transition remains unproved.