Khot's bipartite d-to-1 conjecture

Fix an integer $d>1$. Let $\Phi=(X,Y,\Psi,W)$ be a weighted bipartite $d$-to-$1$ label-cover instance with label sets $\{1,\ldots,R\}$ and $\{1,\ldots,R/d\}$ and total edge weight $w(\Phi)=1$. A labeling $L$ assigns labels from the respective sets, and $w_L(\Phi)$ denotes the total weight of satisfied constraints. Khot's bipartite d-to-1 conjecture. For every $\gamma>0$ there exists a constant $R$ such that it is NP-hard to distinguish between the case that some labeling satisfies all constraints, so $w_L(\Phi)=1$, and the case that every labeling satisfies total weight at most $\gamma$.