Clique is hard to approximate within n1-ϵ

The author proves that unless NP=coR, Max Clique is hard to approximate in polynomial time within a factor n^1-ε for any ε>0. This is done by, for any δ>0, constructing a proof system for NP which uses δ amortized free bits. A central lemma, which might be of independent interest, gives sufficient conditions (in the form of a certain type of agreement) for creating a global function from local functions certain local consistency conditions