Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that, for any e > 0, it is NP-hard to, given a satisfiable instance of Max-NTW (Not-2), find an assignment that satisfies a fraction 5/8 + e of the constraints. This, up to the existence of e, matches the approximation ratio obtained by the trivial algorithm that just picks an assignment at random and thus the result is tight. Said equivalently the result proves that Max-NTW is approximation resistant on satisfiable instances and this makes our understanding of arity three Max-CSPs with regards to approximation resistance complete.
['Johan Håstad']
I am writing a research paper on a idea On the NP-hardness of Max-Not-2
[{"from": "human", "value": "I am writing a research paper on a idea On the NP-hardness of Max-Not-2"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that, for any e > 0, it is NP-hard to, given a satisfiable instance of Max-NTW (Not-2), find an assignment that satisfies a fraction 5/8 + e of the constraints. This, up to the existence of e, matches the approximation ratio obtained by the trivial algorithm that just picks an assignment at random and thus the result is tight. Said equivalently the result proves that Max-NTW is approximation resistant on satisfiable instances and this makes our understanding of arity three Max-CSPs with regards to approximation resistance complete."}]