We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires super-polynomial time. To exhibit the framework, we revisit two famous problems in this paper. The particular results we prove are: MAX-3-SAT$(1,\frac{7}{8}+\epsilon)$ requires exponential time for any constant $\epsilon$ satisfying $\frac{1}{8} \geq \epsilon > 0$. In particular, the gap exponential time hypothesis (Gap-ETH) holds. MAX-3-LIN-2$(1-\epsilon, \frac{1}{2}+\epsilon)$ requires exponential time for any constant $\epsilon$ satisfying $\frac{1}{4} \geq \epsilon > 0$.

翻译：本文基于作者近期提出的理论，为建立近似难度结果提供了一种新方法。该方法允许直接证明：若将某个问题的近似程度推进至特定阈值以上，则需要超多项式时间。为展示这一框架，我们重新审视了文献中的两个著名问题。本文证明的具体结果为：对于任意满足$\frac{1}{8} \geq \epsilon > 0$的常数$\epsilon$，MAX-3-SAT$(1,\frac{7}{8}+\epsilon)$问题需要指数时间。特别地，间隙指数时间假说（Gap-ETH）成立。对于任意满足$\frac{1}{4} \geq \epsilon > 0$的常数$\epsilon$，MAX-3-LIN-2$(1-\epsilon, \frac{1}{2}+\epsilon)$问题也需要指数时间。