Håstad's general-graph inapproximability result supplies the hardness premise used by the reduction. We use its equivalent rational promise-gap form. For every integer $q>2$, a bounded-error polynomial-step algorithm distinguishing $n$-vertex graphs $H$ with $\alpha(H)\leq n^{1/q}$ from those with $n^{1-1/q}\leq\alpha(H)$ would imply $NP\subseteq BPP$.

This concept only defines that premise. It does not assert Håstad's result as an archive axiom; the main theorem of this submission is the implication from this premise to the triangle-free inapproximability conclusion.