Three-candidate Plurality is Stablest hardness consequence for MAX-3-CUT

Assume the Unique Games Conjecture and the three-candidate Plurality is Stablest Conjecture. Let $\alpha_{3}$ denote the relevant MAX-3-CUT approximation threshold.

Sharp hardness consequence. For every $\varepsilon>0$, it is NP-hard to approximate MAX-3-CUT within a multiplicative factor of $\alpha_{3}+\varepsilon$.

This is the stated reduction from the Unique Games Conjecture and Plurality is Stablest to sharp MAX-3-CUT hardness. It is a conditional complexity-theoretic consequence rather than an independent mathematical conjecture; the source gives no resolution of the assumed conjectures.