Pairwise inequivalence conjecture for seven Dickson-polynomial skew Hadamard difference sets

Let $m$ be an odd integer with $m>7$ and $m\not\equiv 0 \pmod{3}$. In the additive group $({\mathbb F}_{3^m},+)$, let ${\rm P}$, ${\rm DY}(1)$, ${\rm DY}(-1)$, ${\rm RT}(1)$, ${\rm RT}(-1)$, $D_1$, and $D_{-1}$ denote the seven skew Hadamard difference sets constructed in the paper. Pairwise inequivalence conjecture. These seven skew Hadamard difference sets are pairwise inequivalent. For $m=5$ and $m=7$, the paper verifies pairwise inequivalence using the distributions, or the extrema, of their triple intersection numbers; the conjecture extends this distinction to all odd $m>7$ not divisible by $3$.