Alternating quotients conjecture for periodic knots

Let $K\subset S^3$ be an alternating periodic knot, meaning that $K$ admits a finite-order symmetry of the pair $(S^3,K)$ with nonempty fixed-point set disjoint from $K$. The quotient is again a knot in the quotient $3$-sphere. Alternating quotients conjecture. The quotient of $K$ is alternating. This conjecture concerns the preservation of alternation under periodic quotients; the supplied text states it as a conjecture but gives no resolution status.