Integrality conjecture for Seifert-fibered surgeries on hyperbolic knots

A Seifert-fibered surgery is a Dehn surgery on a knot that produces a Seifert-fibered space; a surgery is integral when its slope is an integral slope. A hyperbolic knot is a knot in $S^3$ whose complement admits a complete finite-volume hyperbolic structure.

Integrality conjecture. Any Seifert-fibered surgery on a hyperbolic knot in $S^3$ is integral.

This conjecture is presented as one of the conjectures partially supported by the paper's results. Its resolution is not specified in the supplied text.