The integrality conjecture for Seifert fibered surgery on hyperbolic knots

A Seifert fibered surgery is a Dehn surgery on a knot whose resulting $3$-manifold is Seifert fibered. The integrality conjecture. Any Seifert fibered surgery on a hyperbolic knot is integral. This is one of the biggest open problems in the study of exceptional Dehn surgery; the paper establishes the absence of non-integral small Seifert fibered surgeries for the pretzel-knot families it considers, but the general conjecture remains open.