Primitive/Seifert position conjecture for tunnel-number-one knots

A Seifert-fibered surgery is a Dehn surgery on a knot that produces a Seifert-fibered space. A knot has tunnel number one if its exterior admits a genus-two Heegaard splitting, and a primitive/Seifert position is a position in which the knot is primitive on one handlebody side and Seifert on the other; its surface slope is the slope represented by the relevant boundary curve.

Primitive/Seifert position conjecture. Any Seifert-fibered surgery on a hyperbolic tunnel-number-one knot arises from a primitive/Seifert position whose surface slope corresponds to the surgery slope.

The paper presents this as another conjecture partially supported by its main theorem and corollary. The supplied text does not specify whether it has been resolved.