Folklore conjecture on boundary slopes: only torus knots have two

Establish whether nontrivial torus knots are the only knots in S^3 that have exactly two boundary slopes (the Seifert slope 0 and the cabling slope).

Background

The authors recall the classical link between A-polynomials and boundary slopes via the Newton polygon, where each edge slope corresponds to a boundary slope. Torus knots have precisely two boundary slopes, and a longstanding folklore conjecture asserts they are the only knots with this property.

An affirmative resolution would follow from the parallelogram Newton polygon characterization for A_K(M,L), tying the geometric boundary data to the algebraic invariants captured by the A-polynomial.