Jin's quadrisecant approximation conjecture

Let $K$ be a knot with finitely many quadrisecants intersecting $K$ in finitely many points. These intersection points divide $K$ into finitely many subarcs; replacing each subarc by a straight line produces the polygonal closed curve $\hat{K}$, called the quadrisecant approximation of $K$. The knot type records the ambient isotopy class of a knot, and the set of quadrisecants consists of the lines meeting the knot in four points.

Jin's conjecture. The quadrisecant approximation $\hat{K}$ has the knot type of $K$, and $K$ and $\hat{K}$ have the same set of quadrisecants.

S. Bai, C. Wang and J. Wang proved that this conjecture is false: they gave examples for which the approximation is not embedded or is a left-handed trefoil. Thus the conjecture is refuted, although variants for restricted classes such as minimum-stick-number polygonal knots or ideal knots may remain possible.