Jones' conjecture on the writhe of minimal braid representations

Let $L$ be a link of braid index $b$, and let $B_1$ and $B_2$ be braid diagrams of $L$, each with $b$ strands. The writhe of a braid diagram is the signed crossing number. Jones' conjecture. The writhes of $B_1$ and $B_2$ are equal.

This is the Jones conjecture asserting that all minimal-strand braid representations of a link have the same algebraic crossing number. The source invokes it as an application of the Morton-Franks-Williams inequality, but does not state its resolution; the supplied status is therefore open.