The UTP conjecture for fibered knots

Let $K$ be a fibered knot in $S^3$. The UTP conjecture. $K$ fails the uniform thickness property if and only if $xi_K \cong xi_{std}$, and hence if and only if $K$ is fibered strongly quasipositive. Moreover, if a topologically non-trivial fibered knot $K$ fails the uniform thickness property, then it supports cablings that are transversally non-simple.

This conjecture generalizes the corresponding result for iterated torus knots. It is motivated by the relationship between fibered strongly quasipositive knots, the standard contact structure, maximal self-linking number, and transverse simplicity; the general case remains open.