The tightness characterization of minimal growth rate

Let $H$ be a handlebody with invariant measured lamination $\boldsymbol{\Lambda}$, and let the growth rate refer to the associated irreducible automorphism. A lamination is tight when it admits no growth-reducing tightening disc isotopy, as in the preceding construction. Tightness characterization. The growth rate is minimal if and only if the lamination $\Lambda$ is tight.

This conjecture proposes that tightness exactly characterizes minimal growth among the laminations considered in the paper. The supplied text gives the motivation from examples but does not state a proof or resolution.