Positive-coefficient conjecture for Alexander polynomials of positive 3-braids

Let $w\in\mathrm{Br}_3$ be a positive word whose closure $\widehat w$ is a knot, with length $\#w=2m$. Let $f$ be the monic real polynomial defined from the Burau representation by

$$f(t+t^{-1})=t^{-m}\det(B_t(w)-I),$$

and define

$$h(y)=\operatorname{Re}\big(i^{-m}f(iy)\big)=\sum_{k=0}^{m/2}b_k y^{m-2k}.$$

Positive-coefficient conjecture. Every coefficient of $h$ is positive:

$$b_k>0\qquad(0\leq k\leq m/2).$$

This coefficient condition is supported by substantial experimental evidence and is intended to imply, through the proposition immediately following it, that all roots in the open right half-plane lie on the unit circle; that implication is conditional on the conjecture.