The strong Fox conjecture for alternating knots

Let $K \subset S^3$ be an alternating knot. Its Alexander polynomial is

$$\Delta_K(t)=\sum a_i t^i.$$

Here a polynomial is log-concave when its coefficient sequence satisfies $a_{i-1}a_{i+1}\leq a_i^2$ for every relevant index. Strong Fox conjecture. The Alexander polynomial $\Delta_K(t)$ is log-concave. This strengthens Fox's trapezoidal conjecture, since log-concave sequences are unimodal. The conjecture concerns a broad class of alternating knots and is motivated by the extensive evidence for unimodality of their Alexander-polynomial coefficients.