Shor's conjecture on the peak of normalized tree coefficients

Let $T$ be a tree with $n\geq 3$ vertices. Let $d_k(T)$ denote the normalized coefficients of the distance characteristic polynomial, defined from the coefficients $\delta_k(T)$ by

$$d_k(T)=|\delta_k(T)|/2^{n-k-2}.$$

A sequence is unimodal if it is nondecreasing up to some index and nonincreasing thereafter. Shor's conjecture. The normalized coefficients $d_0(T),\dots,d_{n-2}(T)$ are unimodal, with their peak between $\left\lfloor n/2\right\rfloor$ and $\left\lceil (1-1/\sqrt{5})n\right\rceil$.

This is a revised version attributed by Collins to Peter Shor after the Graham–Lovász peak-location claim was disproved. The survey does not provide evidence that this revised conjecture has been resolved.