The Jones-polynomial norm conjecture for closed braids

Let $\beta\in B_n$ be an $n$-braid, let $\widehat{\beta}$ be its closure, and let $V(t)$ denote the Jones polynomial of $\widehat{\beta}$. For a complex number $t$, choose a square root $\sqrt t$ consistently. Jones-polynomial norm conjecture. If $|t|=1$ and $|\arg t|<2\pi/n$, then

$$|V(t)|\leq (2\operatorname{Re}\sqrt t)^{n-1}.$$

This extends the norm estimates proved in the source for 3- and 4-braids. The source presents the general inequality as a conjecture and gives no resolution status.