Khovanov-homology signature bounds conjecture

Let $K$ be a knot whose integral Khovanov homology $Kh(K,\mathbb{Z})$ is supported on diagonals

$$\{d_1,d_2,\ldots,d_w\},$$

where $w$ is the width of its Khovanov homology, and let $\sigma(K)$ denote its signature. Khovanov-homology signature bounds conjecture. The signature lies strictly between the extreme diagonals:

$$d_1<-\sigma(K)<d_w.$$

The source calls this a folklore conjecture dating from the development of Khovanov homology; no resolution is given in the supplied text.