Jp-speciality conjecture for adequate non-alternating links

Let $L$ be a link. Its Jones polynomial is called Jp-special when it is non-alternating or has gaps, and $L$ is adequate in the usual sense of link diagrams.

Jp-speciality conjecture. Every adequate non-alternating link is Jp-special.

The claim predicts that adequacy together with non-alternation forces the stated Jones-polynomial behaviour. The supplied text gives no resolution status.