Powers-of-two torsion conjecture for Khovanov homology

Let $L$ be a link, and consider its integral Khovanov homology. Torsion has order $p$ if it contains an element whose order is $p$.

Powers-of-two torsion conjecture. The Khovanov homology of every link has no torsion of order $p$ for any $p$ other than a power of $2$.

The conjecture reflects the computational observation that only powers of $2$ had appeared as torsion orders. The supplied text gives no resolution status.