Prasad–Saeki braid conjecture for torsion in Khovanov homology

Consider the Khovanov homology of closures of braids, where $p$ is prime and $r$ is a positive integer.

Prasad–Saeki braid conjecture. The Khovanov homology of a closed $3$-braid can have only $\mathbb{Z}_2$-torsion. The Khovanov homology of a closed $4$-braid cannot have odd torsion, and can have only $\mathbb{Z}_2$- and $\mathbb{Z}_4$-torsion. More generally, the Khovanov homology of a closed $n$-braid cannot have $p$-torsion for $p>n$, and cannot have $\mathbb{Z}_{p^r}$-torsion for $p^r>n$.

The paper introduces counterexamples to parts (2') and (3') for $p=2$, so the listed claim is refuted at least in those parts. The status of the remaining parts is not resolved by the supplied excerpt.