Conjecture on the number of distribution-equivalence classes of length-2 mesh patterns

Let $p_1$ and $p_2$ be mesh patterns of length $2$. They are equivalent when $s_{n,k}(p_1)=s_{n,k}(p_2)$ for all $n,k\geq0$, where $s_{n,k}(p)$ counts $n$-permutations containing exactly $k$ occurrences of $p$. Distribution-class conjecture. There are exactly $105$ equivalence classes with respect to distribution for mesh patterns of length $2$. The paper establishes bounds between $105$ and $108$ classes and presents this exact count as the remaining conjectural value.