Lobb's proportionality conjecture for Gornik invariants

Let $K$ be a knot, and let $s_n(K)\in 2\mathbb{Z}$ denote the even integer determined by the Gornik homology of $K$ for each $n\geq 2$. Lobb's proportionality conjecture. For any knot $K$ and $m,n\geq 2$, one has

$$\frac{s_m(K)}{s_n(K)}=\frac{m-1}{n-1}.$$

Since $s_2(K)=-s(K)$, this conjecture would make every $s_n$ equivalent to Rasmussen's original invariant $s(K)$. Its falsity would have consequences for the non-degeneracy of Rasmussen's spectral sequences, and the authors were seeking a counterexample; the conjecture is therefore open in the source.