dSKP diagonal singularity conjecture

Let $\mathcal{L}$ be the lattice on which the dSKP recurrence is defined, let $x:\mathcal{L}\to\hat{\mathbb{C}}$ be a solution, and set $a_{i,j}=x(i,j,[i+j]_2)$. Suppose $m\in 2\mathbb{N}+2$ and $p\in 2\mathbb{N}+2$, that

$$a_{i,j}=a_{i+m,j+m}=a_{i+p-1,j+p+1}$$

for all $(i,j)\in\mathbb{Z}^2$, and that

$$a_{i,j}=a_{i+1,j+1}$$

for all $(i,j)\in\mathbb{Z}^2$ with $[i+j]_4=0$. dSKP diagonal singularity conjecture. Either

$$x(i,j,m)=x(i+1,j+1,m)$$

for every $(i,j)\in\mathbb{Z}^2$ with $[i+j]_4=[m]_4$, or the same equality holds for every $(i,j)\in\mathbb{Z}^2$ with $[i+j]_4=[m+2]_4$. This conjecture describes a singularity for dSKP initial data with the specified periodicities, distinct from the previously discussed pentagram-map singularity. The source gives no resolution status.