Octad picture stable-reduction conjecture for plane quartics

Let $C$ be a smooth plane quartic over a non-archimedean local field of residue characteristic $p \neq 2$, and let $O$ be any Cayley octad of $C$. The octad picture of $O$ is the picture obtained by overlaying the pictures of the compatible building blocks in its valuation-data decomposition.

Octad picture stable-reduction conjecture. The stable reduction type, including whether or not it is hyperelliptic, of any smooth plane quartic over any non-archimedean local field of residue characteristic $p \neq 2$ is determined by the octad picture of any of its Cayley octads.

This is the paper's central conjecture. It proposes that octad pictures provide the plane-quartic analogue of cluster pictures, encoding both stable reduction type and hyperelliptic reduction, but the general assertion remains open.