Uniqueness of local moves preserving electrical equivalence in punctured-disk networks

Let an rnpd be a resistor network embedded in a disk with exactly one boundary vertex placed inside the disk, and let two such graphs be electrically equivalent when they have the same response matrix. The paper lists local moves on these networks, including the moves introduced in this work.

Local-move completeness conjecture. Any two electrically equivalent graphs associated to rnpds are connected by the local moves stated in this section.

This would give a complete classification of the local transformations preserving electrical equivalence for resistor networks in a punctured disk. The source presents the assertion as a conjecture and provides no resolution.