Positivity testing conjecture for minimal circular planar networks

Let $L$ be the response matrix of a minimal circular planar network with $m$ edges, and let a noninterlaced minor of $L$ mean a minor whose row and column index sets are noninterlaced subsets of the boundary nodes. Positivity testing conjecture. Positivity for the network can be tested using $m$ noninterlaced minors of $L$. This is conjectured as an analogue of the result for well-connected networks, where $\binom{n}{2}$ small central minors suffice to test positivity. The source does not state whether this conjecture has been resolved.