Root-antiroot resistance maximization conjecture for fractal mother graphs

In the graph $\mathcal G(d,m,n)$, call the vertex $00\ldots 00$ the root and the vertex $10\ldots 00$ the antiroot. Let resistance refer to the effective resistance between vertices in the graph.

Root-antiroot conjecture. The root and the antiroot maximize the resistance in $\mathcal G(d,m,n)$.

The authors explicitly say that they have observed this assertion but have not been able to prove it, so it remains an open extremal-resistance problem.