The convex lower-bound conjecture for optimal resistor networks

Let $a(x)$) and $b(x)$ denote the paper's optimal-network functions, and let $f\colon[2,\infty)\to\mathbb{R}$ be the maximal convex function such that

$$f(2)\le 1$$

and

$$f(x)\le \frac{x-1}{x(x-2)}\quad\text{for all }x\in(2,\infty).$$

Convex lower-bound conjecture. For all $x$,

$$a(x)\ge 2f(x),$$

equivalently $b(x)\ge f(x)$.

The conjecture would identify the optimal value at every integer average degree at least four, where the corresponding upper bound is already known. It is posed as part of the problem of determining the optimal average resistance of resistor networks.