Isostatic conjecture for saturated triangulated disk packings

Let $\mathbf{P}$ be a saturated packing with a triangulated graph, consisting of finitely many disks in a torus, with $n_1,n_2,\dots,n_k$ disks of radii $r_1>r_2,\dots>r_k$, respectively, and density $\rho_0$. For an integer $m\geq 1$, consider any packing of a torus with $mn_1,mn_2,\dots,mn_k$ disks of the same respective radii.

Isostatic conjecture. The density $\rho$ of every such packing satisfies

$$\rho\leq\rho_0.$$

The conjecture asserts that scaling the numbers of disks in each size class cannot produce a packing denser than the given saturated triangulated packing. The source presents this as a broad conjecture and gives no resolution.