Stability conjecture for contact numbers of nearly congruent disks

Let $n\ge 2$ and consider a packing of $n$ circular disks whose radii all lie in an interval $[1-\epsilon,1]$. Stability conjecture. There exists an $\epsilon>0$ such that, for every such packing, the number of touching pairs is at most

$$\left\lfloor 3n-\sqrt{12n-3}\right\rfloor.$$

This conjecture asks whether Harborth's exact contact-number bound for congruent disks remains valid for disks whose radii are sufficiently close to one. The source describes this stability version as an open problem; it is relevant to the optimization of colloidal clusters, where maximizing contacts favors low potential energy.