Extension of the finite-disk area bound for generalized Minkowski arrangements

Let $\sqrt{3}-1<\mu<1$, and let $\mathcal{F}$ be a finite $\mu$-arrangement of disks. Write $T$ for the total area of the disks, and let $I(\mathcal{F})$ and $O(\mathcal{F})$ denote the corresponding inner and outer regions. The area bound in Remark 3 is

$$T \leq \frac{4\cdot \arccos\left(\frac{1+\mu}{2}\right)}{(1+\mu)\cdot \sqrt{(3+\mu)(1-\mu)}}\operatorname{area}(I(\mathcal{F}))+\operatorname{area}(O(\mathcal{F})),$$

with equality if and only if every free digon in $\mathcal{F}$ is thick.

Finite-disk area-bound conjecture. The displayed statement in Remark 3 holds for every $\mu$-arrangement of finitely many disks with $\sqrt{3}-1<\mu<1$.

The paper presents this as an open question extending the proven range of the area estimate beyond the range established in the preceding argument. The notation for the regions and free digons is inherited from the paper.