The triangle lower-bound conjecture for intersecting pseudocircle arrangements

Let ${\cal A}$ be a simple arrangement of $n\ge 3$ pairwise intersecting pseudocircles, and let $p_3({\cal A})$ denote the number of triangular cells. Triangle lower-bound conjecture. Every such arrangement contains at least $n-1$ triangles:

$$p_3({\cal A})\ge n-1.$$

The bound is known to be tight for $3\le n\le 7$ by computer-assisted exhaustive enumeration, while the paper leaves open whether it is a tight lower bound for every $n\ge 3$.