Non-Minkowski measurability of the family $C^r$ for all $r>2$

Let $C^r$ denote the self-similar fractal family defined in the paper, and let Minkowski measurability mean existence of a finite, positive Minkowski content. The conjecture for $C^r$. For every real number $r>2$, $C^r$ is not Minkowski measurable. The assertion is presented as a numerically investigated proof idea rather than a rigorously established result, extending the rigorously proved non-Minkowski measurability for $r\geq 30$ to the range $r>2$; its status remains open.