Arithmetic progression conjecture for weakly fractal matroid classes

Let ${\mathcal M}$ be a minor-closed class of matroids, and let $\Gamma_{\mathcal M}(n)$ denote the proportion of $n$-element matroids in the class's boundary, namely its excluded minors, among the members of the class together with its excluded minors. The class is weakly fractal when the sequence $\Gamma_{\mathcal M}(1),\Gamma_{\mathcal M}(2),\Gamma_{\mathcal M}(3),\ldots$ has an infinite subsequence converging to one. Arithmetic progression conjecture. There exist integers $a$ and $b$ such that the sequence

$$\Gamma_{\mathcal M}(a+b),\ \Gamma_{\mathcal M}(2a+b),\ \Gamma_{\mathcal M}(3a+b),\ldots$$

converges to one. The conjecture asks whether every weakly fractal class has a subsequence with this regular arithmetic-progression form; the source verifies it for the class of minors of spikes considered there, with $a=2$ and $b=0$.