Few-differentials conjecture for the Adams spectral sequence

Let $\pi_n\mathbb{S}$ denote the $n$th stable stem and let $\operatorname{rank}_p$ denote its rank at the prime $p$. Few-differentials conjecture. The stable stems satisfy

$$\log\left(\operatorname{rank}_p(\pi_n\mathbb{S})\right)=\Theta(\log(n)^3).$$

This conjecture says that the Adams spectral sequence has few differentials in the sense that its abutment has the same order of logarithmic growth as the relevant Adams $E_2$-page bounds. It is presented as an expectation based on the telescope conjecture and remains open in the supplied text.