Telescopic growth conjecture for finite type h spectra

Let $X$ be a finite spectrum of type $h$, and let $\varpi_{\mathrm{T}(h)}(X,n)$ denote the size function measuring its telescopic homotopy groups through degree $n$. Telescopic growth conjecture. The telescopic homotopy groups satisfy

$$\log\left(\varpi_{\mathrm{T}(h)}(X,n)\right)=\binom{h}{2}\log(n)+O(1).$$

This conjecture is motivated by the calculation for the non-finite spectrum $y(h)$ and Morita invariance of size functions; it predicts the growth for every compact type $h$ spectrum while accounting for the extra polynomial generators present in $y(h)$.