The Hahn-Wilson conjecture on fp-spectra

Let $p$ be a prime, and let a spectrum of fp-type $n$ mean a bounded below, $p$-complete fp-spectrum whose associated thick subcategory of finite spectra has type at least $n+1$. Let $\mathrm{BP} \langle n \rangle$ denote the truncated Brown-Peterson spectrum, and let the thick subcategory generated by it be taken inside the category of $p$-complete spectra. Hahn-Wilson conjecture. Spectra of fp-type $n$ are exactly the thick subcategory of $p$-complete spectra generated by $\mathrm{BP} \langle n \rangle$. The conjecture is known in the cases $n=-1$ and $n=0$; the stated general structure result remains open. It would identify, up to thick subcategories, all fp-spectra with the expected chromatic examples.