In recent work with Yair Hayut, we obtained a model in which, for every $n$, there is a normal ideal $\mathscr{J}$ on $\omega_{n+1}$ such that $\mathscr{P}(\omega_{n+1})/\mathscr{J}$ is forcing-equivalent to $\mathrm{Col}(\omega_n,\omega_{n+1})$. It follows from work of Bannister-Bergfalk-Todorcevic-Moore that in this model, the partition hypotheses they introduced, $\mathrm{PH}_n(\omega_m)$, hold for all $n < m$. In this talk, we sketch how the existence of these ideals implies the partition hypotheses and then outline our consistency proof.