Inductive-freeness conjecture for arrangements of ideal type

Let $\Phi$ be a reduced root system with Weyl arrangement $\mathscr A=\mathscr A(\Phi)$, and let $\mathcal I$ be an ideal in $\Phi^+$. Write $\mathscr A_{\mathcal I}$ for the subarrangement of ideal type associated with $\mathcal I$, and let $m_i^{\mathcal I}$ denote the ideal exponents of $\mathcal I$. Inductive-freeness conjecture. Any subarrangement of $\mathscr A$ of ideal type $\mathscr A_{\mathcal I}$ is inductively free, with non-zero exponents given by the ideal exponents $m_i^{\mathcal I}$. The result is proved in the paper except possibly for 6178 ideals in type $E_8$; those cases were undecided at the time of writing.