Oshima's realizability conjecture for abstract spectral types

Let $\mathbf{S}=(S_i)_{i=1,\ldots,d}$ be a collection of abstract spectral types. A collection is irreducibly realizable if it is the spectral type of an irreducible meromorphic $G$-connection, and versally realizable if it admits an unfolding family of unramified canonical forms realizing the full unfolding diagram, with every member solving the associated additive Deligne–Simpson problem. Let $\mathbf{S}^{\mathrm{reg}}$ denote the finest unfolding of $\mathbf{S}$, namely the collection associated with the finest partitions $\{0\}\sqcup\cdots\sqcup\{k_i\}=\{0,\ldots,k_i\}$ for all $i$. Oshima's conjecture. The following are equivalent: $\mathbf{S}$ is irreducibly realizable; $\mathbf{S}$ is versally realizable; and $\mathbf{S}^{\mathrm{reg}}$ is irreducibly realizable. The conjecture is completely solved affirmatively for $G=\mathrm{GL}_n$; the implication from irreducible realizability to versal realizability is proved in the source, while the converse implication through the finest unfolding is attributed to earlier work in the general setting.