SOP_2 = SOP_3

The new content is $SOP_2 \Rightarrow SOP_3$; the converse implication was known from the start. Dzamonja and Shelah asked whether either implication in $SOP_3 \Rightarrow SOP_2 \Rightarrow SOP_1$ reverses: Mutchnik answered the second ($SOP_1 = SOP_2$), and this answers the first, collapsing the bottom of the hierarchy to $SOP_1 = SOP_2 = SOP_3$. The $SOP_n$ hierarchy for $n \ge 3$ remains, as does everything above it.

One of the two 2004 Dzamonja-Shelah questions that organized two decades of classification theory, repeatedly highlighted in the NSOP_1 literature, and the surviving half after Mutchnik's celebrated SOP_1 = SOP_2. Resolving it collapses the bottom of the SOP hierarchy outright, with consequences for Keisler-order maximality. Central within model theory, little known outside it: placed at 35 with the field-famous specialist band (Feige, Krauth-Mezard), above HRT at 33.