Upon fusion of manganese dioxide (MnO\(_2\)) with potassium hydroxide (KOH) and oxygen at high temperatures, an oxidative fusion process occurs, yielding potassium manganate (K\(_2\)MnO\(_4\)). The balanced chemical equation for this reaction is:
\[
2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O
\]
Potassium manganate (K\(_2\)MnO\(_4\)) is a green substance that can be subsequently oxidized to purple potassium permanganate (KMnO\(_4\)) under acidic conditions.