The Series
The 3D solution required two sequences of moves, the “Edge Piece Series” and “The Corner Piece Series.” The 4D solution will use both of these and a few additional sequences. To hopefully reduce confusion, for this discussion I am going to rename the series.
The 3D “Edge Piece Series” I will call the “Two-Color Series.”
The 3D “Corner Piece Series” I will call the “First Three-Colored Series.”
The reason is that, as you will see, the four-move “Edge Piece Series” is going to be used to solve the “face” pieces of the 4D cube, and the eight-move “Corner Piece Series” will be used to solve “edge” pieces of the 4D cube. Using an edge series for face pieces and a corner series for edge pieces would become too confusing and hence the name change. I got confused just typing that last sentence.