Centres and edge pairing
Make it a 3x3.
Reduction solves the centres (four pieces each), pairs the 24 edge pieces into 12 'dedges', and then solves it as a 3x3 with outer turns. Yau, the usual speed variant, solves two opposite centres, three cross dedges, the last four centres, the remaining edges (often '3-2-3' edge pairing), then the 3x3 stage.
Because a 4x4 has no fixed centres, a reduced 4x4 can show positions a 3x3 cannot: one dedge flipped (OLL parity) or two dedges swapped (PLL parity). They come from the inner slices and need wide-turn algorithms.
OLL parity: a single flipped dedge.
Checked by the engine: 0 corners moved, 2 edges moved
PLL parity: two opposite dedges swapped.
Checked by the engine: PLL parity OPP Parity