OLL parity
Rw U2 x (Rw U2)2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
Use after all six centers are formed and all 12 edge pairs are joined. OLL parity means an odd number of top edge pairs point the wrong way; a single flipped edge pair cannot occur on an ordinary legal 3×3. Keep the affected paired edge at upper front. Rw and Lw turn two layers; U turns only the outer layer and x rotates the whole cube. Follow the complete sequence, including x. This restores center colors and preserves paired edges, but changes last-layer corner/edge permutation; continue with OLL/PLL afterwards. An unfamiliar last-layer case alone does not establish parity.
PLL parity
[(3L')2: U2] (Uw2 (3L')2 Uw2) U2
PLL parity is a mismatch between corner permutation and edge-pair permutation during the reduced 3×3 stage. It can look like two swapped edge pairs or a corner swap that ordinary 3×3 PLL cannot finish. Keep every center formed and every edge paired. This expression exchanges the front and back edge pairs; finish the resulting ordinary PLL case afterwards. Correcting parity alone need not solve the last layer.
Published expression: r2 U2 r2 Uw2 r2 Uw2 (U2)
The source's lowercase r is the right inner slice, not a wide turn. It is physically 3L' here. In app notation 3L2 is its half turn; Rw turns two layers together and Uw2 turns the upper two layers halfway. Final U2 aligns the exchanged front/back edge pairs.
Last two edge pairs
[Uw': R U R' F R' F' R]
Reduction forms six centers and joins each matching pair of wing pieces. Paired edges must match on both adjacent faces, but need not be in their final solved slots. For the last two unpaired edges, put the color combinations at front-left and front-right with matching wings diagonally across, rather than in the same upper or lower slice. The front-right flip R U R′ F R′ F′ R can prepare this setup if needed. The full expression includes the Uw′ setup and Uw undo. After pairing and restoring centers, solve with outer layers as on a 3×3, correcting OLL/PLL parity if necessary.