Chiral quaternary carbon compounds. II. An asymmetric synthesis of (R) or (S)-4,4-dialkyl-2-cyclopentenones

The chiral bicyclic lactam ($\text{5}$) derived from levulinic acid and (S)-valinol is sequentially alkylated and then cleaved to 2,2-dialkyl levulinaldehyde ($\text{8}$) which is cyclized to the title products ($\text{9}$) in > 99% ee.